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Seismic Isolation for and

Designers

Structural Engineers R. Ivan Skinner Trevor E. Kelly Bill (W.H.) Robinson

Seismic Isolation for Designers and Structural

Engineers

R. Ivan Skinner Trevor E. Kelly Holmes Consulting Group www.holmesgroup.com Bill (W.H.) Robinson Robinson Seismic Ltd www.rslnz.com

CONTENTS Preface

(i)

Acknowledgements

(iii)

Author Biographies

(iv)

Frequently Used Symbols And Abbreviations

(v)

CHAPTER 1: 1.1 1.2 1.3 1.4 1.5 1.6

Seismic Isolation in Context........................................................................................................................... 1 Flexibility, Damping and Period Shift ........................................................................................................... 3 Comparison of Conventional & Seismic Isolation Approaches ............................................................. 5 Components in an Isolation System ............................................................................................................ 6 Practical Application of the Seismic Isolation Concept.......................................................................... 7 Topics Covered in this Book .......................................................................................................................... 9

CHAPTER 2: 2.1 2.2

2.3

2.4

2.5 2.6

3.2 3.3

3.4

GENERAL FEATURES OF STRUCTURES WITH SEISMIC ISOLATION ............................. 11

Introduction ..................................................................................................................................................... 11 Role of Earthquake Response Spectra and Vibrational Modes in the Performance of Isolated Structures...................................................................................................................................... 11 2.2.1 Earthquake Response Spectra ................................................................................................... 11 2.2.2 General Effects of Isolation of the Seismic Responses of Structures .................................... 15 2.2.3 Parameters of Linear and Bilinear Isolation Systems ............................................................... 16 2.2.4 Calculation of Seismic Responses .............................................................................................. 20 2.2.5 Contributions of Higher Modes to the Seismic Responses of Isolated Structures............... 21 Natural Periods and Mode Shapes of Linear Structures – Unisolated and Isolated............................ 22 2.3.1 Introduction .................................................................................................................................... 22 2.3.2 Structural Model and Controlling Equations ............................................................................ 22 2.3.3 Natural Periods and Mode Shapes ............................................................................................ 24 2.3.4 Example – Modal Periods and Shapes ...................................................................................... 25 2.3.5 Natural Periods and Mode Shapes with Bilinear Isolation...................................................... 26 Modal and Total Seismic Responses ........................................................................................................... 27 2.4.1 Seismic Responses Important for Seismic Design..................................................................... 27 2.4.2 Modal Seismic Responses ............................................................................................................ 28 2.4.3 Structural Responses for Modal Responses............................................................................... 30 2.4.4 Example – Seismic Displacements and Forces ........................................................................ 30 2.4.5 Seismic Responses with Bilinear Isolators ................................................................................... 31 Comparisons of Seismic Responses of Linear and Bilinear Location Systems ...................................... 34 2.5.1 Comparative Study of Seven Cases.......................................................................................... 34 Guide to Assist the Selection of Isolation Systems..................................................................................... 38

CHAPTER 3: 3.1

INTRODUCTION......................................................................................................... 1

ISOLATOR DEVICES AND SYSTEMS........................................................................... 43

Isolator Components and Isolator Parameters.......................................................................................... 43 3.1.1 Introduction .................................................................................................................................... 43 3.1.2 Combination of Isolator Components to Form Different Isolation Systems ........................ 43 Plasticity of Metals .......................................................................................................................................... 46 Steel Hysteretic Dampers .............................................................................................................................. 49 3.3.1 Introduction .................................................................................................................................... 49 3.3.2 Types of Steel Damper ................................................................................................................. 51 3.3.3 Approximate Force-Displacement Loops for Steel-Beam Dampers.................................... 52 3.3.4 Bilinear Approximation to Force-Displacement Loops ........................................................... 55 3.3.5 Fatigue Life of Steel-Beam Dampers ......................................................................................... 57 3.3.6 Summary of Steel Dampers ......................................................................................................... 59 Lead Extrusion Dampers ................................................................................................................................ 59 3.4.1 General ........................................................................................................................................... 59 3.4.2 Properties of the Extrusion Damper ............................................................................................ 62 3.4.3 Summary and Discussion of Lead Extrusion Dampers............................................................. 65

3.5

3.6 3.7

Laminated-Rubber Bearings for Seismic Isolators...................................................................................... 66 3.5.1 Rubber Bearings for Bridges and Isolators................................................................................. 66 3.5.2 Rubber Bearing, Weight Capacity Wmax ................................................................................... 67 3.5.3 Rubber Bearing Isolation: Stiffness, Period and Damping..................................................... 68 3.5.4 Allowable Seismic Displacement Xb .......................................................................................... 70 3.5.5 Allowable Maximum Rubber Strains .......................................................................................... 72 3.5.6 Other Factors in Rubber Bearing Design ................................................................................... 74 3.5.7 Summary of Laminated Rubber Bearings ................................................................................. 74 Lead Rubber Bearings.................................................................................................................................... 74 3.6.1 Introduction .................................................................................................................................... 74 3.6.2 Properties of the Lead Rubber Bearing..................................................................................... 77 Further Isolator Components and Systems................................................................................................. 83 3.7.1 Isolator Damping Proportional to Velocity ............................................................................... 83 3.7.2 PTFE Sliding Bearings ..................................................................................................................... 84 3.7.3 PTFE Bearings Mounted on Rubber Bearings............................................................................ 85 3.7.4 Tall Slender Structures Rocking with Uplift ................................................................................. 85 3.7.5 Further Components for Isolator Flexibility ................................................................................ 86 3.7.6 Buffers to Reduce the Maximum Isolator Displacement........................................................ 87 3.7.7 Active Isolation Systems ............................................................................................................... 88

CHAPTER 4: 4.1 4.2

4.3

4.4

4.5 4.6 4.7 4.8

Sources of Information ................................................................................................................................... 89 Engineering Properties of Lead Rubber Bearings...................................................................................... 89 4.2.1 Shear Modulus ............................................................................................................................... 90 4.2.2 Rubber Damping........................................................................................................................... 90 4.2.3 Cyclic Change in Properties ....................................................................................................... 91 4.2.4 Age Change in Properties ........................................................................................................... 93 4.2.5 Design Compressive Stress........................................................................................................... 94 4.2.6 Design Tension Stress..................................................................................................................... 94 4.2.7 Maximum Shear Strain.................................................................................................................. 95 4.2.8 Bond Strength ................................................................................................................................ 97 4.2.9 Vertical Deflections....................................................................................................................... 97 Engineering Properties of High Damping Rubber Isolators...................................................................... 100 4.3.1 Shear Modulus ............................................................................................................................... 100 4.3.2 Damping ......................................................................................................................................... 101 4.3.3 Cyclic Change in Properties ....................................................................................................... 102 4.3.4 Age Change in Properties ........................................................................................................... 103 4.3.5 Design Compressive Stress........................................................................................................... 103 4.3.6 Maximum Shear Strain.................................................................................................................. 103 4.3.7 Bond Strength ................................................................................................................................ 103 4.3.8 Vertical Deflections....................................................................................................................... 103 4.3.9 Wind Displacements ..................................................................................................................... 104 Engineering Properties of Sliding Type Isolators ......................................................................................... 104 4.4.1 Dynamic Friction Coefficient ...................................................................................................... 105 4.4.2 Static Friction Coefficient............................................................................................................. 106 4.4.3 Effect of Static Friction on Performance ................................................................................... 108 4.4.4 Check on Restoring Force ........................................................................................................... 110 4.4.5 Age Change in Properties ........................................................................................................... 110 4.4.6 Cyclic Change in Properties ....................................................................................................... 111 4.4.7 Design Compressive Stress........................................................................................................... 111 4.4.8 Ultimate Compressive Stress ........................................................................................................ 111 Design Life of Isolators .................................................................................................................................... 111 Fire Resistance ................................................................................................................................................. 111 Effects of Temperature on Performance.................................................................................................... 112 Temperature Range for Installation............................................................................................................. 112

CHAPTER 5: 5.1

ENGINEERING PROPERTIES OF ISOLATORS .............................................................. 89

ISOLATION SYSTEM DESIGN ..................................................................................... 113

Introduction ..................................................................................................................................................... 113 5.1.1 Assessing Suitability........................................................................................................................ 113 5.1.2 Design Development for an Isolation Project .......................................................................... 115

5.2

5.3

5.4

Design Equations for Elastomeric Bearing Types ....................................................................................... 116 5.2.1 Codes .............................................................................................................................................. 116 5.2.2 Empirical Data ............................................................................................................................... 116 5.2.3 Definitions........................................................................................................................................ 116 5.2.4 Range of Rubber Properties ........................................................................................................ 117 5.2.5 Vertical Stiffness and Load Capacity ........................................................................................ 118 5.2.6 Vertical Stiffness ............................................................................................................................. 118 5.2.7 Compressive Rated Load Capacity .......................................................................................... 119 5.2.8 AASHTO 1999 Requirements ........................................................................................................ 120 5.2.9 Tensile Rated Load Capacity...................................................................................................... 121 5.2.10 Bucking Load Capacity ............................................................................................................... 121 5.2.11 Lateral Stiffness and Hysteresis Parameters for Bearing.......................................................... 122 5.2.12 Lead Core Confinement.............................................................................................................. 125 Basis of an Isolation System Design Procedure.......................................................................................... 126 5.3.1 Elastomeric Based Systems .......................................................................................................... 127 5.3.2 Sliding and Pendulum Systems.................................................................................................... 127 5.3.3 Other Systems................................................................................................................................. 127 Step-By-Step Implementation of a Design Procedure ............................................................................. 127 5.4.1 Example of Illustrate Calculations .............................................................................................. 128 5.4.2 Design Code .................................................................................................................................. 129 5.4.3 Units.................................................................................................................................................. 129 5.4.4 Seismic and Building Definition ................................................................................................... 130 5.4.5 Material Definition ......................................................................................................................... 131 5.4.6 Isolator Types and Load Data ..................................................................................................... 133 5.4.7 Isolator Dimensions........................................................................................................................ 134 5.4.8 Calculate Bearing Properties ...................................................................................................... 136 5.4.9 Gravity Load Capacity ................................................................................................................ 138 5.4.10 Calculate Seismic Performance................................................................................................. 139 5.4.11 Seismic Load Capacity ................................................................................................................ 143 5.4.12 Assess Factors of Safety and Performance .............................................................................. 144 5.4.13 Properties for Analysis ................................................................................................................... 146 5.4.14 Hysteresis Properties ...................................................................................................................... 147

CHAPTER 6: 6.1

6.2

Prototype Buildings ......................................................................................................................................... 149 6.1.1 Building Configuration.................................................................................................................. 149 6.1.2 Design of Isolators.......................................................................................................................... 150 6.1.3 Evaluation Procedure................................................................................................................... 156 6.1.4 Comparison with Design Procedure .......................................................................................... 158 6.1.5 Isolation System Performance..................................................................................................... 164 6.1.6 Building Inertia Loads.................................................................................................................... 166 6.1.7 Floor Accelerations ....................................................................................................................... 175 6.1.8 Optimum Isolation Systems .......................................................................................................... 180 Example Assessment of Isolator Properties................................................................................................. 182

CHAPTER 7: 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10

7.11 7.12

EFFECT OF ISOLATION ON BUILDINGS ..................................................................... 149

SEISMIC ISOLATION OF BUILDINGS AND BRIDGES.................................................. 185

Introduction to Isolation of Buildings............................................................................................................ 185 Scope of Building Example ........................................................................................................................... 185 Seismic Input .................................................................................................................................................... 186 Design of Isolation System ............................................................................................................................. 187 Analysis Models ............................................................................................................................................... 189 Analysis Results ................................................................................................................................................ 191 7.6.1 Summary of Results ....................................................................................................................... 195 Test Conditions ................................................................................................................................................ 195 Production Test Results................................................................................................................................... 196 Summary .......................................................................................................................................................... 197 Implementation in Spreadsheet .................................................................................................................. 198 7.10.1 Material Definition ......................................................................................................................... 198 7.10.2 Project Definition ........................................................................................................................... 199 7.10.3 Isolator Types and Load Data ..................................................................................................... 200 7.10.4 Isolator Dimensions........................................................................................................................ 201 7.10.5 Isolator Performance .................................................................................................................... 203 7.10.6 Properties for Analysis ................................................................................................................... 205 Introduction to Isolation for Bridges ............................................................................................................. 207 Seismic Separation of Bridges....................................................................................................................... 208

7.13 7.14 7.15 7.16 7.17

7.18

Design Specifications for Bridges ................................................................................................................. 209 7.13.1 The 1991 AASHTO Guide Specifications.................................................................................... 209 7.13.2 The 1999 AASHTO Guide Specifications.................................................................................... 210 Use of Bridge Specifications for Building Isolator Design ......................................................................... 210 Design of Isolation Systems............................................................................................................................ 212 7.15.1 Non-Seismic Loads ........................................................................................................................ 212 7.15.2 Effect of Bent Flexibility ................................................................................................................. 213 Analysis of Isolated Bridges ........................................................................................................................... 215 Design Procedure for Bridge Isolation......................................................................................................... 216 7.17.1 Example Bridge.............................................................................................................................. 216 7.17.2 Design of Isolators.......................................................................................................................... 218 7.17.3 Accounting for Bent Flexibility in Design ................................................................................... 220 7.17.4 Evaluation of Performance ......................................................................................................... 224 7.17.5 Effect of Isolation System on Displacements............................................................................ 228 7.17.6 Effect of Isolation on Forces ........................................................................................................ 229 7.17.7 Summary ......................................................................................................................................... 231 Implementation in Spreadsheet .................................................................................................................. 231 7.18.1 Material Properties ........................................................................................................................ 232 7.18.2 Dimensional Properties ................................................................................................................. 232 7.18.3 Load and Design Data................................................................................................................. 233 7.18.4 Isolation Solution ............................................................................................................................ 234

CHAPTER 8: 8.1 8.2

8.3

8.4

8.5

8.6

Introduction ..................................................................................................................................................... 237 Structures Isolated in New Zealand ............................................................................................................. 239 8.2.1 Introduction .................................................................................................................................... 239 8.2.2 Road Bridges .................................................................................................................................. 242 8.2.3 South Rangitikei Viaduct with Stepping Isolation .................................................................... 244 8.2.4 William Clayton Building............................................................................................................... 245 8.2.5 Union House ................................................................................................................................... 247 8.2.6 Wellington Central Police Station............................................................................................... 249 Structures Isolated in Japan.......................................................................................................................... 251 8.3.1 Introduction .................................................................................................................................... 251 8.3.2 The C-1 Building, Cuchu City, Tokyo .......................................................................................... 255 8.3.3 The High-Tech R&D Centre, Obayashi Corporation ............................................................... 255 8.3.4 Comparison of Three Buildings with Different Seismic Isolation Systems ............................. 256 8.3.5 Oiles Technical Centre Building .................................................................................................. 258 8.3.6 Miyagawa Bridge.......................................................................................................................... 259 Structures Isolated in the USA ....................................................................................................................... 261 8.4.1 Introduction .................................................................................................................................... 261 8.4.2 Foothill Communities Law and Justice Centre, San Bernandino, California ...................... 263 8.4.3 Salt Lake City and Country Building: Retrofit........................................................................... 264 8.4.4 USC University Hospital, Los Angeles .......................................................................................... 265 8.4.5 Sierra Point Overhead Bridge, San Francisco........................................................................... 266 8.4.6 Sexton Creek Bridge, Illinois ......................................................................................................... 267 Structures Isolated in Italy .............................................................................................................................. 268 8.5.1 Introduction .................................................................................................................................... 268 8.5.2 Seismically Isolated Bridges ......................................................................................................... 268 8.5.3 The Mortaiolo Bridge..................................................................................................................... 269 Isolation of Delicate or Potentially Hazardous Structures or Substructures........................................... 274 8.6.1 Introduction .................................................................................................................................... 274 8.6.2 Seismically Isolated Nuclear Power Stations............................................................................. 275 8.6.3 Protection of Capacity Banks, Haywards, New Zealand....................................................... 275 8.6.4 Seismic Isolation of a Printing Press in Wellington, New Zealand .......................................... 277

CHAPTER 9: 9.1 9.2

APPLICATIONS OF SEISMIC ISOLATION ................................................................... 237

IMPLEMENTATION ISSUES.......................................................................................... 279

Introduction ..................................................................................................................................................... 279 Isolator Locations and Types......................................................................................................................... 279 9.2.1 Selection of Isolation Plane ......................................................................................................... 279 9.2.2 Selection of Device Type ............................................................................................................. 283

9.3

9.4

9.5

9.6

9.7

Seismic Input .................................................................................................................................................... 292 9.3.1 Form of Seismic Input.................................................................................................................... 292 9.3.2 Recorded Earthquake Motions................................................................................................... 293 9.3.3 Near Fault Effects .......................................................................................................................... 300 9.3.4 Variations in Displacements ........................................................................................................ 300 9.3.5 Time History Seismic Input ............................................................................................................ 302 9.3.6 Selecting and Scaling Records for Time History Analysis........................................................ 302 9.3.7 Selecting Records from a Set ...................................................................................................... 303 9.3.8 Comparison of Earthquake Scaling Factors............................................................................. 304 Detailed System Analysis ............................................................................................................................... 306 9.4.1 Single Degree-of-Freedom Model ............................................................................................. 307 9.4.2 Two Dimensional Non-Linear Model .......................................................................................... 307 9.4.3 Three Dimensional Equivalent Linear Model ............................................................................ 307 9.4.4 Three Dimensional Model-Elastic Superstructure, Yielding Isolators ..................................... 308 9.4.5 Fully Non-Linear Three Dimensional Model ............................................................................... 308 9.4.6 Device Modeling........................................................................................................................... 308 9.4.7 ETABS Analysis for Buildings .......................................................................................................... 309 9.4.8 Concurrency Effects ..................................................................................................................... 313 Connection Design ........................................................................................................................................ 316 9.5.1 Elastomeric Based Isolators.......................................................................................................... 316 9.5.2 Sliding Isolators ............................................................................................................................... 321 9.5.3 Installation Examples..................................................................................................................... 322 Structural Design 9.6.1 Design Concepts........................................................................................................................... 327 9.6.2 UBC Requirements ........................................................................................................................ 328 9.6.3 MCE Level of Earthquake ............................................................................................................ 332 9.6.4 Non-Structural Components ....................................................................................................... 332 9.6.5 Bridges ............................................................................................................................................. 333 Specifications .................................................................................................................................................. 333 9.7.1 General ........................................................................................................................................... 333 9.7.2 Testing.............................................................................................................................................. 335

CHAPTER 10: 10.1 10.2

10.3

10.4 10.5

10.6 10.7

FEASIBILITY ASSESSMENT, EVALUATION AND FURTHER DEVELOPMENT OF SEISMIC ISOLATION ............................................................................................ 337

Decision-Making in a Seismic Isolation Context ........................................................................................ 337 10.1.1 Seismic Isolation Decisions to be Made .................................................................................... 337 10.1.2 Seismic Isolation Decisions in the Wellington Area.................................................................. 338 Construction Projects in New Zealand and India 1992 to 2005.............................................................. 339 10.2.1 Introduction .................................................................................................................................... 339 10.2.2 Retrofits............................................................................................................................................ 339 10.2.3 Te Papa Tongarewa ..................................................................................................................... 339 10.2.4 Other Seismically Isolated Buildings ........................................................................................... 341 10.2.5 Bhuj Hospital ................................................................................................................................... 341 A Feasibility Study for Seismic Isolation........................................................................................................ 343 10.3.1 Te Papa Tongarewa, the Museum of New Zealand............................................................... 343 10.3.2 Description...................................................................................................................................... 343 10.3.3 Seismic Design Criteria ................................................................................................................. 344 10.3.4 Feasibility Study.............................................................................................................................. 345 10.3.5 Isolation System Design ................................................................................................................ 346 10.3.6 Evaluation of Structural Performance ....................................................................................... 346 10.3.7 Results of ANSR-II Analysis............................................................................................................. 348 10.3.8 Conclusions .................................................................................................................................... 348 Performance in Real Earthquakes ............................................................................................................... 350 New Approaches to Seismic Isolation......................................................................................................... 353 10.5.1 Introduction .................................................................................................................................... 353 10.5.2 The RoBall........................................................................................................................................ 353 10.5.3 The RoGlider ................................................................................................................................... 356 Project Management Approach................................................................................................................. 358 Future ................................................................................................................................................................ 359

Reference List………………………………………………………………………………………………………361 Additional Resources…………………………………………………………………………………………….367

PREFACE This is a revised version of the book “An Introduction to Seismic Isolation” published by Wiley and Sons in 1993. There have been many changes in the course of this revision and this is reflected in the changed title - “Seismic Isolation for Designers and Structural Engineers”. This new book builds on the previous one and uses much of the previous material, but it has different authorship and more focus on practical applications. It acknowledges the pioneering work that has been done over the past 30 to 40 years but aims to present seismic isolation in a different way, as an established technique that could be considered widely, even routinely, as an option by designers and structural engineers. Trevor Kelly’s input as a practising structural engineer has transformed the book into a modern version that makes full use of computer science techniques. (A CD Rom is included). The original book was authored by R I Skinner, W H Robinson and GH McVerry, who were at the time working at the Department of Scientific and Industrial Research (DSIR) in Wellington, New Zealand. The book recorded the innovative earthquake engineering research that had been carried out at the DSIR over the previous 25 years (see Chapter 3 of both books, and Chapter 8 of this book, which is carried over from the previous Chapter 6). However the book also marked the end of an era, as it was written at a time when change was in the air and the DSIR was about to be disestablished. The DSIR was closed down mid-1992 as part of a New-Zealand wide drive to making science more commercial. Bill Robinson has risen to this challenge by forming Robinson Seismic Limited (RSL), an engineering company specialising in applications of seismic isolation to protect structures from earthquake damage. Bill has continued as one of the authors of this new book. The new author is Trevor Kelly, a structural engineer with Holmes Consulting, which has been involved in the design and supply of seismic isolation systems for almost 20 years. Trevor’s interest is in the structural engineering aspects of applying seismic isolation/damping and the new chapters that he has written emphasise the engineering aspects. The new book therefore retains the mathematical tools in Chapters 1, 2 and 3 of “An Introduction to Seismic Isolation” but replaces the empirical methods of succeeding chapters with detailed design and documentation material of the type that a structural engineer would need to implement isolation. This is followed through with examples of practical designs. This book provides both theory and design aspects of seismic isolation. This will be useful for structural engineers and teachers of engineering courses. For other structural components (concrete frames, steel braces etc) the engineering student is taught the theory (lateral loads, bending moments) but then also the design (how to select sizes, detail reinforcing, bolts). This book will do the same for seismic engineering. The book provides practical examples of computer applications as well as device design examples so that the structural engineer is able to do a preliminary design that won’t specify impossible constraints. The book also addresses the steps that need to be taken to ensure the design is code compliant. The structural engineer is the key to adoption of seismic isolation technology. The book aims to provide enough design information so that the structural engineer can be confident on implementing seismic isolation; otherwise he/she won’t want to take the risk even if the architect or owner is enthusiastic. Firms like RSL and Holmes Consulting will continue to be available to provide expert advice and the benefits of their considerable experience in the field of device design and seismic isolation.

(i)

The engineering credentials and expertise of Bill Robinson and his company, RSL, are evident from Chapters 3 and 8 (which describe the invention and development of the Lead Rubber Bearing). Bill Robinson has been honoured world wide for this work and has received recognition in New Zealand from the scientific community and the business community. There has also been considerable interest in the public domain, in the display of seismic isolation in Te Papa Tongarewa, the Museum of New Zealand on the waterfront in Wellington, which was built on Lead Rubber Bearings (see Chapter 9). The engineering credentials of Trevor Kelly are evident from his work as Technical Director of Holmes Consulting Group (HCG), part of the Holmes Group, which is New Zealand's largest specialist structural engineering company, with over 90 staff in three main offices in New Zealand plus 25 in the San Francisco office. Trevor heads the seismic isolation division of HCG in the Auckland office. He has over 15 years experience in the design and evaluation of seismic isolation systems in the United States, New Zealand and other countries and is a licensed Structural Engineer in California. Since 1954 the company has designed a wide range of structures in the commercial and industrial fields. HCG has been progressive in applications of seismic isolation and since its first isolated project, Union House, in 1982, has completed six isolated structures. On these projects HCG provided full structural engineering services. In addition, for over 8 years HCG provided design and analysis services to Skellerup Industries of New Zealand and later Skellerup Oiles Seismic Protection (SOSP), a San Diego based manufacturer of seismic isolation hardware. Isolation hardware used on their projects included Lead Rubber Bearings (LRBs), High Damping Rubber Bearings (HDR), Teflon on stainless steel sliding bearings, sleeved piles and steel cantilever energy dissipators. The company has developed design and analysis software to ensure effective and economical implementation of seismic isolation for buildings, bridges and industrial equipment. Expertise encompasses the areas of isolation system design, analysis, specifications and evaluation of performance. In writing Chapters 4, 5, 6 and 7 of this book Trevor has drawn on his practical experience in the field and explains methods of calculating seismic responses using state-of-the-art computer software such as ETABS, used for the linear and nonlinear analysis of buildings. This book is the product of three expert engineers who have, over a long period of years, worked separately and collaboratively to design and develop earthquake isolation solutions and to incorporate them into existing and new structures. Collaboration on this book is a further joint venture and has a two-fold aim — to be used for the benefit of professionals looking to apply earthquake isolation techniques, and to be used in educating a new generation of structural engineers and designers.

(ii)

ACKNOWLEDGEMENTS In presenting this new book, which builds on and revises the previous book “An Introduction to Seismic Isolation”, thanks are due to all those who made the previous book possible, especially Graeme McVerry, as well as those who have been involved in its revision. Thanks to Barbara Bibby who again provided editing services, to Heather Naik and the staff and shareholders of Robinson Seismic Ltd and Holmes Consulting Group, to the Book Committees at RSL and Holmes Consulting who have reviewed it, and to FORST for providing funding for its production. Trevor Kelly Holmes Consulting Group 34 Waimarei Avenue Paeroa NEW ZEALAND www.holmesgroup.com Bill Robinson Robinson Seismic Ltd P O Box 33093 Petone NEW ZEALAND www.rslnz.com Ivan Skinner 31 Blue Mountains Road Silverstream Wellington New Zealand

(iii)

AUTHOR BIOGRAPHIES Trevor E Kelly, Technical Director, Holmes Consulting Group 34 Waimarei Avenue, Paeroa, New Zealand www.holmesgroup.com Trevor completed a BE at the University of Canterbury in 1973 and an ME in 1974. His research report, related to the nonlinear analysis of concrete structures, initiated an interest in this field which has continued throughout his career. He has worked as a structural engineer in New Zealand and California and is a Chartered Engineer in NZ and licensed Structural Engineer in California. Over the last 20 years, he has specialised in structural engineering fields which utilise nonlinear analysis, such as base isolation, energy dissipation and performance based evaluation of existing buildings. In his current position, Trevor directs the technical developments at Holmes Consulting Group, particularly as they relate to structural analysis and computer software development. Dr William H Robinson, Founder & Chief Engineer, Robinson Seismic Ltd P O Box 33093, Petone, New Zealand www.rslnz.com Bill began his career as a mechanical engineer, graduating ME at the University of Auckland before working for two construction companies. He then changed fields to physical metallurgy, completing a PhD in 1965 at the University of Illinois. Two years as a research fellow followed, working in solid-state physics at the University of Sussex before returning to New Zealand to work as a scientist with the Physics and Engineering Laboratory (PEL) at the Department of Scientific and Industrial Research (DSIR) in December 1967. Bill’s interest in seismic isolation led to the invention and development of the lead extrusion damper (1970) and the lead-rubber bearing (1974) (See Chapter 3) and has become his major research and engineering interest. Other research during his career as a scientist and later Director of PEL has included Antarctic sea-ice research, attempts to detect gravitational waves, the successful development of an ultrasonic viscometer and ultrasonically modulated ESR. The first version of this book was written with Ivan Skinner and Graeme McVerry in the last days of the DSIR. Ten years ago Bill founded Robinson Seismic Ltd, which is based in Lower Hutt, New Zealand and has contacts and clients all over the world. Dr R Ivan Skinner 31 Blue Mountains Road, Silverstream, Wellington, New Zealand Ivan’s early activities prepared him for a contribution towards reducing earthquake impacts on structures, including early applications of seismic isolation such as the Rangitikei stepping bridge and the William Clayton building. He obtained a BE Hons in 1951, and a DSc in 1976, from the University of Canterbury, New Zealand. In 1953 he joined the Physics & Engineering Laboratory, PEL, in Lower Hutt where his wide-ranging activities included designing a vibration isolation system for the lab’s new electron microscope. During 1959-78 he led the Engineering Seismology Section of PEL where he applied his knowledge of electrodynamics to modelling structures and their dynamic responses to severe earthquakes. Other section priorities included the development of a New Zealand strong-motion earthquake recording network used throughout NZ and overseas; engineering studies of informative earthquake attacks worldwide; contributions as a UNESCO expert in earthquake engineering and developing special components for seismic isolation to give more reliable earthquake resistance at lower cost. After the completion of the Seismic Isolation book with Robinson and McVerry in 1993, Ivan became Director of the New Zealand Earthquake Commission’s Research Foundation, from (iv)

which he retired at the end of 2005.

(v)

FREQUENTLY USED SYMBOLS AND ABBREVIATIONS (Chapters 1, 2, 3 and 8) β

:

tuning parameter for combined primary-secondary system, namely (ωp-ωs)/ ωa

βij

:

analogue to β, for multimode primary-secondary systems

Ґe,rn

:

elastic-phase participation factor at position r in mode n

Ґn(z)

:

mode-n participation factor at position z

ҐNn

:

mode-n participation factor at top floor of structure (position N)

Ґn

:

weighting factor for the nth mode of vibration

Ґn(I)

:

isolated mode weight factor

Ґn(U)

:

unisolated mode weight factor

Ґrn

:

participation factor for response to ground excitation for a mass at level r of a structure vibrating in the nth mode

Ґy,rn

:

yielding-phase participation factor at position r in mode n

γxz

:

shear strain of rubber disc

γ

:

interaction parameter of combined primary-secondary system, given by ms/mp

γ

:

‘engineering’ shear strain

γij

:

interaction parameter, analogue to γ, for multimode primary-secondary systems

γn

:

wave number of mode n, possibly complex

γy

:

shear-strain coordinate of yield point

∆n

:

difference between nth root of equation (4.17) and (n-1)π

δd

:

nonclassical damping parameter in combined primary-secondary system

δij

:

analogue to δd, for multimode primary-secondary systems

ε

:

ωb/ωFB1 = ratio of frequencies of rigid-mass isolated structure and first-mode unisolated structure, used for expressing orders of perturbation

ε

:

strain = (increment in length)/(original length)

εm

:

maximum amplitude of cyclic strain

εy

:

strain coordinate of yield point

Θn

:

variation of spatial phase of mode-n displacement down shear beam

(v)

ζs

:

damping of secondary structure

ζp

:

damping of primary structure

ζa

:

ζd

:

damping difference of combined primary-secondary system, given by ζd = ζp - ζs

ζFBn

:

fraction of critical viscous damping of (unisolated) fixed-base mode n

ζ

:

velocity- (viscous-) ‘damping factor’ or ‘fraction of critical damping’ for single-mass oscillator

ζb

:

velocity-damping factor for isolator

ζB

:

‘effective’ damping factor of bilinear isolator, given by sum of velocity- and hysteretic-damping factors

ζb1

:

velocity-damping factor in ‘elastic’ region of bilinear isolator

ζb2

:

velocity-damping factor in ‘plastic’ or ‘yielded-phase’ region of bilinear isolator

ζh

:

hysteretic damping factor of bilinear isolator

ζn

:

fraction of critical viscous damping of mode n; also called mode-n damping factor

μj0

:

modal mass of free-free mode j

:

uj0[M]uj0

μsj

:

jth modal mass of secondary system = Φsj [Ms] Φsj

ξn(t)

:

modal (relative displacement) coordinate for mode n at time t

ρ

:

uniform density of shear beam representing a uniform shear structure

σ

:

nominal stress, as used in ‘scaled’ (σ-ε) curves for steel dampers in Chapter 3

σ

:

stress = force/area (Pascals)

σy

:

stress coordinate of yield point

τ

:

nominal shear stress, as used in ‘scaled’ (σ-ε) curves for steel dampers in Chapter 3

τ

:

shear stress = (shear force)/area (Pascals)

τy

:

shear-stress coordinate of yield point

Φ

:

[Φ1, … Φ2, … Φ3], the mode shape matrix, a function of space, not time

Φn,Φm :

average damping of combined primary-secondary system, given by

ζa = (ζp+ζs)/2

T

T

mode shape in the nth or mth mode of vibration

(vi)

Φrn

:

mode shape at the rth level of the structure during the nth mode of vibration

Φe,rn

:

elastic-phase modal shape at position r in mode n

Φy,rn

:

yielding-phase modal shape at position r in mode n

Φn(z,t) :

shape of mode n, used interchangeably with un(z,t); normalized to unity at the top level

Ψn

:

phase angle of participation factor vector Γn

ωs

:

(circular) frequency of secondary structure

ωp

:

(circular) frequency of primary structure

ωa

:

average frequency of combined primary-secondary system, given by

ωa = (ωp + ωs) /2

ωpi

:

analogue to ωp, for multimode primary-secondary system

ωsj

:

analogue to ωs, for multimode primary-secondary system

ω1 (U)

unisolated undamped first-mode natural (circular) frequency, the same as ωFBi

:

ωFFn

:

mode-n natural (circular) frequency with ‘free-free’ boundary conditions

ωb

:

isolator frequency = √(Kb/M) for a rigid mass M

ωFB1

:

natural (circular) frequency of (unisolated) fixed-base made 1, equivalent to ω1 (U)

ωFBn

:

natural (circular) frequency of (unisolated) fixed base mode n

ωn

:

undamped natural (circular) frequency of mode n, related to frequency fn by

ωn = 2πfn

ωd

:

damped natural (circular) frequency of single-mass oscillator

ωn

:

undamped natural (circular) frequency of single-mass oscillator, or nth-mode natural frequency of multi-degree-of-freedom linear oscillator

A

:

area of rubber bearing in Chapter 3

A

:

cross-sectional area of shear beam representing a uniform shear structure

Ah

:

area of bilinear hysteresis loop

an(t)

:

absolute acceleration of mode n

A′

:

overlap area of rubber bearing in Chapter 3

b

:

subscript denoting base isolator

ůb, ůb(t) :

relative velocity of base mass with respect to ground

(vii)

B

:

subscript denoting bilinear isolator

BF

:

‘bulge factor’ describing the ratio Sr/Sr,1 of total shear to first-mode shear at level r in a structure, particularly at mid-height

c(r,s)

:

interlevel velocity-damping coefficient, defined only for r ≥ s

Cb

:

coefficient of velocity-damping for a base isolator, with units such as Nm-1s = kgs s-1

CF

:

correction factor linking displacement of bilinear isolator to equivalent spectral displacement

ck

:

stiffness-proportional damping coefficient of shear beam representing a uniform shear structure

CK

:

overall stiffness-proportional damping coefficient CkA/L of uniform shear structure

cm

:

mass-proportional damping coefficient of shear beam representing a uniform shear structure

CM

:

overall mass-proportional damping coefficient CmAL of uniform shear structure

crs

:

element of damping coefficient matrix

[C]

:

damping coefficient matrix, with elements crs related to c(r,s)

e

:

subscript used to denote ‘elastic-phase’

e

:

subscript used to denote ‘experimental model’ in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

E

:

Young’s modulus = σ/ε in elastic region

f

:

force-scaling factor, as used in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

F

:

force or shear-force as obtained from ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

FAr(T,ξ) :

floor acceleration spectrum at rth level of a structure

Fb

:

isolator force arising from bilinear resistance to displacement

Fe′

:

residual force in elastic phase of bilinear isolator

FF

:

subscript denoting ‘free-free’ boundary condition corresponding to perfect isolation

FFn

:

subscript denoting mode-n ‘free-free’ vibration

Fn(z)

:

maximum seismic force per unit height, at height z of mode n

Fr

:

maximum inertia load on the masss mr at level r

Frn

:

maximum seismic force of mode n at the rth point of a structure

Fy′

:

residual force in yielding phase of bilinear isolator

(viii)

G

:

shear modulus = τ/γ in elastic region

G

:

constant shear modulus of shear beam representing a uniform shear structure

G0

:

white noise power spectrum

hr

:

height of rth level of a structure

I

:

‘degree of isolation’ or ‘isolation ratio’ given by ωFB1/ωb=Tb/TFB1=Tb/T1(U)

k

:

stiffness of single-mass oscillator

K

:

overall stiffness GA/L of uniform shear structure

k(r,s)

:

interlevel stiffness, such that k(r,r-1) = KN for a N-mass uniform structure and k(1,o) = Kb it if is isolated

Kb

:

stiffness of linear isolator

KB

:

‘effective’ or ‘secant’ stiffness of bilinear isolator

Kb(r)

:

stiffness of rubber component of lead rubber bearing

Kb1

:

‘initial’ or ‘elastic’ stiffness of bilinear isolator

Kb2

:

‘post-yield’ or ‘plastic’ stiffness of bilinear isolator

Kc

:

stiffness of spring introduced to isolator to reduce higher-mode responses (Figure 2.2c)

Kn

:

stiffness of nth ‘spring’ in discrete linear chain system

krs

:

element of stiffness matrix

[K]

:

stiffness matrix, with elements krs related to k(r,s)

ℓ

:

length-scaling factor, as used in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

L

:

length of shear beam representing a uniform shear structure

m

:

mass of single-mass oscillator

M

:

mass pAL of uniform shear structure

M

:

total mass of structure; together with the mass of the isolator this gives MT

Mb

:

isolator (base) mass

mp

:

mass of primary structure

mr

: :

mass at rth level M/N for a uniform structure with N levels

ms

:

mass of secondary structure

MT

:

total mass of structure plus isolator

(ix)

[M]

:

mass matrix

N .. Xn(z)

:

number of masses in discrete linear system

:

maximum absolute seismic acceleration of mode n at position z

n*

:

complex conjugate associated with mode n

NL

:

nonlinearity factor

OMn(z) :

overturning moment at height z of mode n

OMrn

:

maximum overturning moment at point r, and height hr, of mode-n of a structure

p

:

subscript used to denote ‘primary’ in primary-secondary systems

P

:

peak factor, namely ratio of peak response to RMS response

p

:

subscript used to denote ‘prototype’ in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

P

:

peak factor, namely ratio of peak response to RMS response

Pa

:

amplitude-scaling factor such that üg(t) = Pa üEl Centro (t/Pp)

Pn

:

complex frequency of mode n, see equation (4.7)

Pn0

:

zeroth-order term in the perturbation expression for the complex frequency

Pni

:

i-th term in perturbation expression for the nth-mode complex frequency

Pp

:

frequency-scaling factor such that üg(t) = Pa üEl Centro (t/Pp)

Pps

:

peak factor for secondary structure when mounted on primary structure

Ps

:

peak factor for secondary structure when mounted on the ground

Q

:

force across Coulomb slider at which it yields

Qy

:

yield force at which changeover from elastic to plastic behaviour occurs, at yield displacement Xy

Qy

:

shear-force coordinate of yield point

Qy/W

:

yield force-to-weight ratio of bilinear isolator

S

:

shape factor of elastomeric bearing = (loaded area)/(force-free area)

SA(T,ζ)

:

spectral absolute acceleration for period T and damping ζ, as seen on response spectrum, Figure 2.1

Sb

:

maximum base-level shear

Sbn

:

maximum base shear in mode n

SD(T,ζ)

:

spectral relative displacement for period T and damping ζ, as seen on response spectrum, Figure 2.1

(x)

Sn max

:

maximum shear at any position, in mode n

Sn (z)

:

maximum seismic shear at height z of mode n

Srn

:

maximum shear force at the rth point of a structure oscillating in mode n

Sv(T,ζ)

:

spectral relative velocity for period T and damping ζ

t

:

time

T

:

superscript indicating ‘transpose’

T

:

natural period

T1(U)

:

unisolated undamped first-mode period, the same as TFB1

Tb

:

natural period of linear base isolator = 2π/ωb

TB

:

‘effective’ period for bilinear isolator

Tb1

:

period associated with Kb1, in ‘elastic’ region of bilinear isolator

Tb2

:

period associated with Kb2, in ‘plastic’ region of bilinear isolator

Tn(1)

:

isolated nth period

Tn(U)

:

unisolated nth period

u

:

vector containing the displacements ur

u(z,t)

:

relative displacement, at position z in the structure, in the horizontal x direction, with respect to the ground at time t; often written as u, without arguments, in the differential form of the equation of motion

ü(z,t)

:

relative acceleration with respect to ground of position z at time t

u1

:

displacement of bilinear isolator

ub, ub(t) :

relative displacement of base mass with respect to ground

üb, üb(t) :

acceleration of base mass with respect to ground

ubj0

:

base displacement in free-free mode j

ubn(t)

:

nth-mode relative displacement, with respect to ground, at base of structure at time t

ue,rn

:

elastic-phase displacement at position r in mode n

üe,rn

:

elastic-phase relative acceleration at position r in mode n

uFBn(z,t) :

fixed-base mode-n relative displacement with respect to ground at position z at time t

uFFN(z,t) :

‘free-free’ mode-n relative displacement with respect to ground, at position z and time t

(xi)

üg, üg(t) :

ground acceleration

ULn, UNn :

amplitude of nth-mode displacement at position z=L (top of shear beam) (possibly complex); amplitude at top of discrete N-component structure

un(z)

:

nth mode shape, used interchangeably with Φn(z); usually normalisation is not defined

un(z,t)

:

mode-n relative displacement, with respect to ground, of position z at time t

un0

:

zeroth-order term in the perturbation expression for the mode shape

ups

:

displacement of secondary structure mounted on the primary structure

üps

:

acceleration of secondary structure mounted on the primary structure

urn(t)

:

Φrnξn(t) = displacement of mode-n at rth level of structure, where Φrn is the spatial variation and ξn is the time variation

us

:

displacement of secondary structure mounted on the ground

üs

:

acceleration of secondary structure mounted on the ground

uy,rn

:

yielding-phase displacement at position r in mode n

üy,rn

:

yielding-phase relative acceleration at position r in mode n

un

:

displacement vector for discrete linear system in nth mode

v

:

vector comprising the relative velocity and relative displacement vectors

vn

:

vector v for mode n

W

:

total weight of structure

X

:

displacement, as obtained from ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in Chapter 3

Xb

:

maximum relative displacement of isolator or of base of isolated structure

XNn

:

maximum mode-n relative displacement at top floor of structure (position N)

Xp

:

peak response of primary structure when mounted on the ground

Xp(RMS) :

RMS response of primary structure when mounted on the ground

Xps

:

peak response of secondary structure when mounted on primary structure

Xr

:

maximum relative displacement with respect to ground at any level r

Xrn

:

peak value of mode-n relative displacement at the rth point of a structure

Xs

:

peak response of secondary structure when mounted on the ground

Xs(RMS) :

RMS response of secondary structure when mounted on the ground

(xii)

Xy

:

yield displacement of bilinear isolator

Xy .. Xrn . Xrn

:

displacement coordinate of yield point

:

peak value of mode-n absolute acceleration at the rth point of a structure

:

peak value of mode-n relative velocity at the rth point of a structure

z

:

vertical coordinate; height of a point of a structure

Zn(t)

:

relative displacement response, of one-degree-of-freedom oscillator of undamped natural frequency ωn and damping ζn, to ground acceleration üg(t)

LIST OF COMMONLY USED ABBREVIATIONS CQC

:

abbreviation for ‘Complete Quadratic Combination’, a method of adding responses of several modes

DSIR

:

Department of Scientific and Industrial Research, New Zealand

LRB

:

Lead rubber bearing

MDOF

:

abbreviation for multiple-degree-of-freedom

MWD

:

Ministry of Works and Development, New Zealand

PEL

:

Physics and Engineering Laboratory of the DSIR, later DSIR Physical Sciences

PTFE

:

polytetrafluoroethylene

SRSS

:

abbreviation for ‘Square Root of the Sum of the Squares’, a method of adding responses of several modes

1DOF

:

abbreviation for one-degrees-of-freedom

2DOF

:

abbreviation for two-degrees-of-freedom

(xiii)

Chapter 1 1.1

INTRODUCTION

SEISMIC ISOLATION IN CONTEXT

A large proportion of the world's population lives in regions of seismic hazard, at risk from earthquakes of varying severity and varying frequency of occurrence. Earthquakes cause significant loss of life and damage to property every year. Various a seismic construction designs and technologies have been developed over the years in attempts to mitigate the effects of earthquakes on buildings, bridges and potentially vulnerable contents. Seismic isolation is a relatively recent, and evolving, technology of this kind. Seismic isolation consists essentially of the installation of mechanisms which decouple the structure, or its contents, from potentially damaging earthquake-induced ground, or support, motions. This decoupling is achieved by increasing the flexibility of the system, together with providing appropriate damping. In many, but not all, applications the seismic isolation system is mounted beneath the structure and is referred to as 'base isolation'. Although it is a relatively recent technology, seismic isolation has been well evaluated and reviewed (e.g. Lee & Medland, 1978; Kelly, 1986; May 1990 issue of "Earthquake Spectra" ); and has been the subject of international workshops (e.g., NZ-Japan Workshop, 1987; US-Japan Workshop, 1990; Assisi Workshop, 1989; Tokyo Workshop, 1992); is included in the programmes of international, regional and national conferences on Earthquake Engineering (e.g., 9th WCEE World Conference on Earthquake Engineering, Tokyo, 1988; Pacific Conferences, 1987, 1991; Fourth US Conference, 1990); and has been proposed for specialised applications (e.g., SMIRT 11, Tokyo, 1991). Seismic isolation may be used to provide effective solutions for a wide range of seismic design problems. For example, when a large multi-storey structure has a critical Civil Defence role which calls for it to be operational immediately after a very severe earthquake, as in the case of the Wellington Central Police Station (see Chapter 8), the required low levels of structural and non-structural damage may be achieved by using an isolating system which limits structural deformations and ductility demands to low values. Again, when a structure or sub-structure is inherently non-ductile and has only moderate strength, as in the case of the newspaper printing press at Petone (see Chapter 8), isolation may provide a required level of earthquake resistance which cannot be provided practically by earlier seismic techniques. Careful studies have been made of classes of structure for which seismic isolation may find widespread application. This has been found to include common forms of highway bridges. The increasing acceptance of seismic isolation as a technique is shown by the number of retrofitted seismic isolation systems which have been installed. Examples in New Zealand are the retrofitting of seismic isolation to existing bridges and to the electrical capacitor banks at Haywards (see Chapter 8), while the retrofit of isolators under the old New Zealand Parliamentary Buildings was completed in 1993. Many old monumental structures of high cultural value have little earthquake resistance. The completed isolation retrofit of the Salt Lake City and County Building in Utah is described in some detail in Chapter 8. Isolation may often reduce the cost of providing a given level of earthquake resistance. The New Zealand approach has been to design for some increase in earthquake resistance, together with some cost reduction, a typical target being a reduction by 5% of the structural cost.

1

Reduced costs arise largely from reduced seismic loads, from reduced ductility demand and the consequent simplified load-resisting members, and from lower structural deformations which can be accommodated with lower-cost detailing of the external cladding and glazing. Seismic isolation thus has a number of distinctive beneficial features not provided by other aseismic techniques. We believe that seismic isolation will increasingly become one of the many options routinely considered and utilised by engineers, architects and their clients. The increasing role of seismic isolation will be reflected, for example, in widespread further inclusion of the technique in the seismic provisions of structural design codes. When seismic isolation is used, the overall structure is considerably more flexible and provision must be made for substantial horizontal displacement. It is of interest that, despite the widely varying methods of computation used by different designers, a consensus is beginning to emerge that a reasonable design displacement should be of the order of 50 to 400 mm, and possibly up to twice this amount if 'extreme' earthquake motions are considered. A 'seismic gap' must be provided for all seismically isolated structures, to allow this displacement during earthquakes. It is imperative that present and future owners and occupiers of seismically isolated structures are aware of the functional importance of the seismic gap and the need for this space to be left clear. For example, when a road or approach to a bridge is resealed or re-surfaced, extreme care must be taken to ensure that sealing material, stones etc, do not fall into the seismic gap. In a similar way, the seismic gap around buildings must be kept secure from rubbish, and never used as a convenient storage space. All the systems presented in this book are passive, requiring no energy input or interaction with an outside source. Active seismic isolation is a different field, which confers different aseismic features in the face of a different set of problems. As it develops, it will occupy a niche among aseismic structures which is different from that occupied by structures with passive isolation. In a typical case, a mass which is a fraction of a percent of the structural mass is driven with large accelerations so that the reaction to its inertia forces tend to cancel the effects of inertia forces arising in the structure as a result of earthquake accelerations. Such a system may be a practical, but expensive, means of reducing the effective seismic loads during moderate, and in some locations frequent, earthquakes. Practical limitations on the size and displacements of the active mass would normally render the system much less effective during major earthquakes. Moreover, it is difficult to ensure the provision of the increasing driving power required during earthquakes of increased severity. In principle, such an active isolation system might be used to complement a passive isolation system in certain special cases. For example, a structure with passive seismic isolation may be satisfactory in all respects, except that it may contain components which are particularly vulnerable to high-frequency floor-acceleration spectra. The active-mass power and displacement requirements for the substantial cancellation of these short-period low-acceleration floor spectra may be moderate, even when the earthquake is very severe. Moreover, such moderate power might be supplied by an in-house source, with its dependability increased by the reduced seismic attack resulting from isolation. A number of factors need to be considered by an engineer, architect or client wishing to decide whether a proposed structure should incorporate seismic isolation. The first of these is the seismic hazard, which depends on local geology (proximity to faults, soil substructure), recorded history of earthquakes in the region, and any known factors about the probable characteristics of an earthquake (severity, period, etc). Various proposed solutions to the design problem can then be put forward, with a variety of possible structural forms and materials, and with some designs incorporating seismic isolation, some not. The probable level of seismic damage can then be evaluated for each design, where the degree of seismic damage can be broadly categorised as: 2

(1)

minor

(2)

repairable (up to about 30% of the construction cost)

(3)

not repairable, resulting in the building being condemned.

The whole thrust of seismic isolation is to shift the probable damage level from (3) or (2) towards (1) above, and thereby to reduce the damage costs, and probably also the insurance costs. Maintenance costs should be low for passive systems, though they may be higher for active seismic isolation. As discussed above, the construction costs including seismic isolation usually vary by + 5 to 10% from unisolated options. The total 'costs' and 'benefits' of the various solutions can then be evaluated, where the analysis has to include the 'value' of having the structure or its contents in as good as possible a condition after an earthquake, and the reduced risk of casualties with reduced damage. In many cases such additional benefits may well follow the adoption of the seismic isolation option.

1.2

FLEXIBILITY, DAMPING AND PERIOD SHIFT

The 'design earthquake' is specified on the basis of the seismicity of a region, the site conditions, and the level of hazard accepted (for example, a '400-year return period' earthquake for a given location would be expected to be less severe than one which occurred on average once every 1000 years). Design earthquake motions for more seismic areas of the world are often similar to that experienced and recorded at El Centro, California, in 1940, or scalings of this motion, such as '1.5 El Centro'. The spectrum of the El Centro accelerogram has large accelerations at periods of 0.1 to 1 second. Other earthquake records, such as that at Pacoima Dam in 1971 or 'artificial' earthquakes A1 or A2 are also used in specifying the design level. It must also be recognised that occasionally earthquakes give their strongest excitation at long periods. The likelihood of these types of motions occurring at a particular site can sometimes be foreseen, such as with deep deposits of soft soil which may amplify low-frequency earthquake motions, the old lake-bed zone of Mexico City being the best-known example. With this type of motion, flexible mountings with moderate damping may increase rather than decrease the structural response. The provision of high damping as part of the isolation system gives an important defence against the unexpected occurrence of such motions. Typical earthquake accelerations have dominant periods of about 0.1 to 1 seconds as shown in Figure 2.1 in the next Chapter, with maximum severity often in the range 0.2 to 0.6 s. Structures whose natural periods of vibration lie within the range 0.1 to 1 seconds are, therefore, particularly vulnerable to seismic attack because they may resonate. The most important feature of seismic isolation is that its increased flexibility increases the natural period of the structure. Because the period is increased beyond that of the earthquake, resonance and near-resonance are avoided and the seismic acceleration response is reduced. This period shift is shown schematically in Figure 1.1(a) and in more detail in Figure 2.1 in Chapter 2.

3

(a) (b)

Figure 1.1: Effect of increasing the flexibility of a structure: The increased period and damping lower the seismic acceleration response; The increased period increases the total displacement of the isolated system, but this is offset to a large extent by the damping. (After Buckle & Mayes, 1990.)

The increased period, and consequent increased flexibility, also affects the horizontal seismic displacement of the structure, as shown in Figure 1.1(b) for the simplest case of a single-mass rigid structure and as shown in more detail in Figure 2.1 in Chapter 2. Figure 1.1(b) shows how excessive displacements are counteracted by the introduction of increased damping. Real values of the maximum undamped displacement for isolated structures could be as large as 1 m in typical strong earthquakes; damping typically reduces this to 50 to 400 mm, and this is the displacement which has to be accommodated by the 'seismic gap.' The actual motion of parts of the structure depends on the mass distribution, the parameters of the isolating system, and the 'participation' of various modes of vibration. This is discussed in detail in Chapters 2 and 6. Seismic isolation is thus an innovative aseismic design approach aimed at protecting structures against damage from earthquakes by limiting the earthquake attack rather than resisting it. Conventional approaches to aseismic design provide a structure with sufficient strength, deformability and energy-dissipating capacity to withstand the forces generated by an earthquake, and the peak acceleration response of the structure is often greater than the peak acceleration of the driving ground motion. On the other hand, seismic isolation limits the effects of the earthquake attack, since a flexible base largely decouples the structure from the horizontal motion of the ground, and the structural response accelerations are usually less than the ground accelerations. The forces transmitted to the isolated structure are further reduced by damping devices which dissipate the energy of the earthquake-induced motions. Figure 1.2(a) illustrates the seismic isolation concept schematically. The building on the left is conventionally protected against seismic attack and that on the right has been mounted on a seismic isolation system. The performance of a pair of real test buildings of this kind, at Tohoku University, Sendai, Japan, is described in Chapter 8. Similar schematic diagrams can be drawn to illustrate the seismic isolation of bridges and of parts of buildings which contain delicate or potentially hazardous contents.

4

(a)

(b)

Figure 1.2: (a) Schematic seismic response of two buildings; that on the left is conventionally protected against earthquake, and that on the right has been mounted on a seismic isolation system. (b) Maximum base shear for a single-mass structure, represented as a linear resonator, with and without seismic isolation. The structure is subjected to Pa times the El Centro NS 1940 accelerogram. (From Skinner & McVerry, 1975).

In Figure 1.2(a) it can be seen that large seismic forces act on the unisolated, conventional structure on the left, causing considerable deformation and cracking in the structure. In the isolated structure on the right, the forces are much reduced, and most of the displacement occurs across the isolation system, with little deformation of the structure itself, which moves almost as a rigid unit. Energy dissipation in the isolated system is provided by hysteretic or viscous damping. For the unisolated system, energy dissipation results mainly from structural damage. Figure 1.2(b) illustrates the reduction of earthquake induced shear forces which can be achieved by seismic isolation. The maximum responses of seismically isolated structures, as a function of unisolated fundamental period are shown by a solid line and those of the unisolated structures as a dotted line, with results shown for three scalings of the El Centro NS 1940 earthquake motion. It is seen that seismic isolation markedly reduces the base shear in all cases.

1.3

COMPARISON OF CONVENTIONAL & SEISMIC ISOLATION APPROACHES

Many of the concepts of seismic isolation using hysteretic isolators are similar to the conventional failure-mode-control approach ('capacity design') which is used in New Zealand for providing earthquake resistance in reinforced concrete and steel structures. In both the seismic isolation and failure-mode-control approaches, specially selected ductile components are designed to withstand several cycles well beyond yield under reversed loading, the yield levels being chosen so that the forces transmitted to other components of the structure are limited to their elastic or low ductility, range. The yielding lengthens the fundamental period of the structure, detuning the response away from the energetic period range of most of the earthquake ground motion. The hysteretic behaviour of the ductile components provides energy dissipation to damp the response motions. The ductile behaviour of the selected components ensures sufficient deformation capacity, over a number of cycles of motion, for the structure as a whole to ride out the earthquake attack. However, seismic isolation differs fundamentally from conventional seismic design approaches in the method by which the period lengthening (detuning) and hysteretic energy dissipating mechanisms are provided, as well as in the philosophy of how the earthquake attack is withstood. 5

In well-designed conventional structures, the yielding action is designed to occur within the structural members at specially selected locations ('plastic hinge zones'), e.g. mostly in the beams adjacent to beam-column joints in moment-resisting frame structures. Yielding of structural members is an inherently damaging mechanism, even though appropriate selection of the hinge locations and careful detailing can ensure structural integrity. Large deformations within the structure itself are required to withstand strong earthquake motions. These deformations cause problems for the design of components not intended to provide seismic resistance, because it is difficult to ensure that unintended loads are not transmitted to them when the structure is deformed considerably from its rest position. Further problems occur in the detailing of such items as windows and partitions, and for the seismic design of building services. In the conventional approach, it is accepted that considerable earthquake forces and energy will be transmitted to the structure from the ground. The design problem is to provide the structure with the capacity to withstand these substantial forces. In seismic isolation, the fundamental aim is to reduce substantially the transmission of the earthquake forces and energy into the structure. This is achieved by mounting the structure on an isolating layer (isolator) with considerable horizontal flexibility, so that during an earthquake, when the ground vibrates strongly under the structure, only moderate motions are induced within the structure itself. Practical isolation systems must trade-off between the extent of force isolation and acceptable relative displacements across the isolation system during the earthquake motion. As the isolator flexibility increases, movements of the structure relative to the ground may become a problem under other vibrational loads applied above the level of the isolation system, particularly wind loads. Acceptable displacements in conjunction with a large degree of force isolation can be obtained by providing damping, as well as flexibility in the isolator. A seismic isolation system with hysteretic force-displacement characteristics can provide the desired properties of isolator flexibility, high damping and force-limitation under horizontal earthquake loads, together with high stiffness under smaller horizontal loads to limit wind-induced motions. A further trade-off is involved if it is necessary to provide a high level of seismic protection for potentially resonant contents and substructures, where increased isolator displacements and/or structural loads are incurred when providing this additional protection.

1.4

COMPONENTS IN AN ISOLATION SYSTEM

The components in a seismic isolation system are specially designed, distinct from the structural members, installed generally at or near the base of the structure. However, in bridges, where the aim is to protect relatively low-mass piers and their foundations, they are more commonly between the top of the piers and the superstructure. The isolator's viscous damping and hysteretic properties can be selected to maintain all components of the superstructure within the elastic range, or at worst so as to require only limited ductile action. The bulk of the overall displacement of the structure can be concentrated in the isolator components, with relatively little deformation within the structure itself, which moves largely as a rigid body mounted on the isolation system. The performance can be further improved by bracing the structure to achieve high stiffness, which increases the detuning between the fundamental period of the superstructure and the effective period of the isolated system and also limits deformations within the structure itself. Both the forces transmitted to the structure and the deformation within the structure are reduced, and this simplifies considerably the seismic design of the superstructure, its contents and services, apart from the need for the service connections to accommodate the large displacements across the isolating layer.

6

Figure 1.3: Schematic representation of the force-displacement hysteresis loops produced by: (a) a linear damped isolator; (b) a bilinear isolator with a Coulomb damper.

Figure 1.3 is a schematic representation of the two major models encountered in the practical design of seismic isolating systems. Figure 1.3(a) represents a linear damped isolator by means of a linear spring and 'viscous damper'. The resultant force-displacement loop has an effective slope (dashed line) which is the 'stiffness', or inverse flexibility, of the isolator. Figure 1.3(b) represents a 'bilinear' isolator as two linear springs, one of which has a 'Coulomb damper' in series with it. The resultant hysteresis loop is bilinear, characterised by two slopes which are the 'initial' and 'yielded' stiffnesses respectively, corresponding to the elastic and plastic deformation of the isolator. A variety of seismic isolation and energy dissipation devices has been developed over the years, all over the world. The most successful of these devices also satisfy an additional criterion, namely, they have a simplicity and effectiveness of design which makes them reliable and economic to produce and install, and which incorporates low maintenance, so that a passively isolated system will perform satisfactorily, without notice or forewarning, for 5 to 10 seconds of earthquake activity at any stage during the 30- to 100-year life of a typical structure. In order to ensure that the system is operative at all times, we suggest that zero or low maintenance be part of good design. Detailed discussion of the material and design parameters of seismic isolation devices is given in Chapter 3.

1.5

PRACTICAL APPLICATION OF THE SEISMIC ISOLATION CONCEPT

The seismic isolation concept for the protection of structures from earthquakes has been proposed in various forms numerous times this century. Many systems have been put forward, involving features such as roller or rocker bearings, sliding on sand or talc, or compliant first-storey columns, but these have generally not been implemented. 7

The practical application of seismic isolation is a new development pioneered by a few organisations around the world in recent years. The efforts of these pioneers are now blossoming, with seismic isolation becoming increasingly recognised as a viable design alternative in the major seismic regions of the world. The authors' group at DSIR Physical Sciences, previously the Physics and Engineering Laboratory of the Department of Scientific and Industrial Research (PEL, DSIR) in New Zealand, has pioneered seismic isolation, with research starting in 1967. Several practical techniques for achieving seismic isolation and a variety of energy-dissipating devices have been developed and implemented in over 40 structures in New Zealand, largely through the innovative approach and cooperation of engineers of the Ministry of Works and Development (MWD), as well as private structural engineering consultants in New Zealand. All the techniques developed at DSIR Physical Sciences have had a common element, in that damping has been achieved by the hysteretic working of steel or lead (see Chapter 3). Flexibility has been provided by a variety of means: transverse rocking action with base uplift (South Rangitikei railway bridge, and chimney at Christchurch airport), horizontally flexible lead-rubber isolators (William Clayton Building, Wellington Press Building, Petone, and numerous road bridges), and flexible sleeved-pile foundations (Union House in Auckland and Wellington Central Police Station). Hysteretic energy dissipation has been provided by various steel bending-beam and torsional-beam devices (South Rangitikei Viaduct, Christchurch airport chimney, Union House, Cromwell bridge and Hikuwai retrofitted bridges), lead plugs in laminated steel and rubber bearings (William Clayton Building and numerous road bridges); and lead-extrusion dampers (Aurora Terrace and Bolton Street motorway overpasses in Wellington and Wellington Central Police Station). More details of these structures are given in Chapter 8. Before their use in structures, all these types of devices have been thoroughly tested at full scale at DSIR Physical Sciences, in dynamic test machines under both sinusoidal and earthquake-like loadings. Other tests have been performed at the Universities of Auckland and Canterbury. Shaking-table tests of elastomeric and lead rubber bearings and steel dampers have been performed at the University of California, Berkeley, and in Japan on large-scale model structures. Quick-release tests on actual structures containing these types of bearings and damping devices have been performed in New Zealand and Japan. Some seismically isolated structures have performed successfully during real, but so far, minor, earthquake motions. A number of organisations around the world have developed isolation systems different from those at DSIR Physical Sciences. Most have used means other than the hysteretic action of ductile metal components to obtain energy dissipation, force limitation and base flexibility. Various systems have used elastomeric bearings without lead-plugs, damping being provided either by the use of high-loss rubber or neoprene materials in the construction of the bearings or by auxiliary viscous dampers. There have been a number of applications of frictional sliding systems, both with and without provision of elastic centring action. There has been substantial work recently on devices providing energy-dissipation alone, without isolation, in systems not requiring period shifting, either because of the substantial force reduction from large damping or because the devices were applied in inherently long-period structures, such as suspension bridges or tall buildings, where isolation itself produces little benefit. There has also been work on very expensive mechanical linkage systems for obtaining three-dimensional isolation. Seismic isolation has often been considered as a technique only for 'problem' structures or for equipment which requires a special seismic design approach. This may arise because of their function (sensitive or high-risk industrial or commercial facilities such as computer systems, semiconductor manufacturing plant, biotechnology facilities and nuclear power plants); their special importance after an earthquake (e.g., hospitals, disaster-control centres such as police stations, bridges providing vital communication links); poor ground conditions; proximity to a major fault; or other special problems (e.g., increasing the seismic resistance of existing structures). 8

Seismic isolation does indeed have particular advantages over other approaches in these special circumstances, usually being able to provide much better protection under extreme earthquake motions. However, its economic use is by no means limited to such cases. In New Zealand, the most common use of seismic isolation has been in ordinary two-lane road bridges of only moderate span, which are by no means special structures, although admittedly the implementation of seismic isolation required little modification of the standard design which already used vulcanised laminated rubber bearings to accommodate thermal and other movements.

1.6

TOPICS COVERED IN THIS BOOK

In this book we seek to present a parallel development of theoretical and practical aspects of seismic isolation, as well as presenting information about buildings and bridges that have been built using this technique all over the world, and how they have performed in real earthquakes. Mathematical rigour is achieved by retaining Chapters 2 of “An Introduction to Seismic Isolation” which presents mathematical concepts derived from the basic equations of damped simple harmonic motion. In Chapter 2 the principal seismic response features conferred by isolation are outlined, with descriptions and brief explanations. Seismic response spectra are introduced as the maximum seismic displacements and accelerations of linear 1.mass damped vibrators. It is later shown that these spectra give good approximations to the maximum displacements, accelerations and loads of structures mounted on linear isolation systems, which respond approximately as rigid masses with little deformation and little higher-mode response. The spectra vary depending on the accelerogram used to excite the seismic response, with El Centro NS 1940, or appropriately scaled versions of this design earthquake, being used most commonly throughout this book. When the single mass is mounted on a bilinear isolation system, the maximum seismic displacement and acceleration responses can be represented in terms of 'effective' periods and dampings. This concept is an oversimplification but is valid for a wide range of bilinear parameters. It is convenient to introduce an 'isolator nonlinearity factor' NL, which is defined in terms of the force-displacement hysteresis loop. However, unlike the case with linear isolation, many bilinear isolation systems result in large higher-mode effects which may make large or even dominant contributions to the maximum seismic loads throughout the isolated structure. They may also result in relatively severe appendage responses, as given by floor acceleration spectra, for periods below 1.0 seconds. The above and other features of the maximum seismic responses of isolated structures are illustrated at the end of Chapter 2 by seven case studies, as summarised in Table 2.1 and Figure 2.7 and further by Table 2.2. Features examined include the maximum seismic responses of a simple uniform shear structure and of 1.mass top-mounted appendages, when the structure is unisolated and when it is supported on each of six isolation systems. Chapter 3, which is also carried over from “An Introduction to Seismic Isolation”, presents details of seismic isolation devices, with particular reference to those developed in our laboratory over the past 25 years, including steel-beam dampers, lead extrusion dampers and lead rubber bearings. The treatment discusses the material properties on which the devices are based, and outlines the principal features which influence the design of these devices.

9

Chapters 4 and 5 of the original manuscript “an Introduction to Seismic isolation” have not been carried over into this new book. Chapters 4, 5, 6 and 7 of this book contain new material written by Trevor Kelly. Chapter 4 continues from Chapter 3, giving engineering properties of the devices described in the previous chapter. Chapter 5 presents detailed procedures for isolation system design. Chapter 6 is a detailed analysis of the seismic responses of various prototype buildings each of which is provided with different isolating systems. Chapter 7 continues this work with examples of seismic isolation of a building and a bridge. Chapter 8 of this new book carries over Chapter 6 of “An Introduction to Seismic Isolation” and gives some details of seismically isolated structures worldwide. The original Chapter 6 has been virtually unchanged in being transposed to Chapter 8 of the new book, and it presents information on the world-wide use of seismic isolation in buildings, bridges and special structures which are particularly vulnerable to earthquakes. The information was compiled in 1992 with the help of colleagues world-wide, who have enabled us to build up a picture of the isolation approaches which have been adopted in response to a wide range of seismic design problems. We should like to thank these colleagues for their contributions. Chapter 9 discusses implementation issues which arise in seismic isolation projects and provides guidance for dealing with these issues. It is clear that engineers, architects and their clients world-wide are building up extensive experience in the development, design and potential uses of isolation systems. In time, these isolated structures will also provide a steadily increasing body of information on the performance of seismically isolated systems during actual earthquakes. In this way the evolving technology of seismic isolation may contribute to the mitigation of earthquake hazard worldwide. Chapter 10 presents ideas as to where seismic isolation could go in the new millennium, when it is widely recognised as a practical means of reducing death, injury, property damage in the event of an earthquake. Chapter 10 also presents additional devices that have been developed or are under development, such as in-structure damping and the RoBall seismic isolator.

10

Chapter 2

2.1

GENERAL FEATURES OF STRUCTURES WITH SEISMIC ISOLATION

INTRODUCTION

For many structures the severity of an earthquake attack may be lowered dramatically by introducing a flexible isolator as indicated by Figure 1.1. The isolator increases the natural period of the overall structure and hence decreases its acceleration response to earthquake-generated vibrations. A further decrease in response occurs with the addition of damping. This increase in period, together with damping, can markedly reduce the effect of the earthquake, so that less-damaging loads and deformations are imposed on the structure and its contents. This chapter examines the general changes in vibrational character which different types of seismic isolation confer on a structure, and the consequent changes in seismic loads and deformations. The study is greatly assisted by considering structural modes of vibration and earthquake response spectra, an approach which has proved very effective in the study and design of non-isolated aseismic structures (Newmark & Rosenblueth, 1971; Clough & Penzien, 1975). The seismic responses of general linear structures are introduced early to provide the concepts used throughout this Chapter and later in the book. Attention is also given to seismic response mechanisms since they assist in understanding the seismic responses of isolated structures and how they are related to the responses of similar structures which are not isolated. The general consequences of seismic isolation are illustrated using 6 different isolation systems. This chapter leads to some useful approaches for the study of seismic isolation, gives a greater understanding of the mechanisms involved, and indicates some useful design approaches. The discussions throughout this chapter assume simple torsionally-balanced structures in which the structural masses at rest are centred on a vertical line, as illustrated in the figures 2.1 to 2.7.

2.2

ROLE OF EARTHQUAKE RESPONSE SPECTRA AND VIBRATIONAL MODES IN THE PERFORMANCE OF ISOLATED STRUCTURES

2.2.1

Earthquake Response Spectra

The horizontal forces generated by typical design-level earthquakes are greatest on structures with low flexibility and low vibration damping. The seismic forces on such structures can be reduced greatly by supporting the structure on mounts which provide high horizontal flexibility and high vibration damping. This is the essential basis of seismic isolation. It can be illustrated most clearly in terms of the response spectra of design earthquakes. The main seismic attack on most structures is the set of horizontal inertia forces on the structural masses, these forces being generated as a result of horizontal ground accelerations. For most structures, vertical seismic loads are relatively unimportant in comparison with horizontal seismic loads. For typical design earthquakes, the horizontal accelerations of the masses of simple shorter-period structures are controlled primarily by the period and damping of the first vibrational mode, i.e., that form in which the system resonates at the lowest frequency. 11

The dominance of the first mode occurs in isolated structures, and in unisolated structures with first-mode periods up to about 1.0 seconds, a period range which includes most structures for which isolation may be appropriate. Neglecting the less important factors of mode shape and the contribution of higher modes of vibration, the seismic acceleration responses of the isolated and unisolated structures may be compared broadly by representing them as single-mass oscillators which have the periods and dampings of the first vibrational modes of the isolated and unisolated structures respectively. The natural (fundamental) period T, natural frequency  and damping factor  of such a single-mass oscillator, of mass m, are obtained by considering its equation of motion:

mÅ + cu + ku = - m Åg

(2.1)

where u is the displacement of the single-mass oscillator relative to the ground, ug is the ground displacement, k is the 'spring stiffness' and c is the 'damping coefficient'. The natural (fundamental) frequency of undamped, unforced oscillations (c=0 and üg=0) is

 2 = k/m

(2.2)

T = 2 m/k

(2.3)

or

The solution for damped, unforced oscillations is

u = A e-(c/ 2 m) t cos ( d t +  ) where 2  d2 = (k/m) - (c/ 2 m )

and where A and  are constants representing the initial displacement amplitude and initial phase of the motion. The damped, unforced oscillation has thus a lower frequency d than the natural frequency, and d decreases as the value of the damping coefficient c is increased. If c is increased to a 'critical value' ccr such that d=0, the system will not oscillate. The critical damping is given by

ccr = 2 mk A 'damping factor'  can then be defined which expresses the damping as a fraction of critical damping:

 = c/ c cr = c/(2 mk ) = c/ 2 m  = cT/ 4 m

(2.4)

The equation of motion can then be divided by m to give

u +

c k u + u = - ug m m

or

u + 2 u +  2 u = - ug 12

(2.5)

For this (damped, forced) dynamic system, the displacement response to ground accelerations may be given in closed form as a Duhamel integral, obtained by expressing ü g(t) as a series of impulses and summing the impulse responses of the system. When the system starts from rest at time t = 0, this gives the relative displacement response as:

u(t) = - (1 /  d )  0 Å g ( ) exp[- (t -  )] sin  d (t -  ) d  t

(2.6)

By successive differentiation, similar expressions may be obtained for the relative velocity response u  and the total acceleration response ü + üg. For particular values of  and , the responses to the ground accelerations of a given earthquake may be obtained from step-bystep evaluation of equation (2.6) or from other evaluation procedures. Since structural designs are normally based on maximum responses, a convenient summary of the seismic responses of single-mass oscillators is obtained by recording only the maximum responses for a set of values of the oscillator parameters  (or T) and . These maximum responses are the earthquake response spectra. They may be defined as follows:

S A (T , ) = (Å + Å g )(t ) max ; S V (T ,  ) = u(t ) max ; S D (T ,  ) = u(t ) max

(2.7)

Such spectra are routinely calculated and published for important accelerograms, e.g. EERL Reports (1972.5). Figure 2.1 shows response spectra for various damping factors (0, 2, 5, 10 and 20 percent of critical) for a range of earthquakes.

(a)

13

(b)

(c)

Figure 2.1: (a) (b) (c)

Response spectra for various damping factors. In each figure, the curve with the largest values has 0% damping and successively lower curves are for damping factors of 2, 5, 10 and 20% of critical. Acceleration response spectrum for El Centro NS 1940 Acceleration response spectrum for the weighted average of eight accelerograms (El Centro 1934, El Centro 1940, Olympia 1949, Taft 1952). The symbols U and I refer to unisolated and isolated structures respectively. Displacement spectra corresponding to Figure 2.1(b).

Figure 2.1(a) shows acceleration response spectra for the accelerogram recorded in the S0oE direction at El Centro, California, during the 18 May 1940 earthquake (often referred to as 'El Centro NS 1940'). This accelerogram is typical of those to be expected on ground of moderate flexibility during a major earthquake. The El Centro accelerogram is used extensively in the following discussions because it is typical of a wide range of design accelerograms, and because it is used widely in the literature as a sample design accelerogram. Seismic structural designs are frequently based on a set of weighted accelerograms, which are selected because they are typical of site accelerations to be expected during design-level earthquakes. 14

The average acceleration response spectra for such a set of 8 weighted horizontal acceleration components are given in Figure 2.1(b). Each of the 8 accelerograms has been weighted to give the same area under the acceleration spectral curve, for 2% damping over the period range from 0.1 to 2.5 seconds, as the area for the El Centro NS 1940 accelerogram (Skinner, 1964). Corresponding response spectra can be presented for maximum displacements relative to the ground, as given in Figure 2.1(c). These displacement spectra show that, for this type of earthquake, displacement responses increase steadily with period for values up to about 3.0 seconds. As in the case of acceleration spectra, the displacement spectral values decrease as the damping increases from zero. The spectra shown in Figures 2.1(b) and 2.1(c) are more exact presentations of the concept illustrated in Figure 1.1. While the overall seismic responses of a structure can be described well in terms of ground response spectra, the seismic responses of a light-weight sub-structure can be described more easily in terms of the response spectra of its supporting floor. Floor response spectra are derived from the accelerations of a point or 'floor' in the structure, in the same way that earthquake response spectra are derived from ground accelerations. Thus they give the maximum response of light-weight single-degree-of-freedom oscillators located at a particular position in the structure, assuming that the presence of the oscillator does not change the floor motion. It is also possible to derive floor spectra which include interaction effects. Floor response spectra tend to have peaks in the vicinity of the periods of modes which contribute substantial acceleration to that floor. The response spectrum approach is used throughout this book to increase understanding of the factors which influence the seismic responses of isolated structures. The response spectrum approach also assists in the seismic design of isolated structures, since it allows separate consideration of the character of design earthquakes and of earthquake-resistant structures. A technique which is given some emphasis is the extension of the usual response spectrum approach for linear isolators to the case of bilinear isolators.

2.2.2

General Effects of Isolation on the Seismic Responses of Structures

The first mode of a simple isolated structure is very different from all its other modes, which have features similar to each other. We treat the first mode separately from all the other modes, which are usually referred to herein as 'higher modes'. The first-mode period and damping of an isolated structure, and hence its seismic responses, are determined primarily by the characteristics of the isolation system and are virtually independent of the period and damping of the structure. In the first isolated mode the vertical profiles of the horizontal displacements and accelerations are approximately rectangular, with approximately equal motions for all masses (see later, Figure 2.5). Hence an isolated structure may be approximated by a rigid mass when assessing the seismic responses of its first vibrational mode. Except for special applications, the seismic responses of structures with linear isolation can be described in terms of earthquake response spectra, and the simple first mode of vibration. When the isolation is strongly nonlinear, many important seismic responses can still be described in terms of mode 1, but higher modes can be of importance. Figures 2.1(a) and (b) show acceleration response spectra for typical design earthquakes. It is seen that these maximum accelerations, and hence the general inertia attacks on structures, are most severe when the first vibrational period of the structure is in the period range from about 0.1 to 0.6 seconds and when the structural damping is low. This period range is typical of buildings which have from 1 to 10 storeys. 15

The shaded area marked (U) in Figure 2.1(b) gives the linear acceleration spectral responses for the range of first natural periods (up to about 1.0 second) and structural dampings (up to about 10% of critical) to be expected for structures which are promising candidates for seismic isolation. Similarly, the shaded area marked (I) in Figure 2.1(b) gives the acceleration spectral responses for the range of first-mode periods and dampings which may be conferred on a structure by isolation systems of the types described in Chapter 3. A comparison of the shaded areas for unisolated and isolated structures in Figure 2.1(b) shows that the acceleration spectral responses, and hence the primary inertia loads, may well be reduced by a factor of 5 to 10 or more by introducing isolation. While higher modes of vibration may contribute substantially to the seismic accelerations of unisolated structures, and of structures with non-linear isolation, this does not seriously alter the response comparison based on the shaded areas of Figure 2.1(b). This figure therefore illustrates the primary basis for seismic isolation. The contributions of higher modes to the responses of isolated structures are described in general terms below, and in more detail later in this chapter. Almost all the horizontal seismic displacements, relative to the ground, are due to the first vibrational mode, for both unisolated and isolated structures. The seismic displacement responses for unisolated and isolated structures are shown in Figure 2.1(c) by the shaded areas (U) and (I) respectively. These shaded areas have the same period and damping ranges as the corresponding areas in Figure 2.1(b). As noted above, the first-mode period and damping of each isolated structure depend almost exclusively on the isolator stiffness and damping. Figure 2.1(c) shows a considerable overlap in the displacements which may occur with and without isolation. This may arise when high isolator damping more than offsets the increase in displacement which would otherwise occur because the isolator has increased the overall system flexibility. Moreover, while displacements without isolation normally increase steadily over the height of a structure, the displacements of isolated structures arise very largely from isolator displacements, with little deformation of the structure above the isolator, giving the approximately rectangular profile of mode 1. Figure 2.1(c) shows that isolator displacements may be quite large. The larger displacements may contribute substantially to the costs of the isolators and to the costs of accommodating the displacements of the structures, and therefore isolator displacements are usually important design considerations. A convenient feature of the large isolator displacements is that the isolator location provides an effective and convenient location for dampers designed to confer high damping on the dominant first vibrational mode. Moreover, some dampers require large strokes to be effective. Such damping reduces both the accelerations which attack the structure and the isolator displacements for which provision must be made.

2.2.3

Parameters of Linear and Bilinear Isolation Systems

A typical isolated structure is supported on mounts which are considerably more flexible under horizontal loads than the structure itself. It is assumed here that the isolator is at the base of the structure and that it does not contribute to rocking motions. As a first approximation, the structure is assumed to be rigid, swaying sideways with approximately constant displacement along its height, corresponding to the first isolated mode of vibration. Some isolation systems used in practice are 'damped linear' systems such as presented in equations (2.1) and (2.5). However, an alternative approach, for the provision of high isolator flexibility and damping, is to use nonlinear hysteretic isolation systems, which also inhibit wind-sway. 16

Such nonlinearity is frequently introduced by hysteretic dampers, or by the introduction of sliding components to increase horizontal flexibility, as discussed in Chapter 3. These isolation systems can usually be modelled approximately by including a component which slides with friction, and gives a bilinear force-displacement loop when the model is cycled at constant amplitude. Models of linear and bilinear isolation systems, with the structure modelled by its total mass M, are shown in Figures 2.2(a) and 2.3(a).

(a)

(b)

(c)

Figure 2.2: (a) (b) (c)

Schematic representation of a damped linear isolation system. Structure of mass M supported by linear isolator of shear stiffness Kb, with velocity damper (viscous damper) of coefficient Cb. Shear force S versus displacement X showing the hysteresis loop and defining the secant stiffness of the linear isolator: Kb = Sb/Xb. Linear isolator with high damping coefficient and higher-mode attenuator Kc.

17

(a)

(b)

(c)

Figure 2.3: (a) (b)

(c)

Schematic representation of a bilinear isolation system. Structure of mass M supported by bilinear isolator which has linear 'spring' components of stiffnesses Kb1 and Kb2, together with a sliding (Coulomb) damper component. Shear force versus displacement showing the bilinear hysteresis loop and defining the secant stiffness of the bilinear isolator: KB = Sb/Xb. The individual stiffnesses Kb1 and Kb2 are the slopes (gradients) of the hysteresis loop as shown, and (Xy, Qy) is the yield point. Comparison of linear hysteresis loop with a circumscribed rectangle, to enable definition of the nonlinearity factor NL.

The linear isolation system (Figure 2.2) has shear stiffness Kb and its coefficient of (viscous-) velocity-damping is Cb, where the subscript b is used to denote parameters of the linear isolator. These parameters may be related to the mass M or the weight W of the isolated structure using equations (2.3) and (2.4). This gives the natural period Tb and the velocity damping factor b:

and

Tb = 2 ( M/ K b)

(2.8a)

 b = C b T b /(4M)

(2.8b)

Figure 2.2(b) shows the 'shear force' versus 'displacement' hysteresis loop of such a damped linear isolator, which is traversed in the clockwise direction as the shear force and displacement cycle between maximum values +Sb and +Xb respectively. The 'effective stiffness' of the isolator is then defined as (2.9) K b = Sb / X b The design values chosen for Tb and b will usually be based on a compromise between seismic 18

forces, isolator displacements, their effects on seismic resistance and the overall costs of the isolated structure. When the isolator velocity-damping is quite high, say b greater than 20%, higher-mode acceleration responses may become important, especially regarding floor acceleration spectra. Such an increase in higher-mode responses may be largely avoided by anchoring the velocity dampers by means of components of appropriate stiffness Kc, as modelled in Figure 2.2(c). The bilinear isolator model (Figure 2.3(a)) has a stiffness Kb1 without sliding, (the 'elastic-phase stiffness'), and a lower stiffness Kb2 during sliding or yielding, (the 'plastic-phase stiffness'). By analogy with the linear case, these stiffnesses can be related to corresponding periods of vibration of the system:

T b1 , T b2 = 2 ( M/ K b1 ) , 2 ( M/ K b2 )

(2.10a)

Corresponding damping factors can also be defined:

 b 1 ,  b 2 = C b T b1 /(4 M), C b T b 2 /(4 M)

(2.10b)

An additional parameter required to define a bilinear isolator is the yield ratio Qy/W, relating the yield force Qy of the isolator, Figure 2.3(b), to the weight W of the structure. Yielding occurs at a displacement Xy given by Qy/Kb1. When the design earthquake has the severity and character of the El Centro NS 1940 accelerogram it has been found that a yield ratio Qy/W of approximately 5% usually gives suitable values for the isolator forces and displacements. In order to achieve corresponding results with a design accelerogram which is a scaled version of an El Centro-like accelerogram, it is necessary to scale Qy/W by the same factor, as described in Chapters 4 and 5. It is found useful to describe the bilinear system using 'effective' values, namely an appropriately defined 'effective' period TB and 'effective' damping factor B. The subscript B is used for these effective values of a bilinear isolator. The effective bilinear values TB and B are obtained with reference to the 'shear force' versus 'displacement' hysteresis loop shown in Figure 2.3(b). This balanced-displacement bilinear loop is a simplification used to define these parameters of bilinear isolators. In practice, the reverse displacements, immediately before and after the maximum displacement Xb will have lower values. In general, the concept of these 'effective' values is a gross approximation, but it works surprisingly well. Note also that the simplified bilinear loop shown does not include the effects of velocity-damping forces. The damping shown is 'hysteretic', depending on the area of the hysteresis loop. The 'effective' stiffness KB (also known as the 'secant' stiffness) is defined as the diagonal slope of the simplified maximum response loop shown in Figure 2.3(b):

K B = Sb / X b

(2.11a)

This gives the effective period

T B = 2

19

M/ K B

(2.11b)

An equivalent viscous-damping factor h can be defined to account for the hysteretic damping of the base. Any actual viscous damping b of the base must be added to h to obtain the effective viscous-damping factor B for the bilinear system. In practice h is usually larger than b, i.e. the damping of a bilinear hysteretic isolator is usually dominated by the hysteretic energy dissipation rather than by the viscous damping b. Thus

 B = b + h

where, from equation (2.4),

 b  Cb T B /(4 M)

(2.11c)

(2.12)

and where h is obtained by relating the maximum bilinear loop area to the loop area of a velocity-damped linear isolator vibrating at the period TB with the same amplitude Xb, to give

 h = (2/ ) Ah /(4 S b X b )

(2.13)

where Ah = area of the hysteresis loop. For nonlinear isolators, it is convenient to have a quantitative definition of nonlinearity. We have found it useful to define a nonlinearity factor, NL, in terms of Figures 2.3(b) and 2.3(c), as the ratio of the maximum loop off-set, from the secant line joining the points (Xb,Sb) and (-Xb,-Sb), to the maximum off-set of the axis-parallel rectangle through these points, i.e., P1/P2. Hence the nonlinearity factor increases from 0 to 1 as the loop changes from a zero-area shape to a rectangular shape. For a bilinear isolator this is equivalent to the ratio of the loop area Ah to that of the rectangle. The nonlinearity factor NL is thus given by

NL = A h / (4 S b X b) = Q y / S b - X y / X b

(2.14)

From equations (2.13) and (2.14) it is seen that the hysteretic damping factor h is proportional to the non-linearity factor NL for bilinear hysteretic loops. However, re-entrant bilinear loops may have a much lower ratio of damping to nonlinearity.

2.2.4

Calculation of Seismic Responses

When the isolator is linear and the base flexibility sufficient for the first mode to dominate the response, the maximum seismic responses of the system may be approximated by design-earthquake spectral values, as given for example in Figure 2.1, for the isolator period Tb and damping b. For the approximately rigid-structure motions of the first isolated mode, the maximum displacement Xr at any level r in the structure is given by

X r  S D ( T b , b )

(2.15a)

The maximum inertia load Fr, on the r-th mass mr, is given by

F r  mr S A ( T b , b )

(2.15b)

The inertia forces are approximately in phase and may be summed to give the shear at each level. In particular the base-level shear is given by 20

S b  MS A ( T b , b )

(2.15c)

When the isolator is bilinear, seismic responses may still be obtained from design-earthquake spectral values, but the solutions are less exact than in the linear case. The results of a separate analysis, not given here, allow the seismic responses of a range of isolators to be compared in section 2.5 below. These results were obtained by calculating the responses of 81 different isolator-structure systems and analysing the patterns which emerged. It was found that the effective period TB and effective damping B of equations (2.11) to (2.13) may be used with earthquake spectra to obtain rough approximations for the seismic responses of the first mode. The maximum base displacement Xb and the maximum base shear Sb (neglecting velocity-damping forces) may be derived from the isolator parameters and 'bilinear' spectral displacement SD(TB,B) as follows:

X b  CF S D(T B ,  B ) Sb  Q y + K b 2 (X b - X y)

(2.16a) (2.16b)

Here CF is a correction factor which was found empirically. For the El Centro NS 1940 accelerogram, the correction factor CF lies approximately in the range 0.85 to 1.15 for a wide range of the bilinear isolator parameters Tb1, Tb2 and Qy/W. This gives an idea of the uncertainties associated with this method. Note that the method is also iterative, as TB and B are functions of Xb and Sb. 2.2.5

Contributions of Higher Modes to the Seismic Responses of Isolated Structures

The contributions of higher modes of vibration to the seismic responses of isolated structures can be described briefly in general terms. A linear isolation system with a high degree of linear isolation and moderate isolator damping, (i.e. b < 20%) or with high isolator damping which includes a higher-mode attenuator as in Figure 2.2(c), gives small higher-mode acceleration responses. Hence all the seismic responses of a structure with such linear isolation are approximated reasonably well by first-mode responses and by a rigid-structure model. Without higher-mode attenuation, high isolator damping may seriously distort mode shapes, and complicate their analysis. Also, higher-mode responses may increase as the damping increases, because greater base impedances caused by the base damping result in larger effective participation factors. When a bilinear isolator has a high degree of nonlinearity, there are usually relatively large higher-mode acceleration responses. These usually give substantial increases in the seismic inertia forces, compared to those produced by the first mode. Shear forces at various levels of the structure are typically increased by somewhat smaller amounts, the exception being nearbase shears which remain close to their mode-1 values because shears arising from higher isolated modes have a near-zero value at the isolator level. Increased floor acceleration spectra may result from increased higher-mode acceleration responses and may be of concern when the seismic loads on light-weight substructures, or on the contents of the structure, are an important design consideration. The higher-mode acceleration responses are generally reduced by reducing the nonlinearity of the isolator, but other isolator parameters may modify the effects of nonlinearity. When the isolator is bilinear the degree of nonlinearity can usually be reduced by reducing the period ratio Tb2/Tb1 and the yield ratio Qy/W, since these changes usually give a less rectangular loop. However, the nonlinearity should normally be left at the highest acceptable value, since the hysteretic damping of a bilinear isolator is proportional to the degree of nonlinearity, and the first-mode response generally decreases as the damping increases. 21

For a given degree of nonlinearity, the higher-mode acceleration responses can generally be reduced by making the elastic period Tb1 considerably greater than the first unisolated period T1(U). This approach becomes more practical and effective for structures whose period T1(U) is relatively low.

2.3

NATURAL PERIODS AND MODE SHAPES OF LINEAR STRUCTURES UNISOLATED AND ISOLATED

2.3.1

Introduction

It has been stated above that most or all of the important seismic responses of a structure with linear isolation, and many of the seismic responses with nonlinear isolation, can be approximated using a rigid-structure model. However, more detailed information is often sought, such as the effects of higher modes of vibration on floor spectra, especially for special-purpose structures for which seismic isolation is often the most appropriate design approach. Such higher-mode effects are conveniently studied by modelling the superstructure as a linear multi-mass system mounted on the isolators. Linear models and linear analysis can be used for unisolated structures and also when the structure is provided with linear isolation, except that high isolator damping may complicate responses. Simplified system models may be adopted to approximate the isolated natural periods and mode shapes when there is a high degree of modal isolation, namely when the effective isolator flexibility is high in comparison with the effective structural flexibility. The 'degree of modal isolation' is a useful concept. When a structure is provided with a bilinear isolator, it is found that the distribution of the maximum seismic responses of higher modes can be interpreted conveniently in terms of the natural periods and mode shapes which prevail during plastic motions of the isolator. This approach is effective for the usual case in which the yield displacement is much less than the maximum displacement. These mode shapes and periods are given by a linear isolator model which has an elastic stiffness equal to the plastic stiffness Kb2 of the bilinear isolator. These mode shapes explain the distribution of maximum responses through the structure, but in general the amplitudes of the responses will be different to those of a linear system with base stiffness Kb2. The elastic-phase isolation factor I(Kb1)=Tb1/T1(U) and the nonlinearity factor NL are important parameters affecting the strengths of the higher-mode responses.

2.3.2

Structural Model and Controlling Equations

The earthquake-generated motions and loads throughout non-yielding structures has been studied extensively, e.g., Newmark & Rosenblueth, (1971); Clough & Penzien, (1975). The structures are usually approximated by linear models with a moderate number N of point masses mr, as illustrated in Figure 2.4(a) for a simple 1-dimensional model.

22

Figure 2.4:

(a) Linear shear structure with concentrated masses. The seismic displacements of the ground and of the r-th mass mr are ug and (ur+ug) respectively. The relative displacement of the r-th mass is ur. Here k(r,s) and c(r,s) are, respectively, the stiffness and the velocity-damping coefficient of the connection between masses r and s. (b) Uniform shear structure with total mass M and overall unisolated shear stiffness K, such that the level mass mr=M/N and the intermass shear stiffness kr=KN. If N tends to infinity, the overall height l=hN, the mass per unit height m=M/l and the stiffness per unit height k=Kl.

In general, each pair of masses mr, ms is interconnected by a component with a stiffness k(r,s) and a velocity damping coefficient c(r,s). In Figure 2.4(a), each mass mr has a single horizontal degree of freedom, ur with respect to the supporting ground, or ur + ug with respect to the preearthquake ground position, where the horizontal displacement of the ground is ug. At each point r, the mass exerts an inertia force -(ür+üg)mr, while each interconnection exerts an elastic force -(ur - us)k(r,s) and a damping force -(ur -u s)c(r,s). The N equations which give the balance of forces at each mass can be expressed in matrix form:

[M]Å + [C] u + [K] u = - [M]1u g

(2.17)

where [M], [C] and [K] are the mass, damping and stiffness matrices, and where the matrix elements crs and krs are simply related to the damping coefficients and the stiffnesses, c(r,s) and k(r,s) respectively. Here [M], [C] and [K] are N x N matrices since the model has N degrees of freedom, and u is an N-element displacement vector. The model in Figure 2.4(a) and the force-balance equation (2.17) can be extended readily to a 3-dimensional model with 3N translational degrees of freedom (and 3N rotational degrees of freedom if the masses have significant angular momenta). However, Figure 2.4 and equation (2.17) are sufficiently general for most of the discussions here. 23

2.3.3

Natural Periods and Mode Shapes

The seismic responses of the N-mass linear system, defined by Figure 2.4(a) and equation (2.17), can be obtained conveniently as the sum of the responses of N independent modes of vibration. Each mode n has a fixed modal shape  n 29 (provided the damping matrix satisfies an orthogonality condition as discussed below), and a fixed natural frequency n and damping n. These modal parameters depend on M, C and K. Other features of modal responses follow from their frequency, damping, shape and mass distribution, and the frequency characteristics of the earthquake excitation. Modal responses are developed here in outline, with attention drawn to features which clarify the mechanisms involved. Important steps in the analysis parallel those for a simpler single-mass structure. The natural frequencies of the undamped modes are obtained by assuming that there are free vibrations in which each mass moves sinusoidally with a frequency . Let

u =  sin ( t +  )

(2.18)

where the displaced shape  31 varies with position in the structure and with , but is independent of t. Substitute equation (2.18) in equation (2.17), with the damping and ground acceleration terms removed:

( [K] -  2[M]) sin ( t +  ) = 0

(2.19)

Applying Cramer's rule it may be shown that non-trivial solutions are given by the roots of an Nth-order equation in 2:

det([K] -  2[M]) = 0

(2.20)

For a general stable structure, equation (2.20) is satisfied by N positive frequencies n, termed the undamped natural or modal frequencies of the structure. The N natural frequencies are usually separate, although repeated natural frequencies can occur. The shape  n 34 of mode n is now found by substituting n in equation (2.19) to give N linear homogeneous equations:

( [K] -  2n[M])  n = 0

(2.21)

Since the scale factor of each mode shape  n 36 is arbitrary it is here assumed, unless otherwise stated, that the top displacement of each mode is unity: Nn=1. A mode-shape matrix may then be defined as:

[ ] = [ 1 , . . . ,  n , . . .,  N ]

(2.22)

At each natural frequency n, the undamped structure can exhibit free vibrations with a normal mode shape  n 38 which is classical; that is, all masses move in phase (or antiphase where rn is negative).

24

2.3.4

Example - Modal Periods and Shapes

Natural periods and mode shapes for unisolated and well-isolated structures may be illustrated using a continuous uniform shear structure, hereafter referred to as the standard structure. If a frame building has equal-mass rigid floors, and if the columns at each level are inextensible and have the same shear stiffness, the building can be approximated as a uniform shear structure. This may be modelled as shown in Figure 2.4(b) with mr = M/N and k(r, r-1) = KN for r = 1 to N, and with all other stiffnesses removed. The model is given linear isolation by letting k(1,0) = Kb, where Kb is typically considerably less than the overall shear stiffness K. It is given base velocity damping by letting c(1,0) = Cb. The structural model is made continuous by letting N  . From the partial differential form of equations (2.17) which arises in the limit of N  , or otherwise, it may be shown that the mode shapes  n 39 have a sinusoidal profile, and that the modal frequencies n are proportional to the number of quarter-wavelengths in the modal profile. Unisolated modes have (2n-1) quarter-wavelengths and isolated modes have just over (2n-2) quarter-wavelengths, as shown in Figure 2.5. If the stiffnesses K and Kb are chosen to give first unisolated and isolated periods of 0.6 and 2.0 seconds respectively, the periods of other modes follow from the number of quarter-wavelengths as shown in Figure 2.5. Moreover, there are 0.6/2.1 quarter-wavelengths in isolated mode 1, so that the first-mode shape value b1 at the base of the structure, above the isolator, is given by b1 = cos (0.29 x 90o) = 0.90, as shown. Higher isolated modes rapidly converge towards (2n-2) quarter-wavelengths with increasing n, and corresponding periods occur.

Figure 2.5:

Variation, with height hr, of rn, which is the approximate shape of the n-th mode at the r-th level of the continuous uniform shear structure obtained by letting N tend to infinity in the structural model of Figure 2.4(b), when T1(U)=0.6 s and Tb=2.0 s. The modal shapes and periods are shown when the structure is unisolated (U) and isolated (I). Note that the responses interleave, with periods Tn(I) and Tn(U) alternating between 2.09, 0.6, 0.29, 0.2, 0.15 and 0.12 seconds respectively.

25

Modal acceleration profiles have the same shapes as the corresponding displacement profiles but are of opposite sign, and hence, for a uniform mass distribution, the modal force profiles also have the same shapes as the displacement profiles. The shear at a given level may be obtained by summing the forces above that level, so it is evident from Figure 2.5 that the shear profiles for the higher modes (n > 1) of the isolated structures have small near-nodal values at the base level, because of the cancelling effects of the positive and negative half-cycles of the profile. The unisolated and isolated natural periods and modal profiles of Figure 2.5 may be expressed as follows: (2.23a) T n (U) = 0.6 /(2 n- 1) - seconds

T 1 (I) = 2.1 ; T n (I)  0.6 /(2 n - 2) , for n > 1 - seconds

(2.23b)

 rn (U) = sin[(2 n - 1)( / 2)(h r / h N )]

(2.23c)

 r 1 (I)  cos[(0.3 (1 - h r / h N )( / 2))]

(2.23d)

 rn (I)  cos[(2 n - 2)( / 2)( h r / h N )]

(2.23e)

For structures which are non-shear and non-uniform, and have inter-mass stiffnesses in addition to k(r, r-1), period ratios are less simple but retain the general features given by Figure 2.5. For a well-isolated structure, the first-mode period is controlled by the isolator stiffness. All other isolated and unisolated periods are controlled by the structure and are interleaved in the order given by Figure 2.5. The isolated mode-1 profile is still approximately rectangular. Higher-mode profiles are no longer sinusoidal but have the same sequences of nodes and antinodes. Moreover the shear profiles of higher isolated modes still have small near-nodal values at the isolator level. For all well-isolated structures, the damping of mode 1 is controlled by the isolator damping. The damping of all higher modes is controlled by structural damping, provided the velocity damping of the isolator is not much greater than that of the structure. It is commonly assumed that the structural damping is approximately equal for all significant modes. 2.3.5

Natural Periods and Mode Shapes with Bilinear Isolation

When a structure is provided with a bilinear isolator there are two sets of natural periods and two corresponding sets of mode shapes; one set is given by a system model which includes a linear isolator which has the elastic stiffness Kb1 of Figure 2.3, while the other set is given when the linear isolator has the plastic stiffness Kb2. The yield level of a bilinear isolator is normally chosen to ensure that the maximum seismic displacement response, for a design-level excitation, is much larger than the isolator yield displacement. With such isolators the distribution of the maximum seismic motions and loads, and the floor spectra, can be expressed effectively in terms of the set of modes for which the shapes, and the higher-mode periods, are those of the normal modes which arise when the structure has a linear isolator of stiffness Kb2. An approximate effective period for mode 1 is derived from the secant stiffness KB at maximum displacement, as given by equation (2.11a) and illustrated in Figure 2.3(b). The relevance of the normal modes arising with stiffness Kb2 is to be expected, since maximum or near-maximum seismic responses should normally occur when the isolator is moving in its plastic phase, with an incremental stiffness Kb2. 26

2.4

MODAL AND TOTAL SEISMIC RESPONSES

2.4.1

Seismic Responses Important for Seismic Design

This section considers the seismic response quantities which are commonly important for the design of non-isolated or isolated structures. Important seismic responses normally include structural loads and deformations and may include appendage loads and deformations. Appendage responses indicate the level of seismic attack on light-weight substructures, and on plant and facilities within the structures. For an isolator, seismic displacement is likely to be the most important and limiting design factor. The contributions of structural modes and response spectra to the important seismic responses are indicated on the left of Figure 2.6. The earthquake accelerations give acceleration response spectra which combine with structural modes to give mass accelerations and hence structural seismic forces. Similarly floor (or structural-mass) acceleration response spectra give the appendage seismic forces.

Figure 2.6:

Schematic representation of the responses which dominate seismic design. The floor spectra have the same role in the response of the appendage as the earthquake spectra have in the response of the structure.

27

2.4.2

Modal Seismic Responses

The modal seismic responses of linear multi-mass structures can be expressed in a simple form when the shapes of all pairs of modes are orthogonal with respect to the stiffness, mass and damping matrices. It may be shown that undamped free-vibration mode shapes are orthogonal with respect to the mass and stiffness matrices. Moreover structural damping can usually be represented well by a matrix which gives classical in-phase mode shapes. Such a damping matrix does not couple or change the shape of the undamped modes. Particular exceptions to orthogonal damping may arise with highly-damped isolators or with damped appendages, but this is beyond the scope of this book. The orthogonality of the mode shapes, with respect to the mass and stiffness matrices, may be obtained from equation (2.21) by noting that the mass and stiffness matrices are unaltered by transposition; the mass matrix because it is diagonal, and the stiffness matrix because it is symmetric. T, and again the transpose of equation (2.21), If equation (2.21), for mode n, is pre-multiplied by m for mode m, is post-multiplied by n, this gives:

2  n  m [M] n =  m [K] n T T T T 2  m  m [M]  n =  m [K]  n T

T

(2.24a) (2.24b)

Since [M]T = [M] and [K]T = [K], subtraction of equation (2.24b) from equation (2.24a) gives, for the usual case when m2  n2, the orthogonality condition:

 m [M] n = 0 , when n _ m

(2.25a)

m

(2.25b)

T

Similarly

T

[K] n = 0 , when n _ m

For the special case where two or more modes share the same frequency m, the mode shapes for modes m and n with the common frequency can be chosen such that equations (2.25a) and (2.25b) hold. It is found that the responses of damped linear structures can also be described in terms of the same classical (in-phase) normal modes if the damping coefficients are also constrained by a similar orthogonality condition. That is, provided

 m T [C] n = 0 , when n _ m

(2.25c)

It can be shown that equations (2.25) imply that the inertia forces, the spring forces and the damping forces of any mode (n) do no work on the motions of any other mode (m). The displacements u(t) of equation (2.17) may be expressed as the sum of factored mode shapes: u (t) =  1N n n (t) (2.26) Substituting from equation (2.26) into equation (2.17), then pre-multiplying each term by nT and eliminating all terms given as zero by equations (2.25) produces:

28

n +

T  n [C] n T  n [M] n

 n +

T  n [K ] n T  n [M] n

n=-

T  n [M]1 T  n [M ] n

Åg

(2.27a)

When compared with equation (2.5), equation (2.27a) is seen to describe a single-degree-offreedom damped oscillator with damping factor n and frequency n given by:

 n [C] n T  n [M ] n

(2.27b)

 n [K ] n n = T  n [M ] n

(2.27c)

T

2 n  n =

T

2

Here equations (2.27) are the N-degree-of-freedom counterparts of equations (2.2), (2.4) and (2.5). Since u =  n =1 u n 54 it follows from equation (2.26) that the displacement at level r of the n-th mode is given by: N

ur n =  r n  n

(2.28)

Substituting from equation (2.28) into equation (2.27) gives:

Å r n + 2  n  n u r n +  n u r n = -  r n Å g 2

(2.29)

where

 n [M ]1 r n =  r n T  n [M ] n T

r n =  r n

i =1 mi  i n

(2.30a)

N

i =1 mi  i n N

2

=  r n n

(2.30b) (2.30c)

Hence, since [M] is a diagonal matrix, The factor r n may be called a participation factor since it is the degree to which point r of mode n is coupled to the ground accelerations. Equation (2.30c) defines a mode weight factor n. It is here convenient to define Nn as unity. For simple tower-like structures, when Nn = (-1)n-1 then n is positive. When equations (2.5) and (2.7) are compared with equation (2.29) and (2.30c) it is seen that:

X r n =  r n  n SD (T n ,  n )

(2.31a)

 r n =  r n  n SV (T n , n ) X

(2.31b)

 r n =  r n n SA (T n ,  n ) X

(2.31c)

29

 rn and X¨ rn are defined as urn max, u where the peak values Xrn, X  rn max, and (ürn + r nüg)max respectively. Note that these maximum seismic responses do not occur simultaneously, so, for . instance the maximum accelerationX is NOT the derivative of the maximum velocity X The maximum seismic displacements of mode n are given by equation (2.31a). The maximum seismic forces Frn follow directly from equation (2.31c). Moreover, since all the mass accelerations for these classical normal modes are in phase, and therefore reach maximum values simultaneously, maximum shear forces Srn and overturning moments OM rn, at level r, may be obtained by successive summation of maximum forces. This gives:

 r n Fr n = m r X

(2.32a)

where hr = height to mass mr. N

Sr n =  Fi n

(2.32b)

i=r

N

OM r n =

 (h

i

- h i-1) Si n 

(2.32c)

i = r+1

2.4.3

Structural Responses from Modal Responses

Usually the maximum structural responses cannot be obtained from the maximum responses of a set of modes by direct addition, since modal maxima occur at different times. The response levels of a mode, when plotted against time, vary in a somewhat noise-like way and the probable maximum combined response of several modes may usually be approximated by the square root of the sum of squares (SRSS) method (Der Kiureghian, 1980). For example, the probable force at level r, may be expressed as:

Fr =



Fr i  2

i

(2.33)

where the mode i ranges over the significant modes. However, if near-maximum responses of 2 or more modes are correlated in time by close modal periods (often arising with torsional unbalance or with near-resonant appendages), or by very short periods or very long periods, then the complete quadratic combination (CQC) method may need to be used. Strongly nonlinear isolators may well provide a further mechanism which correlates modal responses, so that the SRSS combination is not accurate. 2.4.4

Example - Seismic Displacements and Forces

Important features of equations (2.30), (2.31) and (2.32) can be illustrated for the unisolated and the linearly isolated continuous uniform shear structure. Top mass participation factors for successive modes are

 Nn (U) = 1.27, 0.42, 0.25, . . . , 4 /[ (2 n- 1)] 2  Nn (I)  1.0, 0.045, 0.011, . . . , 2 /[(2 n- 2) / 0.3 ] ,

where T1(U)/Tb = 0.3. 30

Higher isolated modes are seen to have much lower participation factors than corresponding unisolated modes. The above mode-participation factors, together with the periods from equation (2.23) and the spectra of Figures 2.1(b) and (c), can now be used to find important seismic motions and loads for modes 1 and 2 from equations (2.31) and (2.32). For simplicity, a low damping factor of 5% is assumed for all modes. With practical isolated structures a higher damping would normally be provided for mode 1. Since modal displacements may be represented by top displacements, consider

X Nn =  Nn SD (T n , 5) :

X N 1(U) = 0.085; X N 2(U) = 0.0037 , m X N 1(I)  0.18 ; X N 2(I)  0.0009 , m Notice that displacements are completely dominated by mode 1 for both unisolated and isolated structures. Moreover, for any well-isolated structure, the base displacement is almost as large as the top displacement:

X b  X N 1(I ) Since modal loads may be represented by the force per unit height at the top of the structure FNn, consider FNn /  =  Nn SA (T n ,5), 72 where  = M/ h N : 73 2 F N 1(U) /  = 9.31 ; F N 2(U) /  = 3.60 , m/ s 2 F N 1(I) /   1.80 ; F N 2(I) /  _ 0.37 , m/ s

Note that the force for isolated mode 1 is relatively small because it has a low response spectrum factor, while the forces for higher isolated modes are relatively small because they have small participation factors. 2.4.5

Seismic Responses with Bilinear Isolators

When the isolator is bilinear, there are a number of possible ways of defining the modes. For any of the definitions we consider, the total response of a linear structure with bilinear isolation can be expressed exactly as the sum of the modal responses, as for a linear system. However, the modal equations of motion will be coupled, unlike those for classically damped linear systems. Several of the possible definitions of the mode shapes with bilinear isolation are useful for interpreting the response or estimating the maximum response quantities. In section 2.2c, we discussed the responses of a first mode defined by a rigid structure mounted on an 'equivalent' linear isolator with 'effective stiffness' KB, 'effective period' TB and 'effective damping' B. This model gives good approximations to the displacements and base shear of a structure on a bilinear isolator. 31

A useful set of modes for systems with bilinear isolation are those obtained by using the post-yield stiffness of the isolator. Then the higher-mode periods and all mode shapes are given by equations (2.20) and (2.21) for a linear system with Kb = Kb2. Hence, as with moderately damped linear isolators, the bilinear modes are classical and normal. These modes are relevant for the maximum responses because they relate to the post-yield phase, when the maximum displacements and shears occur. When the bilinear isolator has a high degree of nonlinearity, the seismic responses of higher modes are often much greater than the responses which occur with the above 'equivalent' linear modes. Bilinearity usually gives greater higher-mode accelerations and loads, and particularly it usually gives greater values for floor acceleration spectra over the period range covered by significant higher modes. The reasons for the larger seismic responses of the higher modes are summarised briefly here. With bilinear isolation, the inputs of seismic energy, and the energy level of the overall system, are given roughly by a rigid-structure model with a linear isolator of effective period TB and effective damping factor B. When the structure is sufficiently flexible to give a substantial contrast between the mode-1 shapes for the first and second isolator stiffnesses, then there is usually significant energy in the higher modes, where relatively small fractions of the structural energy can result in relatively high modal accelerations and forces. In terms of the modes for the plastic-phase stiffness Kb2, each isolator transition through the elastic phase redistributes the energy between the modes. This should result in a net transfer of energy from the large-energy mode 1 to the small-energy higher modes. The effects of the relatively large seismic responses of higher modes, with many bilinear isolators, are seen in the case studies below. The mode-shapes corresponding to the post-yield stiffness Kb2 are usually very similar in shape to the free-free mode shapes, obtained when the isolator stiffness is zero. It is sometimes more convenient to interpret the responses in terms of the free-free modes rather than those based on Kb2, because of the symmetry of the free-free modes and because there is no need to calculate new mode shapes for different values of Kb2. Decomposition of the response in terms of the free-free mode shapes also has the useful properties that the base shear is contributed entirely by the first mode, and that the first-mode displacements are uniform within the structure. Also, the base shear scaled by appropriate participation factors provides the driving forces for the higher modes. The seismic responses of isolated structures can be decomposed into the contributions from suitably defined modes by a mode-sweeping technique. Either the modes based on base-stiffness Kb2 or the free-free modes can be used with this technique. The free-free mode shapes have been used to obtain the results given in Section 2.5 below.

32

Table 2.1: Responses to the El Centro NX 1940 Accelerogram of an Unisolated Uniform Shear Structure, and of Six Isolated Structures

33

2.5

COMPARISONS OF SEISMIC RESPONSES OF LINEAR AND BILINEAR ISOLATION SYSTEMS

2.5.1

Comparative Study of Seven Cases

This section demonstrates many of the key features of seismic isolation, through seven examples which show the seismic responses of structures and appendages for various ranges of isolation system parameter values and structural flexibility. The examples are summarised in Table 2.1 in terms of the physical parameters of the systems, the maximum overall and modal response quantities, and the values of the nonlinearity factor and elastic-phase isolation factor which are important parameters governing the isolated response.

Figure 2.7:

Responses to the El Centro NS 1940 accelerogram of a uniform shear structure when unisolated, when linearly isolated (2 cases) and when bilinearly isolated (3 cases). The information in this figure complements that in Table 2.1. The floor spectra are for the low-damping case of 2%. The solid lines are the total response, while dotted and chain-dotted lines are the seismic responses of modes 1 and 2 respectively. Note the 5-fold differences in scale of the unisolated and isolated cases. The scale changes are along the abscissae for X,X /g and S/W, and along the ordinate for the floor spectra. Note also that the shear-force/displacement hysteresis loops have been drawn for cyclic displacements of +0.4 Xb in order to show the various stiffnesses clearly.

Figure 2.7 shows the maximum values of the displacements, accelerations and shears and the 2% damped top floor spectra calculated for an unisolated structure and six isolated structures in response to the El Centro 1940 NS ground acceleration. The solid lines represent maximum total responses, with the maximum values obtained from response history analysis. The dotted lines and chain-dotted lines where given, represent, respectively, the maximum first- and secondmode responses at the various levels. In some cases the first-mode responses dominate to the extent that dotted and solid lines coincide (e.g., parts of the floor spectra, particularly at longer periods). In other cases, the difference between the solid and dotted lines indicates the highermode contribution to the response. 34

The modal responses were obtained from the overall response histories at all masses in the structures by sweeping with the free-free mode shapes, except for the unisolated structure, where the modal responses are in terms of the true unisolated modes. The 'un-isolated' structure (case (i)) is a uniform linear chain system, with 4 equal masses and 4 springs of equal stiffness, the lowest being anchored to the ground. It has a first-mode undamped natural period of 0.5s, and 5% damping in all its modes. Most of the 'isolated' cases represent systems obtained simply by adding below this structure an isolation system modelled as a base mass, a linear or bilinear-hysteretic base spring and a linear viscous base damper. However, two of the 'isolated' cases involve stiffer structures, with unisolated periods of 0.25 seconds, in order to show the effects of high elastic-phase isolation factors. In all the isolated cases, the added base mass is of the same value as the other masses, comprising 0.2 of the total isolated mass. The viscous damping of the isolated structures is 5% of critical for all the free-free modes, with the nonlinear isolation systems having linear viscous base dampings b2 which are 5% of critical in the post-yield phases, as well as hysteretic damping. The table shows values of b for the linear isolators, and values of b, b1 and b2 for the bilinear isolators, where b = b2 TB/Tb2. The cases were chosen to represent a wide variety of isolation systems, with various degrees of nonlinearity and pre- and post-yield isolation ratios. In calculating the isolation factors, I=Tb/T1(U) and I(Kb1)=Tb1/T1(U), the unisolated period T1(U) corresponds to that of the structure when the isolator is rigid, while the isolator periods Tb and Tb1 are calculated for the 5 masses, from the structure and the isolator, with all their interconnecting springs treated as rigid, mounted on the isolator spring. Cases (ii) and (iii) represent medium-period structures with a high degree of linear isolation (T1(U)=0.5s, Tb=2.0s, I=4), and with low (b=5%) and high (b=20%) values for the viscous damping of the isolator, respectively. Case (iv) is a bilinear hysteretic system with similar characteristics to that of the William Clayton Building (Section 6.2(d)), which was the first building isolated on lead rubber bearings. The parameter values are typical for structures with this type of isolation system. The unisolated period of the structure is 0.25s (the William Clayton Building has a nominal unisolated period of 0.3s), with a pre-yield isolator period Tb1 of 0.8s and a post-yield isolator period Tb2=2.0s. The yield force ratio Qy/W is 0.05, less than the William Clayton Building's value of 0.07. However, the latter value was chosen to give a near-optimal base shear response (see section 4.3.2) in 1.5 El Centro, so scaling down the yield-force/weight ratio by approximately 2/3 is appropriate for a system with El Centro as the design motion. The post-yield isolator period is equal to the isolator period of the linear systems of cases (ii) and (iii). The equivalent viscous damping from the combined hysteretic and viscous base damping at the amplitude of its maximum response to El Centro is 24% (Table 2.1), comparable with the viscous damping of 20% for the linear system (iii). Case (v) represents bilinear systems with elastic- and yielding-phase isolation factors towards the low ends of their practical ranges. The unisolated period is 0.5s, with the isolator periods Tb1=0.3s and Tb2=1.5s, giving isolation factors of 0.6 and 3 in the two phases. The yield force ratio Qy/W is 0.05, as for all the nonlinear cases. This system has a moderate nonlinearity factor which is virtually identical to that of case (iv) (0.33 compared to 0.32), but considerably reduced isolation factors, most importantly in the elastic phase where it is 0.6. The low elastic-phase isolation gives response characteristics similar to those for a system with an isolator which is rigid before it yields. In case (vi), the post-yield period of the isolator has been doubled from that of case (v), to Tb2=3.0s, but the other parameter values are the same. This change produces a considerably higher nonlinearity factor of 0.60, but still a low elastic-phase isolation factor of only 0.6. 35

The response characteristics are similar to those for what is sometimes referred to as a 'resilientfriction base isolator' (Fan & Ahmadi (1990, 1992); Mostaghel & Khodaverdian (1987)). The final example, case (vii), is a strongly nonlinear system, with a nonlinearity factor of 0.71, but unlike case (vi) it has high isolation factors in both phases of the response. The forcedisplacement characteristics of the isolator are almost elasto-plastic, with a post-yield period of 6.0s. The unisolated period of the structure (T1 (U)=0.25s) and the yield-force ratio (Qy/W=0.05) are identical to case (iv), and the pre-yield isolator period (Tb1=0.8s) and hence the elastic-phase isolation factor are very similar to those in case (iv). This represents a system with high hysteretic damping, high isolation in both phases of the response, and a maximum base shear closely controlled by the isolator yield force because of the nearly perfectly plastic characteristic in the yielding phase. The response characteristics of this wide range of examples are illustrated in Figure 2.7, and demonstrate many of the key features of the response characteristics of base-isolated structures. Comparisons can be made between features of the responses of unisolated and isolated structures, and between those of various isolated structures. Systematic variations in response quantities can be seen as the equivalent viscous damping, the nonlinearity factor and the elastic-phase isolation factor are varied. The first point to note in Figure 2.7 is that the response scales for the unisolated structure of case (i), as emphasised by heavy axis lines, are five times larger than those for all the isolated cases shown in the other parts of the figure. The next general comment regarding Figure 2.7 is that the force-displacement hysteresis loops have been drawn for cyclic displacements of +0.4 Xb. This has been done in order to show the relative slopes. Direct comparisons of various response quantities can be made for the unisolated structure and the four cases (ii), (iii), (v) and (vi) involving the same structure on various isolation systems. Cases (iv) and (vii) involve shorter-period structures on the isolators, so direct comparisons of these with case (i) are not appropriate. The base shears of the isolated systems with the 0.5s structure are reduced by factors of 4.6 (for the lightly damped linear isolator of case (ii)) to over 10 (for case (vi) with high hysteretic damping). Base displacements, which contribute most of the total displacement at the top of the isolated structures, range from 0.7 to 2.5 times the top displacement of the unisolated structure. Inter-storey deformations in the isolated structures are much reduced from those in the unisolated structures, since they are proportional to the shears. Since large deformations are responsible for some types of damage, the reduction in structural deformation is a beneficial consequence of isolation. First-mode contributions to the top-mass accelerations in the isolated structures are reduced by factors of about 6 to 14 compared to the values in the unisolated structure. The linear isolation systems show marked reductions in the higher-frequency responses as well, but the second-mode responses for the systems with the greatest nonlinearities are only slightly reduced from those in the unisolated structure. These effects are most evident in the top-floor response spectra. Figure 2.7 shows several important characteristics of the response of isolated structures in general. In isolated systems, increased damping reduces the first-mode responses, but generally increases the ratio of higher-mode to first-mode responses, particularly where the damping results from nonlinearity. The elastic-phase isolation factor I(Kb1) has a marked effect on highermode responses, which increase strongly as I(Kb1) reduces from about 1.0 towards zero. The effects of these parameters are demonstrated by considering each of the isolated cases in turn. The lightly damped linear isolation system of case (ii) reduces the base shear by a factor of 4.6 from the unisolated value, but requires an isolator displacement of 180mm. 36

The response is concentrated almost entirely in the first mode, as shown by the comparison of the first-mode and total acceleration and shear distributions and by the top floor spectra. The differences between the first-mode and total distributions largely arise from the difference between the free-free first-mode shape which was used in the sweeping procedure and the actual first-mode shape with base stiffness Kb. The maximum second-mode acceleration calculated by sweeping with the second free-free mode shape is only about 1/6th that found by sweeping with the first free-free mode shape. By increasing the base viscous damping from b=5% to 20% of critical, as in case (iii), the maximum base displacement is reduced from 180mm to 124mm, with less percentage reduction in the base shear. The mode-2 acceleration more than doubles, showing the effects of increased base impedance from the increased base damping and modal coupling from the nonclassical nature of the true damped modes. The first-mode response still dominates, however. The floor response spectra reflect the reduction in first-mode response, but show increases in the second- and third-mode responses compared to case (ii). Case (iv) has an effective base damping similar to case (iii), but with the main contribution coming from hysteretic damping. All first-mode response quantities, and those dominated by the first-mode contribution, including the base shear and the base displacement, are reduced from the values for the linear isolation systems. The nonlinearity of this system is only moderate (0.32), and there is a high elastic-phase isolation factor of 3.2, but the second-mode response is much more evident than for the linear isolation systems, particularly in the floor response spectrum. Case (v) has the same degree of nonlinearity as the previous case, but a much reduced elastic-phase isolation factor of 0.6. The low elastic-phase isolation factor has produced a much increased second-mode acceleration response, which is 50% greater than the first-mode response on the top floor. The distribution of maximum accelerations is much different from the uniform distribution obtained for a structure with a large linear isolation factor. The accelerations are much increased from the first-mode values near the top and near the base, while the shear distribution shows a marked bulge away from the triangular first-mode distribution at mid-height. Strong high-frequency components are evident in the top floor acceleration response spectrum, with prominent peaks corresponding to the second and third post-yield isolated periods. Case (vi) is an exaggerated version of case (v). The post-yield isolator period has been increased to 3.0s, giving a high nonlinearity factor as well as a low elastic-phase isolation factor, both conditions contributing to strong higher-mode response. The nearly plastic behaviour of the isolator in its yielding phase produces a more than 40% reduction in the base shear from case (v), at the expense of a 33% increase in the base displacement. The maximum secondmode acceleration response at the top floor is 2.5 times the first-mode response, being the highest value of this ratio for any of the seven cases. The acceleration at the peak of the topfloor response spectrum at the second-mode post-yield period has the greatest value of any of the isolated cases, almost identical to the second-mode value in the unisolated structure, which, however, occurs at a shorter period. Case (vii) demonstrates that high elastic-phase isolation can much reduce the relative contribution of the higher modes for highly nonlinear systems. The nonlinearity factor of 0.71 is the highest of any of the cases, but the second-mode response is less than 40% that of cases (v) and (vi), which have poor elastic-phase isolation. The high nonlinearity has reduced the base shear to 70% of that of case (iv). The mode-2 acceleration response has been reduced by 13% from that of case (iv), but its ratio with respect to mode 1 has increased from 0.85 to 1.25.

37

Maximum base shears and displacements of isolated structures are dominated by first-mode responses. Maximum first-mode responses of bilinear hysteretic isolation systems can in turn be approximated by the maximum responses of equivalent linear systems, as discussed earlier in this chapter. The final section of Table 2.1 demonstrates the degree of validity of the equivalent linearisation approach. It gives effective dampings and periods calculated for the equivalent linearisation of the bilinear isolators, using equation (2.11b) for TB and equations (2.11c) to (2.13) for B. The response spectrum accelerations and displacements for these values of period and damping are listed. The spectral values for the base displacements give reasonable approximations to the actual values, with correction factors CF of approximately unity, except for case (vii), with the nearly plastic post-yield stiffness, for which the correction factor is 1.6. However, the spectral accelerations SA(TB,B) provide much poorer estimates of either the firstmode or overall base-mass accelerationX b. Much improved estimates of the base shear Sb can be obtained from KBXb, which has a smaller relative error than the estimate of Xb from SD(TB,B). This is the procedure we recommend when using the equivalent linearisation approach (Section 2.2).

2.6

GUIDE TO ASSIST THE SELECTION OF ISOLATION SYSTEMS

The examples summarised in Figure 2.7 and Table 2.1 show the effects of various ranges of isolation system parameters. In particular, the effects of base damping, nonlinearity factor and elastic-phase isolation factor have been demonstrated. Table 2.2 generalises the results found for these examples and presents them in a more qualitative way, providing guidance to the sets of parameter values appropriate for particular purposes, and giving examples of practical isolation systems which can provide the desired parameter values. In Table 2.2, we are considering classes of systems, rather than examples with specific parameter values. The examples (i) to (vii) considered in Figure 2.7 and Table 2.1 fit into the corresponding categories in Table 2.2. However, the qualitative descriptions of the nature of various response quantities show minor deviations from those which would be obtained solely by consideration of these examples. Use has been made of results of other cases considered by the authors or reported in the literature in order to generalise the results from the specific ones given above.

38

Table 2.2: Guide to the behaviour of isolation systems, showing seven classes corresponding broadly to the cases in Figure 2.7.

39

Thus, class (vi) has been extended to include rectangular hysteresis loops (Kb1=, Kb2=0), while the example of case (vi) has 'high' and 'low' values of these stiffnesses respectively. The response characteristics of simple sliding friction systems included by this generalisation are similar to those of the example of case (vi). The ways in which the various cases of Table 2.1 have been generalised to the classes of Table 2.2 are discussed below. Class (i) represents unisolated linear structures with periods up to about 1 second and damping up to about 10%. This class is provided only for purposes of comparison. Most short- to moderate-period unisolated structures will be designed to respond nonlinearly, so their acceleration- and force-related responses may be considerably less than those of the linear elastic cases considered here. Isolation still provides benefits in that nonlinear response in such unisolated structures requires ductile behaviour of the structural members, with the considerable energy dissipation within the structure itself often associated with significant damage. Class (ii) represents lightly-damped, linear isolation systems, with the isolator damping less than 10%. Only systems providing a high degree of isolation are considered, with an isolation factor Tb/T1(U) of at least 2 and a period Tb of at least 1.5 s for El Centro-type earthquakes. The response of such systems is almost purely in the first mode, with very little higher-frequency response, so they virtually eliminate high-frequency attack on contents of the structure. This type of isolation can be readily obtained with laminated rubber bearings, with the low isolator damping provided by the inherent damping of the rubber. Higher-damping rubbers may be necessary to achieve the 10% damping end of the range without the provision of additional damping devices. The higher-damping rubbers may not behave as linear isolators since they are often amplitude dependent and history dependent. Various mechanical spring systems with viscous dampers fall into this category. Class (iii) corresponds to linear isolation with heavier viscous damping, ranging between about 10% and 25% of critical. Increased damping reduces the isolator displacement and base shear, but generally at the expense of increased high-frequency response. The high-frequency response results from increased isolator impedance at higher frequencies. These systems still provide a high degree of protection for subsystems and contents vulnerable to motions of a few Hz or greater, but with reduced isolator displacements compared to more lightly damped systems. We consider class (iv), bilinear hysteretic systems with good elastic-phase isolation (Tb1/T1(U) > 2) and moderate nonlinearity (corresponding to equivalent viscous base damping of 20-30% of critical), as a reference class. For many applications, this represents a reasonable design compromise to achieve low base shears and low isolator displacements together with low to moderate floor response spectra. This type of isolation can often be provided by lead rubber bearings. Class (v) represents bilinear isolators with poor elastic-phase isolation (Tb1/T1(U) < 1) and relatively short post-yield periods (~ 1.5s). The relatively high stiffnesses of these isolation systems produce very low isolator displacements, but strong high-frequency motions and stronger base shears than the reference bilinear-hysteretic isolator class. Class (vi) is similar in many respects to class (v), but with a long post-yield period (Tb2 > ~ 3s), which gives nearly elasto-plastic characteristics and thus high hysteretic damping and a high nonlinearity factor. Rigid-plastic systems, such as given by simple sliding friction without any resilience, are extreme examples of this class. Low base shears can be achieved because of the low post-yield stiffness and high hysteretic damping, but at the expense of strong highfrequency response. Even this advantage is lost with high yield levels. This class of bilinear isolator is not appropriate when protection of subsystems or contents vulnerable to attack at frequencies less than 1 Hz is important, but some systems in this class can provide low base shears and moderate isolation-level displacements very cheaply. Displacements can become very large in greater than anticipated earthquake ground motions. 40

Class (vi) consists of nonlinear hysteretic isolation systems with a high degree of elastic-phase isolation (Tb1/T1(U) > 3) and a long post-yield period (Tb2 > ~ 3s), producing high hysteretic damping. The low post-yield stiffness means that the base shear is largely controlled by the yield force, is insensitive to the strength of the earthquake, and can be very low. The high degree of elastic-phase isolation largely overcomes the problem of strong high-frequency response usually associated with high nonlinearity factors. Systems of this type are particularly useful for obtaining low base shears in very strong earthquakes when provision can be made for large isolator displacements. One application of this class of system was the long flexible pile system used in the Wellington Central Police Station (Chapter 8.2 (f)), with the elastoplastic hysteretic damping characteristics provided by lead-extrusion energy dissipators mounted on resilient supports. As indicated by the preceding descriptions of the isolator systems and the discussion of the response characteristics of the various examples in the last section, the selection of isolation systems involves 'trade-offs' between a number of factors. Decreased base shears can often be achieved at the cost of increased base displacements and/or stronger high-frequency accelerations. High-frequency accelerations affect the distribution of forces in the structure and produce stronger floor response spectra. If strong highfrequency responses are unimportant, acceptable base shears and displacements may be achieved by relatively crude but cheap isolation systems, such as those involving simple sliding. In some cases, limitations on acceptable base displacements and shears and the range of available or economically acceptable isolation systems may mean that strong high-frequency accelerations are unavoidable, but these may be acceptable in some applications. Some systems may be required to provide control over base shears in ground motions more severe than those expected, requiring nearly elasto-plastic isolator characteristics and provision for large base displacements. The selection of appropriate isolation systems for a particular application depends on which response quantities are most critical to the design. These usually can be specified in terms of one or more of the following factors: i) ii) iii) iv) v)

base shear base displacement high-frequency (i.e., > ~ 2Hz) floor response spectral accelerations control of base shears or displacements in greater than design-level earthquake ground motions cost

Isolation systems are easily subdivided on the basis of those for which high-frequency (> 2Hz) responses can be ignored and those where they make significant contributions to the acceleration distributions and floor spectra. Floor spectral accelerations are important when an important design criterion is the protection of low-strength high-frequency subsystems or contents. In well-isolated linear systems, high-frequency components, which correspond to higher-mode contributions, can generally be ignored, although they become more significant as the base damping increases (Figure 2.7, cases (ii) and (iii)). In nonlinear systems, there will generally be moderate to strong high-frequency components when there is a low elastic-phase isolation factor, less than about 1.5. This generally eliminates systems with rigid-sliding type characteristics when strong high-frequency response is to be avoided. For a given elastic-phase isolation factor, high-frequency effects have been found to generally increase with the nonlinearity factor. These considerations suggest that the selection of isolation systems for the protection of high-frequency subsystems is limited to linear systems, or nonlinear systems with high elasticphase isolation factors and moderate nonlinearity factors (i.e., corresponding to cases (ii), (iii) or (iv) in Figure 2.7). Some systems with high nonlinearity factors but also with high elastic-phase isolation factors may also produce acceptably low high-frequency response. 41

For example, case (vii) in Figure 2.7 with a high nonlinearity factor has a similar top-floor response spectrum to case (iv) for which the nonlinearity factor is moderate, and has a spectrum not much stronger than that of the linearly-isolated case (iii) with high viscous damping. The linear systems usually give better performance strictly in terms of high-frequency floor-response spectral accelerations, but the introduction of nonlinearity can reduce the base shear and isolator displacement, which may give a better overall performance when the structure, subsystems and contents are considered together. For situations where a need for small floor-response spectral accelerations is not a major design criterion, the range of acceptable nonlinear isolation systems is likely to be much greater. The main performance criteria are then usually related to base shear and base displacement. Both these quantities depend primarily on the first-mode response. Except for nearly elasto-plastic systems, the base shear decreases as Qy/W increases from zero, passes through a minimum value at an optimal yield force, and then increases as Qy/W continues to increase. Thus the base shear of most linear isolation systems can be reduced by selecting a nonlinear isolation system with Tb2=Tb of the linear system and an appropriate yield force ratio and elastic-phase period. For a given yield force, the base shear generally decreases as Tb2 increases, i.e., the system becomes more elasto-plastic in character. This is illustrated by the examples in Figure 2.7. This is generally at the expense of greater base displacement, as for case (vii), or strong high-frequency response when the elastic-phase isolation is poor, as in case (vi). When base shear and base displacements are the controlling design criteria, systems with rigid-plastic type characteristics, such as simple pure friction systems, which are not appropriate when the protection of high-frequency subsystems or contents is a concern, may give cheap, effective solutions provided the coefficient of friction remains less than the maximum acceptable base shear. However, some centring force is usually a desirable isolator characteristic. For protection against greater than design-level excitations, systems with a nearly plastic yielding-phase characteristic have the advantage that the base shear is only weakly dependent on the strength of excitation, but the disadvantage that their isolator displacements may become excessive. A system similar to our reference case with characteristics of moderate nonlinearity and good elastic-phase isolation is often a good design compromise when minimisation of high-frequency floor-response spectral accelerations is not an overriding design criterion.

42

Chapter 3

ISOLATOR DEVICES AND SYSTEMS

3.1

ISOLATOR COMPONENTS AND ISOLATOR PARAMETERS

3.1.1

Introduction

The successful seismic isolation of a particular structure is strongly dependent on the appropriate choice of the isolator devices, or system, used to provide adequate horizontal flexibility with at least minimal centring forces and appropriate damping. It is also necessary to provide an adequate seismic gap which can accommodate all intended isolator displacements. It may be necessary to provide buffers to limit the isolator displacements during extreme earthquakes, although an incorrectly selected buffer may negate important advantages of seismic isolation. The primary function of an isolation system is to support a structure while providing a high degree of horizontal flexibility. This gives the overall structure a long effective period and hence low maxima for its earthquake-generated accelerations and inertia forces, in general accordance with Figure 2.1(b). However, with low damping, maximum isolator displacements Xb may reach 500 mm or more during severe earthquakes, as shown by Figure 2.1(c). High isolator damping usually reduces these displacements to between 100 and 150 mm. High damping may also reduce the costs of isolation since the displacements must be accommodated by the isolator components and the seismic gap, and also by flexible connections for external services such as water, sewage, gas and electricity. Another benefit of high isolator damping is a further substantial reduction in structural inertia forces. Also, in crowded areas there is the possibility of structures colliding with each other. Since the expected life of an isolated structure will typically range from 30 to 80 or more years, the isolation system should remain operational for such lifetimes, and its maintenance problems should preferably be no greater than those of the associated structure. This will usually call for relatively simple, well-designed and thoroughly tested isolator devices. The primary force-limiting function of an isolator may be called on for only one, or a few, brief periods of operation during the life of the structure, for example, one 15-second episode in 50 years. However, at these times the isolator must operate successfully despite all environmental hazards, including those tending to corrode metal surfaces, cause deterioration of elastomers, or change the physical properties of component materials. In addition to the very infrequent seismic loads, isolators will often be subject to smaller but relatively frequent wind loads which they must resist without serious deterioration. Diurnal temperature changes will result in displacements which need to be accommodated by the isolation system without the build-up of excessive forces. Finally, since isolator devices which satisfy the above criteria will usually be intended to reduce the overall structural cost, the components must be sufficiently simple to allow supply and installation at moderate cost. 3.1.2

Combination of Isolator Components to Form Different Isolation Systems

The design and performance of various isolator components is described in this chapter. Emphasis is placed on components which were developed in our laboratory, namely steel dampers, lead-extrusion dampers and the lead rubber bearing. The elastomeric bearing is also described since its properties underlie those of the lead rubber bearing isolation system. Some description is also given of other isolator components. The discussion and results presented in Chapters 1 and 2, particularly in Figure 2.7, Tables 2.1 and 2.2 and the associated text, form a context in which to analyse the properties of real isolator components and real isolation systems. The isolation systems considered provide horizontal flexibility and damping and support the weight of the isolated structure. 43

In the simplest case a linear isolation system is produced by using components with linear flexibility and linear damping. In other cases the isolation system may be nonlinear. A special case of nonlinearity, the bilinear system, occurs when the shear-force/displacement loop is a parallelogram, as shown in Figure 2.3 and discussed in the associated text. Different seismic responses result from linear, bilinear and other nonlinear isolation systems. In the simplest case, a system which has both a linear flexibility component and a linear damping component can be modelled in terms of the differential equation (2.1), i.e.

m u + cu + ku = - m ug where the flexibility is the inverse of the stiffness constant 'k' and the velocity-damping is described by a constant 'c'. Figure 2.2 and the associated text define this kind of system and show the elliptical velocity-damped shear-force/displacement hysteresis loop which results. However, the components may not be linear. The most common source of nonlinearity in a component is amplitude-dependence. For example, in the typical bilinear isolation system the stiffness is amplitude-dependent, changing from Kb1 to Kb2 at the yield displacement. The damping in this case is also nonlinear because the hysteretic contribution to the damping, which usually dominates, depends on the area of the hysteresis loop and therefore also depends on the maximum amplitude Xb. Table 3.1 analyses the flexibility and damping of some common isolator components, examining each to see if it is linear or nonlinear. The analysis is somewhat idealised and over-simplified, since material properties can vary. Also, it is worthwhile checking to see if a particular system is rate- or history-dependent. For example, types of high-damping rubber depend both on the amplitude and on the number of cycles which the sample has undergone. PROPERTY

LINEAR

NONLINEAR

Restoring Force (providing spring constant and flexibility)

*Laminated rubber bearing *Flexible piles or columns *Springs *Rollers between curved surfaces (gravity)

*High-damping rubber bearing *Lead rubber bearing *Buffers *Stepping (gravity)

Damping

*Laminated rubber bearing *Viscous damper

*High-damping rubber bearing *Lead rubber bearing *Lead extrusion damper *Steel dampers *Friction (e.g. PTFE)

Table 3.1: Flexibility and Damping of Common Isolator Components

44

As seen in Table 3.1, the laminated rubber (elastomeric) bearing is the only single-unit isolation system, among those considered, which has both linear restoring force and linear damping. In the commercially used form, this comprises layers of rubber vulcanised to steel plates. Considerable experience exists for the design and use of the elastomeric bearing, since its initial major application was to accommodate thermal expansion in bridges and it was only later adopted as a solution to seismic isolation problems. However, for seismic isolation, this system has the disadvantage that the maximum achievable damping is very low, approximately 5% of critical. Attempts to overcome this disadvantage by increasing the inherent damping of the rubber have not yet produced an ideal system with linear stiffness and linear damping. Flexible piles or columns provide a simple, effective linear restoring force but dampers need to be added to control the displacements during earthquakes and on other occasions. If the dampers are linear, e.g., viscous dampers, then a linear system results. Viscous dampers are excellent candidates for linear dampers, but may be difficult to obtain at the required size, may be strongly temperature-dependent and may require maintenance, given that the required lifetime may be 30 to 80 years. Springs with the required stiffness are likely to be difficult to produce, but do provide a linear restoring force. The German GERB system achieves this, mainly intended for industrial plant, such as large silos. Rollers or spheres between curved (parabolic) surfaces can provide linear restoring forces. Since they have 'line' or 'point' contact it is difficult to provide for high loads. Again, damping will usually need to be added in practice and linear damping will produce a linear system. Gravity in the form of a 'stepping' behaviour (see, for example the Rangitikei viaduct, Chapter 6) can provide an excellent nonlinear restoring force. Such systems need additional damping for effective isolation. The resultant isolation systems are nonlinear. High-capacity hysteretic dampers may be based on the plastic deformation of solids, usually lead or steel. The damper must ensure adequate plastic deformation of the metal when actuated by large earthquakes. It must be detailed to avoid excessive strain concentrations; for example these may cause premature fatigue failure of a steel damper at a weld. Excessive plastic cycling of steel dampers, for example by wind gusts, must be avoided since this gives progressive fatigue deterioration. Steel damping devices, often in the form of bending beams of various cross-sections, have a high initial stiffness and are effective dampers but care must be taken in their manufacture to ensure a satisfactory lifetime. They are strongly amplitude-dependent. Combined with components to provide flexibility, they can result in bilinear or nonlinear isolation systems. Elastoplastic steel dampers have been used in New Zealand and other countries, including the seismic isolation of many bridges in Italy (see Chapter 8). The lead extrusion damper behaves as a plastic device operating at a constant force with very little rate- or amplitude-dependence at earthquake frequencies. It creeps at low loads (see Figure 3.10), enabling thermal expansion to be accommodated. When combined with a linear component for flexible support, e.g., flexible piles, then a bilinear system can result, as was used in the Wellington Central Police Station (see Chapter 8). The lead rubber bearing, which comprises an elastomeric bearing with a central lead plug, gives structural support, horizontal flexibility, damping and a centring force in a single easily installed unit. It has high initial stiffness, followed by a lower stiffness after yielding of the lead, and is for many situations the most appropriate isolation system. The hysteretic damping of this device is via the plastic deformation of the lead. The device is nonlinear but can be well described as bilinear, i.e., it has a parallelogram-shaped hysteresis loop as shown in Figure 2.3 and discussed in the associated text. 45

Friction devices behave in a similar way to the extrusion damper, are simple but may require maintenance. Changes may occur in the friction coefficient due to age, environmental attack, temperature or wear during use. A further problem is that of 'stick-slip', where after a long time under a vertical load the device requires a very large force to initiate slipping. A dramatic example of a system isolated by this means is the Buddha at Kamakura; a stainless steel plate was welded to the base of the statue and it was rested on a polished granite base without anchoring.

3.2

PLASTICITY OF METALS

The damping devices which have been found to be most economic and suitable for use in isolators are usually those which rely on the plastic deformation of metals. To understand the behaviour of these devices and to gain some knowledge of their limitations it is necessary to examine the mechanisms enabling plastic deformation to occur. Figure 3.1(a) shows the stress-strain curve for a metal in simple tension. Initially the stress  is proportional to the strain , and the constant of proportionality is the Young's modulus E. This elastic region of the stress-strain curve is reproduced on loading and unloading and has the equation of state  = E_ (3.1a) so that the slope of the (-) graph is E. The corresponding relationship between shear stress  and engineering strain  (where  is twice the tensor strain) is given by  = G (3.1b) where G = shear modulus. If the strain is continually increased, it reaches a value (point B, the yield point, in Figure 3.1(a)) at which the material yields plastically. The yield point is of particular importance in the design of isolator components. It has coordinates (y, y), (y, y) and (Xy, Qy) on the stress-strain, shear stress-strain and force-displacement curves respectively. Further increase in the stress results in a 'plastic-region' curve which is nearly horizontal, in the case of lead, or which rises moderately in the case of mild steel. If the stress is reduced to zero from a very large value of strain, then the curve follows the line CD in Figure 3.1(a). On unloading, the metal no longer returns to its initial state but has a 'set', i.e. an added plastic deformation. The unloading curve has the same gradient as that in the elastic region, namely the Young's modulus or shear modulus (Van Vlack, 1985).

46

(b)

(a)

Figure 3.1:

(a)

Stress-strain curves for a typical metal which changes from elastic to plastic behaviour at the yield point (B). (b) Stress-strain curves for a typical mild steel under cyclic loading.

It should be noted that the area ABCE in Figure 3.1(a) represents input work while the area DCE represents elastic energy stored in the metal at point C and released on unloading to point D. The difference area ABCD represents the hysteretic energy absorbed in the metal. In the case of lead, the absorbed energy is rapidly converted into heat, while in the case of mild steel it is dominantly converted to heat, but a small fraction is absorbed during the changes of state associated with work hardening and fatigue. Since metal-hysteresis dampers involve cyclic plastic deformation of the metal components, it is appropriate to consider the stress-strain relationship for a metal cycled plastically in various strain ranges, as shown in Figure 3.1(b) for a metal with the features typical of mild steel. Included in Figure 3.1(b) is the initial stress-strain curve of Figure 3.1(a). Notice the increasing stress levels with increasing strain range, and the lower yield levels during plastic cycling. With lead, the hysteretic loops are almost elastic-plastic, i.e., an elastic portion is followed by yield at a constant stress (zero slope in the plastic region). Typical operating strains are much greater than the yield strain, the loop tops are almost level, and the loop height is not significantly influenced by strain range. To understand the behaviour of a metal as it is plastically deformed, it is necessary to look at it on an atomic scale. Previous to the 1930's, the plastic deformation of a metal was not understood, and theoretical calculations predicted yield stresses and strains very different from those observed in practice. It was calculated that a perfect crystal, with its atoms in well-defined positions, should have a shearing yield stress y of the order of 1010 Pa, and should break in a brittle fashion, like a piece of chalk, at a shear strain y of the order of 0.1. In practice, metal single crystals start to yield at a stress of 106 to 107 Pa (a strain of 10-4 to 10-3) and continue to yield plastically up to strains of 0.01 to 0.1 or more. The weakness of real metal crystals could in part be attributed to minute cracks within the crystal, but the model failed in that it did not indicate how the crystal could be deformed plastically (Van Vlack (1985); Read (1953); Cottrell (1961)). The dislocation model was then devised and overcame these difficulties. Since its inception the dislocation model has been extremely successful in explaining the strength, deformability and related properties of metal single crystals and polycrystals.

47

The plastic deformation in a crystalline solid occurs by planes of atoms sliding over one another like cards in a pack. In a dislocation-free solid it would be necessary for this slip to occur uniformly in one movement, with all the bonds between atoms on one slip plane stretching equally and finally breaking at the same instant, where the bond density is of the order of 1016 bonds per square centimetre. In most crystals, however, this slip, or deformation, is not uniform over the whole slip plane but is concentrated at dislocations. Figure 3.2(a) is a schematic drawing of the simplest of many types of dislocation, namely an edge dislocation with the solid spheres representing atoms. The edge dislocation itself is along the line AD and it is in the region of this line that most of the crystal distortion occurs. Under the application of the shear stress this dislocation line will move across the slip plane ADCB, allowing the crystal to deform plastically. The bonds, which must be broken as the dislocation moves, are of the order of 108 per centimetre, and are concentrated at the dislocation core, thus enabling the dislocation to move under a relatively low shear stress. As the dislocation moves from the left-hand edge of the crystal (Figure 3.2a) it leaves a step in the crystal surface, which is finally transmitted to the right-hand side. Figure 3.2(b) shows the other major type of dislocation, namely a simple screw dislocation, which may also transmit plastic deformation by moving across the crystal.

(a)

(b)

Figure 3.2:

Atomic arrangements corresponding to:

(a) an edge dislocation, (b) a screw dislocation.

Here b is the Bergers vector, a measure of the local distortion and AD is the dislocation line.

The dislocations in crystals may be observed using electron microscopy, while the ends of dislocations are readily seen with the optical microscope after the surface of the crystal has been suitably etched. Typical dislocation densities are 108 dislocations per square centimetre in a deformed metal and about 105 per square centimetre in an annealed metal, namely one which has been heated and cooled slowly to produce softening. Dislocations are held immobile at points where a number of them meet, and also at points where impurity atoms are clustered. The three main regions of a typical stress-strain curve are interpreted on the dislocation model as follows: (1)

Initial elastic behaviour is due to the motion of atoms in their respective potential wells; existing dislocations are able to bend a little, causing microplasticity.

(2)

A sharp reduction in gradient at the yield stress is due to the movement of dislocations.

48

(3)

An extended plastic region, whose gradient is the plastic modulus or strain-hardening coefficient, occurs when further dislocations are being generated and proceed to move. As they tangle with one another, and interact with impurity atoms, they cause work hardening.

It is also possible to model a polycrystalline metal as a set of interconnected domains, each with (different) hysteretic features of the type conferred by dislocations, which give the general stress-strain features displayed by the hysteresis loops of Figure 3.1(b). Since dislocations are not in thermal equilibrium in a metal, but are a result of the metal's history, there is no equation of state which can be used to predict accurately the stress-strain behaviour of the metal. However, the behaviour of a metal may be approximately predicted in particular situations, if the history and deformation are reasonably well characterised.

3.3

STEEL HYSTERETIC DAMPERS

3.3.1

Introduction

General By the late 1960's a number of damping mechanisms and devices were being used to increase the seismic resistance of a range of structures. At that time the logical approach to developing high-capacity dampers for structures was to utilise the plastic deformation of steel beams. During that decade the plastic deformation of steel structural beams had been increasingly used to provide damping and flexibility for aseismic steel beam-and-column (frame) buildings. The cyclic ductile capacity of structural members was limited by material properties, local buckling and the effects of welding (Popov, 1966). Early steel-beam dampers developed in the Engineering Seismology Section of the Physics and Engineering Laboratory, DSIR, were given a much greater fatigue resistance than typical steel structural members by adopting suitable steels and beam shapes, and attachments with welds remote from regions of plastic deformation. Descriptions of the principal steel-beam dampers developed are given by Kelly, Skinner & Heine (1972) (including possible uses within aseismic buildings, proposed by Skinner); Skinner, Kelly & Heine (1974 and 1975); Tyler & Skinner (1977); Tyler (1978); Cousins, Robinson and McVerry (1991). The principal developers of the three main classes of steel-beam dampers which emerged from the Physics and Engineering Laboratory programme which started in 1968 were Kelly: Twisting-beam dampers (Type E); Tyler: Tapered-beam dampers (Type T); and Skinner & Heine: Uniform-moment dampers (Type U). The earliest bridge structure provided with seismic isolation in New Zealand was a bridge at Motu, rebuilt in 1973, (McKay et al, 1990). The superstructure was provided with seismic isolation to protect the existing slab-wall reinforced concrete piers, which had only moderate strength to resist seismic forces. Isolator flexibility was provided by sliding bearings. Hysteretic damping was provided by plastic deformations near the bases of vertical cantilevers, in the form of structural-type steel columns. Seismic isolation systems using steel-beam dampers developed at the Physics and Engineering Laboratory in New Zealand structures are outlined or listed in Chapter 8. An early New Zealand application of steel-beam dampers was in the stepping seismic isolation system for the tall piers of the South Rangitikei Viaduct. The seismic responses of the proposed stepping bridge, with the inclusion of hysteretic dampers, were studied by Beck and Skinner (1972, 1974). Steel twisting-beam dampers were selected for the isolation system and prototypes were developed. Construction of the bridge commenced in 1974 and it was opened in 1981 (Cormack, 1988). 49

Structures with steel tapered-slab dampers in their isolation systems included a stepping chimney in Christchurch (Sharpe & Skinner, 1983), and Union House, isolated by mounting on flexible piles, in Auckland (Boardman, Wood & Carr, 1983), while conically-tapered steel dampers were used in the isolation systems for the Capacitor Banks at Haywards. Uniform-moment steel dampers were used in the superstructure isolation system for the Cromwell Bridge (Park & Blakeley, 1979). Steel-beam dampers have also been adopted and developed, and used to provide hysteretic damping for seismic isolation in other countries, as outlined in Chapter 8. In Italy, they have been used extensively in seismic isolation systems for bridge superstructures. In Japan, steel dampers have been used in the seismic isolation systems of a range of structures. Features of Steel Hysteretic Dampers Steel was initially chosen as the damper material since it is commonly used in structures and should therefore pose no very unusual design, construction or maintenance problems, apart from possible fatigue failure at welds and stress concentrations. Moreover, it was hoped that the development of these dampers would throw additional light on the performance of steel in ductile aseismic structures. The performance of steel-beam hysteretic dampers during earthquakes is closely related to the performance of high-ductility steel-frame structures. However, the dampers are designed to have a much higher fatigue resistance and to operate at higher levels of plastic strain. This is achieved by using high-ductility mild steels, by using damper forms with nominally equal strain ranges over each plastic-beam cross-section, by using plastic beams of compact section (usually rectangular or circular), and by detailing the connections between the plastic beams and the loading members so as to limit stress concentrations, particularly at welds. In this section, the results of many years of experience with different shapes and designs of steel damper are summarised in terms of a 'scaling' procedure, which generalises all the different findings and also makes it possible to arrive at initial parameters for the design of steel-beam dampers with the desired properties. However, it must be noted that the following discussion is based on a large number of tests on many models and a few full-scale dampers, using in the main one kind of steel (BS4360/43A) after stress relieving. Other steels and heat treatments are expected to give similar, but not necessarily identical, results, particularly for the life of the damper. The procedures suggested here, particularly for 'scaling', are approximations which are included in order to enable a designer to obtain starting parameters for a given design. In practice, the full-scale device should be tested. For a given strain range, the load-displacement loop changes only moderately with repeated cycling, with a moderate reduction in damping capacity, until the yielding beams are near the end of their low-cycle fatigue life. The damper loop parameters and their fatigue life can be estimated adequately, on the basis of cyclic tests on damper prototypes or on small-scale models. Since steel-beam dampers have a strictly limited low-cycle fatigue life, controlled by fatigue-life curves of the type shown in Figure 3.6 below, it is necessary to design the dampers so as to limit the cyclic strain ranges during earthquakes, and to ensure a capacity to resist several design-level earthquakes as well as at least one extreme-level earthquake. For a typical well-designed isolator and for El Centro-type earthquakes, this might call for a nominal maximum strain range of + 3% during design earthquakes and + 5% during extreme earthquakes. Again, to avoid premature failure the isolator installation should ensure that wind loads do not impose more than a few tens of cycles of plastic deformation on damper beams during the design life of the isolated structure. The fatigue life of well-designed steel-beam dampers is discussed further in Section 3.3(e) below. 50

3.3.2

Types of Steel Damper

While steel beams may be subject to shape instability during cyclic deformations into the plastic range, each of the damper geometries described below is stable for a very wide range of member proportions. The three types of steel hysteretic damper to be discussed are shown in Figure 3.3: (i)

A 'uniform'-moment bending-beam damper with transverse loading arms, sloped at an angle as shown in Figure 3.3(a) (Type-U damper).

(ii)

A tapered-cantilever bending-beam damper (Type-T damper). The apex of the tapered slab is at the loading level, while the apex of the tapered cone is substantially above the loading level. The circular-section cantilevered beam in Figure 3.3(b) may be loaded in any direction perpendicular to the beam axis. Figure 3.3(c) shows the load-displacement curves for this cantilever damper, as used in retrofitting Haywards Power Station with seismic isolation (see Chapter 8).

(iii)

A torsional-beam damper with transverse loading arms (Type-E damper). Figure 3.3(d) shows the E-type damper used in the South Rangitikei Viaduct (see Chapter 8).

Note, as shown in Figures 3.3(a) and 3.3(d) that the welds are placed at low-stress regions of the damper.

(b)

(a)

(c)

Figure 3.3:

(d)

(a) (b)

Full-scale steel 'U-type' bending-beam damper prototype (100 kN, + 50 mm). Shaft diameter 100 mm. Note position of welds in low-stress region. Steel cantilever 'T-type' damper (10 kN, + 200 mm), as retrofitted in order to isolate the capacitor banks at Haywards Power Station (see Chapter 6). Shaft diameter 50 mm.

51

(c) (d)

(Cousins, Robinson & McVerry, 1991.) Load-displacement loops for steel cantilever damper shown in Figure 3.3(b). Steel torsional-beam 'E-type' damper with transverse loading arms (450 kN, + 50 mm), as used in South Rangitikei Viaduct with stepping piers (see Chapter 6). Rectangular section 200 mm x 60 mm. Note position of welds in low-stress region.

The cross-section of the beam may be circular, square or rectangular, denoted by the subscripts 'c', 's' or 'r' respectively. Thus the beams shown in Figures 3(a), 3(b) and 3(d) are of Types Uc, Tc and Er respectively. Dampers with improved features for particular applications may be based on combinations of the three basic types. A considerable range of further types of steel-beam damper has been described in the literature. For example, two compact dampers have been introduced in Japan. One uses a short hollow steel cantilever instead of the solid steel core of the T-type damper. This bell damper is compact and has good force-displacement features (Kobori et al, 1988). A second steel-beam damper has a set of beams in the form of vertical axis helices which provide for large yielding displacements in any horizontal direction. It has little height and can therefore be installed between horizontal surfaces with a small vertical clearance (Takayama, Wada, Akiyama and Tada, 1988). In Italy, sets of conical T-type dampers have been mounted on the same base to provide large-force moderate-height steel dampers, as shown in Figures 8.31 and 8.32 of Chapter 8 (Parducci & Medeot, 1987). 3.3.3

Approximate Force-Displacement Loops for Steel-Beam Dampers

Stress-Strain Loops and Force-Displacement Scaling Factors The family of force-displacement loops for a bending-beam or twisting-beam damper can be scaled on the basis of a simple model, to give a set of stress-strain curves. Approximate force-displacement loops for a wide range of steel-beam dampers can then be obtained from the scaled stress-strain curves.

Figure 3.4:

Scaled stress-strain loops for Type-Tr steel-beam damper, made of hot-rolled mild steel complying with BS4360/43A. This diagram can be used to generate approximate force-displacement loops using the scale factors for the 7 types of steel-beam damper given in Table 3.1.

52

Table 3.2: Scaling Factors for Steel Beam Dampers Figure 3.4 shows scaled stress-strain loops for a Type Tr steel-beam damper made of hot-rolled steel complying with BS4360/43A. Table 3.2 shows the force- and displacement-scaling factors, f and l respectively, for 7 types of damper. The scaling factors f and l of Table 3.2 and Figure 3.4 are based on a greatly simplified but effective model of the yielding beam. The extreme-fibre strains  (or ) are based on the shape which the beam would assume if it remained fully elastic. The nominal stresses or^ are related to the force scaling factor f on the assumption that they remain constant over a beam section (as they would for a rigid-plastic beam material.) The circumflex (^) is introduced to emphasise the nominal nature of the stresses and moduli derived using the uniform-stress assumption. It can be shown that premultiplication of the scaling factor f by about 0.6 will correct to some extent for the approximation's nonvalidity. However, if such refinement is required, it is preferable to scale using the method of c(iii) and d(iii) below. The force F and displacement X can then be obtained

X   , (or  ) F  f ˆ (1 + a X 2), (or f ˆ (1 + a X 2))

(3.2a) (3.2b)

where  , ˆ 6 are given by Figure 3.4,  , ˆ 7 are given approximately by Figure 3.4, by letting  =  and  /2, and where 'a' is a small correction factor for large-displacement shape changes. For dampers of Type U, T and E respectively, values of the correction factor 'a' are: 2 2 2 a U  - 1 /(8 R ); a T  2 /(L+ R ) ; a E  1 /(2 R ),

where R and L are defined in Table 3.2. 53

(3.2c)

Figure 3.3(c) is an example of the effect of a positive 'a' value on the loop shapes of Figure 3.1(b). The positive aT and aE values of equation (3.2c) cause an increase in the slope of the force-displacement loop for large yield displacements of T-type and E-type dampers, in accordance with equation (3.2b). Similarly, the negative aU value causes a reduction in the loop slope for large yield displacements of U-type dampers. The stress-strain loops of Figure 3.4 were derived from force-displacement loops for a Tr-type damper, using equations (3.2) and f(Tr) and l(Tr) values from Table 3.2. The force-displacement loops in Figure 3.4 were not corrected for beam-end effects, since these were considered typical for bending-beam dampers. Hence damper designs based on Figure 3.4 and Table 3.2 already includes typical beam-end effects. The initial stiffness of the damper is somewhat uncertain, owing to variations in end-effects and the stiffness of beam-loading arms. When equations (3.2) are used to generate the stress-strain loops from the force-displacement loops of a Tr damper, they eliminate the large-displacement increases in nominal stresses, as is evident from a comparison of Figures 3.3(c) and 3.4. When dampers are then designed using Figure 3.4, equations (3.2) reintroduce appropriate large-displacement changes in force and stiffness. By introducing the very rough approximation ˆ  2ˆ 9 and using =, Figure 3.4 and Table 3.2 can be used to obtain a rough estimate of the force-displacement loops for E-type (torsional) dampers. However, it would be more accurate to generate a separate set of ˆ -  10 loops based on force-displacement loops for an E-type damper and equations (3.2). A representative beam section should be used, say a rectangle with B=2t, where B and t are defined in Table 3.2. Alternatively, the method of c(iii) should be used if more accuracy is required. Errors in Approximate Damper Loops There are four main sources of error in the damper loops and parameters derived by the method described in c(i) above. (1)

Differences between the material properties of the hysteretic beam used to generate the stress-strain loops of Figure 3.4 and the material properties of the hysteretic beam in the prototype.

(2)

End-effects and non-beam deformations. End-effects usually reduce the initial stiffness by about 50% and are particularly important for rectangular-beam type-E dampers.

(3)

Alteration of loop loads, for a given displacement, by changes in the shape of the damper under large deflections. Shape changes reduce Kb2 for type-U dampers and increase Kb2 for type-T and type-E dampers. First-order corrections have been derived for the load changes due to damper shape changes. These have been used to remove large-deflection effects from the loops in Figure 3.4.

(4)

Small changes in the damper loops caused by secondary forces. For example, the Etype damper is deformed by bending as well as by twisting forces. These effects have been small or moderate for all the damper proportions tested.

The inelastic interaction of primary and secondary beam strains results in a gradual progressive cycle-by-cycle change in beam shape. The beam of a U-type damper deforms progressively away from a line through the loading pins. The beams of an E-type damper deform progressively towards the axis of the loading pin. These effects were not serious in any of the dampers tested. The method given below in c(iii) gives a more accurate procedure for generating force-displacement loops for steel-beam dampers. 54

Damper Loops Derived from Models of Similar Proportions A scale-model method partially eliminates the four sources of error given above. In this method, force-displacement loops are derived for an experimental model, or damper of similar but not identical proportions as the prototype, and made of the same material. The scaling is then done in terms of the force- and displacement-scaling factors, f and l, given in Table 3.2. If subscripts p and e are used for the 'prototype' and the 'experimental model' respectively, then, neglecting the correction factors involving 'a' of equation (3.2c)

Fp / Fe = f p / f e

(3.3a)

X p / Xe =  p / e

(3.3b)

For example, for a Uc damper, Table 3.2 gives

X p / Xe = Lp R p d e 

Le R e dp .

Section (d) below describes how the stiffness ratios and yield-point ratios can also be obtained. 3.3.4

Bilinear Approximation to Force-Displacement Loops

Method of Obtaining Bilinear Approximation For design purposes, the curved force-displacement loops (such as shown, for example in Figure 3.3(c)) are usually approximated by bilinear hysteresis loops with an initial stiffness Kb1, a yielded stiffness Kb2 and a yield force Qy. The method adopted here for selecting a bilinear approximation to a hysteresis loop is shown in Figure 3.5.

Figure 3.5: The method adopted for selecting a bilinear approximation to a curved hysteresis loop.

In Figure 3.5 the curved loop A'B'ABA' is symmetric about the centre O, and the coordinates of the vertices A and A' are the maximum displacements + Xb and the maximum force + Sb. The initial stiffness Kb1 is approximated by the slope of the parallel lines AB, A'B', where B and B' are the loop intercepts on the X-axis. 55

The yield stiffness Kb2 is approximated by the slope of the parallel lines AC, A'C', where CC' is the line through O with slope Kb1. Xy and Qy, the coordinates of point C, are the yield displacement and the yield force respectively for the bilinear approximation to the curved hysteresis loop. The stress-strain loops of Figure 3.4 can also be approximated by bilinear loops with an initial modulus Ê1 (or _1), a yielded modulus Ê2 (or _2) and a yield stress ˆ y (or ˆy ). 14 The bilinear loop parameters change rapidly with strain amplitude m at low strains, but more slowly with maximum strain for larger strains. In practice, these parameter changes do not introduce large errors to seismic designs based on bilinear loops, since seismic responses are dominated by relatively large strains, with slowly varying parameters. With fixed values of Kb1, Kb2 and Qy, the bilinear loops nest on a two-slope generating curve with a fixed starting point. Bilinear Damper Parameters from the Bilinear Parameters of Stress-Strain Loops Bilinear approximations to the stress-strain loops of Figure 3.4 have been used to generate the moduli and the yield stresses and strains listed in Table 3.3. These moduli and stresses may be scaled by the factors f and l of Table 3.2 to give the bilinear stiffness and yield parameters for particular dampers, as follows:

K b1  ( f /  ) Eˆ1

(3.4a)

K b 2  ( f / ) Eˆ 2 + a Q y X m (1 +  y /  m )

(3.4b)

Qy  f ˆ y

(3.4c)

where

Xm =   m where m is the maximum amplitude of cyclic strain and 'a', the large-deflection correction factor, is defined in equation 3.2. For a (torsional) E-type damper, Ê1, Ê2 and

ˆ y 19 of Table 3.3 and equations (3.4) are replaced

by _1, _2 and ˆy , 20 which are, very approximately, half as large.

m

Ê1

Ê2

^y

y

%

102 MPa

102 MPa

102 MPa

%

1

700

122

2.70

0.36

2

"

25.6

3.70

0.55

3

"

12.2

4.06

0.59

4

"

7.58

4.24

0.61

5

"

5.34

4.42

0.63

6

"

4.79

4.52

0.65

7

"

4.65

4.58

0.66

Table 3.3: Approximated Moduli, Stresses and Strains, up to a Strain Amplitude m of 7%

56

Stiffness and Yield Parameters from Models of Similar Proportions The modelling procedure described in c(iii) can be used to give the parameters of a proposed damper. Again, subscripts pand e refer to the 'prototype' and 'experimental' dampers respectively, and f and l values are obtained from Table 3.2. If the correction factor involving 'a' is neglected, then equations (3.4) give

and

K b1 (p) / K b1 (e)  K b 2 (p) / K b 2 (e)  ( f p  e) / ( f e  p)

(3.5a)

Qy (p) / Qy (e)  f p / f e

(3.5b)

For the Uc damper, for example, Table 3.2 gives either stiffness ratio of the form:

and

4 2 K b1 (p) / K b1 (e)  d p R e L e 

d

4 e

R p Lp

Q y ( p) / Q y (e)  d 3p R e 

d

3 e

R p

2

The above approach is equivalent to generating a loop or loops of the type shown in Figure 3.4, based on an approximate model of a proposed damper, and then using values from Tables 3.2 without end-corrections or large-deflection corrections, to find the parameters of the proposed damper. 3.3.5

Fatigue Life of Steel-Beam Dampers

While the load-deflection parameters of a steel-beam damper may be achieved readily, using the above design parameters, some sophistication is required in design detailing and in manufacturing techniques which will assure a maximum in the potential fatigue life. The potential fatigue life may be estimated from cyclic tests on simple specimens and from the nominal maximum cyclic strains as derived from simple beam theory. The 'life', or number of cycles a steel hysteretic damper can be expected to survive, is dependent upon the behaviour of the steel under cyclic loading as well as on the design of the damper. The stresses which a material can survive under cyclic loading are far less than for static loading. As the stress amplitude increases, the number of cycles to failure reduces rapidly. These results are normally summarised in 'S-N' curves, in which the cyclic stress amplitude is plotted against the number of cycles to failure. For steel hysteretic dampers to operate, the stress level needs to exceed the yield strength while remaining below the ultimate strength. Fortunately for most seismic isolation solutions, it is the displacement amplitude, and thus the strain, which is the controlling factor. Therefore, for the problem of seismic isolation the important curve is the strain amplitude versus the number of cycles to failure (Figure 3.6). Note the logarithmic scale on the abscissa.

57

Figure 3.6:

Fatigue-life curve for a steel-beam damper. (The strain amplitude versus the number of cycles to failure.) (Based on Tyler, 1978.)

By contrast, the lead devices do not fatigue readily at normal operating temperatures, because the melting point of lead is so low. During and after deformation, the deformed lead undergoes the interrelated processes of recovery, recrystallisation and grain growth. This behaviour is similar to that which occurs for steel above about 400C. When assessing low-cycle fatigue capacity, the cyclic displacements of an earthquake may be characterised by various strain ranges, say 2 cycles at ± 5% strain, 6 cycles of ± 4% strain and 12 cycles at ± 3% strain, as is commonly done when assessing the fatigue capacity of ductile reinforced-concrete structural members. The total fatigue capacity of a well-designed steelbeam damper, for any fixed strain range, may be estimated from Figure 3.6. A rough approximation to the reduction in fatigue resistance caused by given earthquake displacements may be obtained as follows. When a strain range of ± x% gives a damper fatigue life of nx cycles, as indicated by Figure 3.6, assume that m cycles consume m/nx of the total fatigue capacity of the damper. Hence the above earthquake displacement consumes 2/45 + 6/77 + 12/108 = 0.23 of the total damper fatigue capacity, and the damper is estimated to just survive the cyclic deflections of 4 such earthquakes. As suggested by the above example, the fatigue capacity of damper-beam materials may be compared effectively on the basis of the cyclic fatigue capacity of simple standard specimens subject to a single nominal strain range, say ± 5%. The beam and its end fixings must be detailed to avoid severe stress concentrations at locations of high plastic strain. In particular, yielding-beam welds should be confined to lower-strain locations. Again it is appropriate to adopt a damper geometry which gives a decrease in the nominal plastic strain towards the ends of the yielding beams. Large-deformation effects give this end-strain reduction for type-U dampers with prismic yielding beams. It also occurs for typeTc dampers, with circular cones loaded at the level given at the bottom of Table 3.2. For some dampers, such as type-Tr, it is appropriate to use curved transitions between yielding and nonyielding parts of the beam. Rises in the plastic-beam temperature, during design earthquakes or extreme earthquakes, should cause little change in the damper parameters or in the damper fatigue resistance. The plastic-deformation damper beam should be of mild steel, for example BS4360/43A. It may be an advantage to select for low levels of those constituents known to reduce low-cycle fatigue. The damping beam material should not be more than moderately cold-worked. The as-rolled condition is usually appropriate for damper beams. With higher cold-working during manufacture, partial annealing is appropriate. Full annealing will considerably increase fatigue life while reducing damping forces, which will then increase moderately during the first several cycles of damper operation. 58

3.3.6

Summary of Steel Dampers

Steel-beam dampers are characterised by hysteretic force-displacement (stress-strain) loops which can be analysed using a scaling method or approximated by bilinear loops. The 'life' of steel dampers is limited by their fatigue characteristics on cycling.

3.4

LEAD EXTRUSION DAMPERS

3.4.1

General

Another type of damper utilising the hysteretic energy dissipation properties of metals is the Lead Extrusion Damper, developed at PEL (DSIR) (the Physics and Engineering Laboratory of the NZ Department of Scientific and Industrial Research). The cyclic extrusion damper was invented in April 1971 by Bill Robinson, immediately after he had a morning-tea discussion with Ivan Skinner on the problems associated with the use of steel in devices to absorb the energy of motion of a structure during an earthquake. The process of extrusion consists of forcing or extruding a material through a hole or orifice, thereby changing its shape (Figure 3.7). The process is an old one. Possibly the first design of an extrusion press was that of Joseph Bramah who in 1797 was granted a patent for a press "for making pipes of lead or other soft metals of all dimensions and of any given length without joints", (Pearson, 1944).

Figure 3.7: A representation of the extrusion of a metal, showing the changes in microstructure. (Robinson, 1976.)

A lower bound for the extrusion pressure p may be derived from the yield stress y of the material under simple axial load, following Johnson & Mellor (1975). Simple extrusion involves a reduction in the cross-sectional area of a solid prism from A1 to A2 by plastic deformation, with an increase in length corresponding to little volume change. The process may be idealised as the frictionless extrusion of an incompressible elastic-plastic solid which has a constant yield stress y. The minimum work W, required to change the section from A1 to A2, or the equal minimum work to change the section from A2 to A1, arises when A1 and A2 have the same shape and when the deformation involves plane strain. Such plane strain occurs when plane sections prior to deformation remain plane throughout the deformation process. 59

The work W of plane-strain deformation can be derived by considering a prism of section A2 which is compressed between frictionless parallel anvils to form a prism of section A1. The yield force increases with the increasing sectional area to give the work W as

W = A1 L1  y  n A1 / A 2

(3.6a)

where L1 is the length when the prism area is A1. Indeed, equation (3.6a) can be used as a basis for the experimental determination of the simple-strain yield stress y for lead, since a suitably lubricated lead cylinder, compressed between smooth anvils, deforms in almost true plane strain. The work required to cause the reverse change in area by simple frictionless extrusion would be greater than W by an amount which depends on the departures from plane-strain, which should not be great with a gradually-tapered extrusion orifice. For this almost plane-strain case, a result which appears to have been first put forward in 1931 by Siebel and Fangmeier, the extrusion pressure p follows simply from equation (3.6a), giving

p =   y  n ER where the extrusion ratio

ER

=

(3.6b)

A1/A2

and  exceeds 1.0 by a small amount which arises from the departure from plane-strain deformation. A practical extrusion process will involve significant surface friction which will give a further departure from plane-strain and hence an increase in , beyond the zero-friction value. A further increase in pressure occurs in reaction to the axial component of the surface friction forces. If there are significant changes in y over sections of the extruded material, as may well arise when hysteretic heating causes temperature differences, this may change the pattern of extrusion strains substantially, a factor which may be significant with cyclic extrusion. When a back-pressure and a re-expansion throat are included to return a lead plug to its original sectional area A1, as shown in the schematic sketch of an extrusion damper in Figure 3.8, the theoretical frictionless pressure of equation (3.6b) is doubled. For a practical system with effective lubrication, the extrusion pressure, as given by equation (3.6b), should also be roughly doubled when the contraction from area A1 to A2 is followed by an expansion from area A2 to A1.

(a)

60

(b)

Figure 3.8:

(a) Longitudinal section of cyclic lead extrusion damper: constricted-tube type. (Robinson, 1976.) (b) Longitudinal section of cyclic lead extrusion damper: bulged-shaft type.

When the throat profile is well designed, and the lead-surface lubrication is effective, the pressure should be given approximately by

p =  1  y  n A1 / A2 + po

(3.7a)

Another result of interest is the relation between extrusion pressure p and the speed of extrusion v, or the strain rate (Pearson (1944), Pugh (1970)). This is found to be

p = a vb

(3.7b)

where b = 0.12 for lead at 17oC, so that for an increase in extrusion speed by a factor of 10, it is necessary to increase the extrusion pressure by 36 per cent. More complete discussions of the behaviour of metals during plastic deformation are found in Nadai (1950), Mendelsson (1968) & Schey (1970). Deformation of a polycrystalline metal results in elongation of the grains and a large increase in the number of defects (such as dislocations and vacancies) in each grain. After some time the metal may, if the temperature is high enough, return to a state free from the effects of plastic strain by the three interrelated processes of recovery, recrystallisation and grain growth (Wulff et al (1956), Birchenall (1959), Jones et al (1969)). During the process of recovery, the stored energy of the deformed grains is reduced by the dislocations moving, to form lower energy configurations such as subgrain boundaries, and by the annihilation of vacancies at internal and external surfaces. Recrystallisation occurs when small, new, undeformed grains nucleate among the deformed grains and then grow at their expense. Further grain growth occurs as some of the new grains grow at the expense of others. The driving force for recrystallisation is the stored energy of deformation of the extruded grains, while the decrease in the surface energy of the many recrystallised grains causes grain growth to occur. The temperature which is sufficient to cause 50% recrystallisation during one hour is called the recrystallisation temperature (Wulff et al (1956), Van Vlack (1985)). For lead this temperature is well below 20oC, while for aluminium, copper and iron it is 150oC, 200oC and 450oC respectively. The rate at which recrystallisation occurs is strongly dependent on temperature. For example, copper which has been reduced in thickness by 71 per cent, by cold rolling, has a recrystallisation time of 12 min at 300oC, 10.4 days at 200oC and 290 yr at 100oC (Wulff et al (1956)). The rate at which recrystallisation occurs also increases with the amount of deformation.

61

Since the recrystallisation temperature of lead is below room temperature, any deformation of lead at or above room temperature is in fact 'hot work' in which the processes of recovery, recrystallisation and grain growth occur simultaneously. Working lead at room temperature is equivalent to working a piece of iron or steel at a temperature of more than 400oC. Indeed, lead is the only common metal which need not suffer progressive fatigue when cycled plastically at room temperature. A device which acts as a hysteretic damper by utilizing this property of lead (Robinson & Greenbank (1976); Robinson & Cousins (1987, 1988), is shown in Figure 3.8(a). It consists of a thick-walled tube co-axial with a shaft which carries two pistons. There is constriction on the tube between the pistons, and the space between the pistons is filled with lead. The lead is separated from the tube by a thin layer of lubricant kept in place by hydraulic seals around the pistons. The central shaft extends beyond one end of the tube. During operation, axial loads are applied with one attachment point at the protruding end of the central shaft and the other at the far end of the tube. The hysteretic damper is fixed between a point on the structure and a point on the earth, which move relative to one another during an earthquake. As the attachment points move to and fro, the pistons move along the tube and the captive lead is forced to extrude back and forth through the orifice formed by the constriction in the tube. Since extrusion is a process of plastic deformation, work is done, while very little energy is stored elastically, as the lead is forced through the orifice during structural deformation. Thus during an earthquake such a device, by absorbing energy, limits the build-up of destructive oscillations in a typical structure. The successful operation of this hysteretic damper depends on the use of a material, in this case lead, which recovers and recrystallised rapidly at the operating temperature, so that the force required to extrude it is practically the same on each successive cycle. If the extruded material had a recrystallisation temperature much above the operating temperature, it would workharden and be subject to low-cycle fatigue. Moreover, such materials typically have much higher stresses which would present very severe problems for containment, piston sealing and lubrication in a cyclic extrusion device. A hysteretic damper which operates on this same principle but has different construction details is shown in Figure 3.8(b). Here the extrusion orifice is formed by a bulge on the central shaft rather than by a constriction in the outer tube. The central shaft is located by bearings which also serve to hold the lead in place. As the shaft moves relative to the tube, the lead must extrude through the orifice formed by the bulge and the tube. 3.4.2

Properties of the Extrusion Damper

One of the most important properties of a hysteretic damper is its force-displacement loop. If the device acts as a 'plastic solid' or 'Coulomb damper' then over one cycle the forcedisplacement hysteresis loop will be rectangular and the energy absorbed will be a maximum for the particular force and stroke. Figure 3.9(a) shows hysteresis loops typical of constricted tube and bulged-shaft dampers. For both types, the force rises almost immediately on loading while there is no detectable recoverable elasticity on unloading. Note the plastic force is the force Qy for the extrusion damper. The performance factor, defined as the ratio of the work absorbed by the damper to that contained by the rectangle circumscribing the hysteresis loop, is 0.90 to 0.95.

62

(a)

(b)

Figure 3.9:

(a) Typical load-displacement hysteresis loops for lead extrusion dampers. (b) Comparison of hysteresis loops obtained for a constricted-tube lead-extrusion damper tested in 1976 (solid line) and again in 1986 (dashed line). (Cousins & Robinson, 1987.)

The force to operate one of the extrusion hysteretic dampers has also been found to be almost independent of both the stroke and the position from which displacement starts. The hysteresis loops in Figure 3.9(b), which shows the behaviour of the same damper at an interval of 10 years (1976 and 1986), confirm the stability of the extrusion dampers (Robinson & Cousins (1987, 1988)). The extrusion force is rate-dependent, as can be understood on the dislocation model by considering the speeds of dislocation motion and grain boundary sliding. To examine the rate dependence of the extrusion force, for the extrusion energy absorbers, a number of them were tested at speeds ranging from 3x10-10 to 1 m/sec.

63

Figure 3.10

Rate dependence of lead extrusion hysteretic damper. The force is compared with that corresponding to a speed of 1 m/s, and this load ratio is plotted as a function of speed.

The experimental results for the rate dependence of the energy absorbers are shown in Figure 3.10, in which the ordinate is the 'load ratio' relating the force to that which will cause the damper to yield at a speed of 1 m/s. The damper's performance has two different characteristics, with the change occurring at a speed of 10-4 m/sec. Below this speed, the exponential equation (3.7b) is given by b=0.14. Hence if the rate of cycling is increased by a factor of ten, the load increases by 38 per cent, or the rate must be increased 140 times for the load to be doubled. Above a speed of 10-4 m/s, b = 0.03. In this case a 7% increase in load increases the rate by a factor of ten, while a 40% increase in the load requires the rate to be increased 105 times. The value of 0.14 for b, for rates below 10-4 m/s, agrees well with the figure of 0.13 obtained by Pearson (1944) for lead at 17oC. Loads which cause creep may also be compared with the load at an earthquake-like speed of 10-1 m/sec. At a load ratio F/F(101 m/sec) = 0.2, the creep rate becomes ~10 mm/yr. The results above 10-4 m/sec indicate that at these speeds the extrusion energy absorbers are nearly rate-independent; for example, at a rate of ~102 m/sec the extrusion force is expected to be 1.15 times that for an earthquake-like speed of 10-1 m/sec. Above a rate of 2 x 10-2 m/sec, tests on large energy-absorbing devices become difficult because of the large power required. For example, for a 200 kN hysteretic damper operating at 1 Hz with a total stroke of 250 mm, a power of 100 kW must be supplied. The effect of temperature on the extrusion energy absorber is complex, in that an increase in temperature, due either to ambient changes, or to the absorption of energy during an earthquake, has a twofold effect: -

As the temperature increases the extrusion force decreases.

-

The higher the temperature, the more rapidly the lead will undergo recovery, recrystallisation and grain growth, thereby eliminating work hardening and regaining its plasticity.

These factors ensure that the extrusion damper is a stable device which cannot destroy itself by building up excessive forces. A 15 kN constricted-tube extrusion damper was operated continuously at 1 Hz for 1,800 cycles and during this test the temperature on the outside of the orifice reached an equilibrium value of 210oC. The effect of lowering the temperature was checked by cooling an energy absorber to -20oC but no noticeable change in extrusion force, compared to that at 25oC, was observed. The lifetime of an extrusion energy absorber has been tested by operating a 15 kN constrictedtube device continuously at frequencies of 0.5, 1 and 2 Hz for a total of 3,400 cycles (Robinson and Greenbank (1976)). 64

After this test, which provided conditions far more severe than those to be expected in service, (during an earthquake the device would be expected to undergo ~10 cycles), the extrusion energy absorber was found to operate as initially at 1.7 x 10-3 m/sec. This result is not surprising since 'hot worked' lead is forever recovering its original mechanical properties. Therefore the extrusion damper should be able to cope with a very large number of earthquakes. The maximum energy an extrusion damper can absorb in a short time is limited by the heat capacity of the lead and the surrounding steel. To increase the temperature of lead from 20oC to its melting point of 327oC, but without melting it, requires 3.8 x 104 joules/kg of lead. The surrounding steel raises the heat capacity of the device by a factor of ~4 so that the total energy capacity of the extrusion device is ~1.6 x 105 joules/kg (total weight). An extrusion damper with a 30 mm outside diameter had an extrusion force of ~15 kN while a device with a 150 mm outside diameter required a force of ~150 kN to operate it. The stroke of the extrusion energy absorber is not limited in any way by the basic properties of the device. To date the largest extrusion dampers made had a total stroke of 800 mm (±400 mm) and operated at a force of 250 kN. The total length of a device when at its maximum extension is three to four times the length of its stroke. 3.4.3

Summary and Discussion of Lead Extrusion Dampers

The extrusion damper, in which mechanical energy is converted to heat by the extrusion of lead within a tube, is a device that is suitable for absorbing the energy of motion of a structure during an earthquake. The principle is simple but the design is not necessarily so. The extrusion damper has the following properties: (1)

It is almost a pure 'Coulomb damper' in that its force-displacement hysteresis loop is nearly rectangular and is practically rate-independent at earthquake-like frequencies.

(2)

Because the interrelated processes of recovery, recrystallisation and grain growth occur during and after the extrusion of the lead, the energy absorber is not affected by work hardening or fatigue, but instead the lead is forever returning to its original undeformed state. The extrusion damper therefore has a very long life and does not have to be replaced after an earthquake.

(3)

The extrusion damper is stable in its operation and cannot destroy itself by building up excessive forces. As the temperature rises during its operation, then the extrusion force decreases and therefore the energy absorbed and heat generated decrease, and the higher the temperature, the more rapidly the lead will recover and recrystallised, thereby regaining its plasticity.

(4)

The length of stroke of the extrusion energy absorber is limited only by the problem of buckling of the shaft during compression. The dimensions of a 150 kN energy absorber with a stroke of ±200 mm are: Outside diameter ~150 mm Total length ~1.5 m Total mass ~100 kg

These dimensions ensure simple installation in many isolator applications. The lead extrusion damper has, to date, been used in New Zealand in three bridges and to provide damping for one ten-storey building mounted on flexible piles (see Chapter 6). It has also been installed in the walls to increase the damping of two buildings in Japan. In addition to providing damping, the extrusion damper 'locks' the structure in place against wind loading in the case of buildings, and against the braking of motor vehicles in the case of sloping bridges. 65

3.5

LAMINATED-RUBBER BEARINGS FOR SEISMIC ISOLATORS

3.5.1

Rubber Bearings for Bridges and Isolators

Another method of seismically isolating structures is by mounting them on laminated rubber bearings (elastomeric bearings). These bearings are a fully developed commercial product whose main application has been for bridge superstructures, which often undergo substantial dimensional and shape changes due to changes in temperature. More recently their use has been extended to the seismic isolation of buildings and other structures (Chapter 6). These bearings are designed to support large weights while providing only small resistance to large horizontal displacements, and to moderate tilts, of the upper surfaces of the bearings. A typical bridge bearing consists of a stack of horizontal rubber layers vulcanised to interleaved steel plates, as shown schematically in Figure 3.11 for a cylindrical bearing.

Figure 3.11: Sketch of laminated elastomeric bearing, of area A and circumference C, in which rubber layers, of thickness t, are bonded to thin steel plates.

For a given bearing area and rubber composition, the load capacity is increased by reducing the thickness of each rubber layer, while the resistance to horizontal and tilting movements is reduced by increasing the total height of the rubber. Rubber bearings, of the types used for bridges, can be dimensioned to provide the support capacity and the horizontal flexibility required for seismic isolation mounts. Of particular importance is the ratio of bearing weight capacity to horizontal flexibility, which determines the maximum achievable value for the rigid-structure period Tb. Of equal importance is the maximum acceptable horizontal displacement Xb, which is set either by the allowable rubber strain or by the allowable offset between the plan areas of the top and bottom of the bearing. Rubber bearings also provide adequate isolator centring forces during large seismic displacements. Rubber bearings have a considerable range of applications in seismic isolators, as described later in this chapter. In their basic form, rubber bearings may be used to provide support, horizontal flexibility and centring forces. Isolator damping may then be increased by separate components. Alternatively, lead plugs may be inserted in rubber bearings to add high hysteretic damping to the features of the basic bearings, as described in 3.6 below. Again, rubber bearings may be surmounted by horizontal slides which provide increased horizontal flexibility and frictional damping. Additional isolation roles for rubber bearings include tilting supports for rocking structures and elastic components in displacement-limiting buffers. The detailed design and the manufacture of rubber bearings call for some technical sophistication. However, the approximate features of rubber bearings may be derived using simple well-known approaches, as described below. An understanding of the factors influencing the features of elastomeric bearings is useful when developing isolation systems, and may assist during preliminary design studies. 66

3.5.2

Rubber Bearing, Weight Capacity Wmax

The principal features of rubber bearings can be seen from the behaviour of a thin rubber disc, with rigid plates bonded (vulcanised) to its plane surfaces, when subjected to normal (axial) and to parallel (or shearing) loads. The relationship between the load W and the maximum engineering shear strain  in the disc has been derived by Gent & Lindley (1959) as outlined below in modified form. (Following Borg (1962),  = xz = w/x + u/z = 2xz where xz is the tensor shear strain.) When the rubber is assumed incompressible, a vertical compressive strain z causes the rubber to bulge by an amount proportional to its distance from the centre of the disk. When the bulge profile at any radius r is approximated by a parabola, constant rubber volume gives the maximum shear strain xz as: (3.8a)  xz = 6 S  z where the vertical strain z = t/t, the thickness of the rubber layers is denoted t, and the shape factor S = (loaded area)/(force-free area). For example, for a circular disc of unstrained diameter D and thickness t, S = D/4t. The rubber shear forces cause a pressure gradient within the disc which is proportional to the distance from the centre. This gives a parabolic pressure distribution, as shown in Figure 3.12.

Figure 3.12: Sketch of circular layer of rubber, diameter D, thickness t, and of the parabolic pressure distribution p.

The maximum pressure po is given by:

po = 2 GS xz

(3.8b)

where G = shear modulus of rubber. The corresponding load W may be obtained by summing the pressure over a disc area A to give: W = AGS xz (3.8c) Now consider a basic rubber bearing consisting of n equal rubber layers of any compact shape. Also let the top of the bearing be displaced by Xb to give an overlap area A between the top and bottom of the bearing, as shown in Figure 3.13.

67

Figure 3.13: Sketch of rubber cylinder of diameter D, with a shear displacement Xb and overlap A'.

Then experiment and analysis show that equation (3.8c) may be generalised approximately as follows:

W max = A  GS  w

where

Wmax = w A

(3.8d)

allowable weight = allowable shear strain due to weight = overlap of bearing top and bottom

The use of A in equation (3.8d) is a somewhat arbitrary simplification and is probably conservative. 3.5.3

Rubber-Bearing Isolation: Stiffness, Period and Damping

If an isolator consists of a set of equal rubber bearings, each supporting an equal weight, then the isolator period can be calculated directly from the weight and stiffness for a single bearing. In practice the average weight per bearing may be reduced because the weight on some bearings has been reduced to offset vertical seismic loads, or for structural or architectural convenience. However, such weight reductions are neglected here and the isolator parameters are expressed in terms of those for a single bearing. Bearing Horizontal Stiffness Kb A rubber bearing may be approximated as a vertical shear beam, since the steel laminations severely inhibit flexural deformations while providing no impediment to shear deformations. The approximate horizontal stiffness Kb is therefore given by

K b = GA/h where

A h

= =

(3.9)

rubber layer area total rubber height.

There will be some reduction in bearing height with large displacements, partly due to flexural beam action and partly due to increased compression of the reduced overlap area A. 68

The resulting inverted pendulum action, under structural weight, reduces the horizontal stiffness Kb and in extreme cases might cause serious reductions in the centring forces. However, the inverted pendulum forces are reduced by increasing the layer shape factor S, and these forces are unlikely to be serious for S values in the range from 10 to 20, a range appropriate for isolator mounts. Bearing Period Tb The bearing weight capacity, Wmax, from equation (3.8d), and the horizontal stiffness, Kb, from equation (3.9), can be combined to give the bearing and isolator period Tb, when the bearing is supporting its maximum weight, as ‰ T b = 2 (Sh  w A /Ag )

(3.10)

where w is the allowable shear strain due to the weight W. For example let S = 16, h = 0.15 m, A/A = 0.6, and w,max = 0.2 L/L, where the breaking tensile strain L/L = 5, (typically 4.5 to 7.0). Then Tb = 2.4 seconds. Bearing Damping zb Energy losses in the deforming rubber layers provide damping which is predominantly velocity-dependent. Typical bridge bearings provide bearing and isolator damping factors in the range from 5% to 10% of critical. However, acceptable bearing rubbers have been manufactured which increase the bearing and isolator damping to about 15%, and development aimed at higher damping values continues. Bearing Vertical Stiffness Kz Some isolator applications of rubber bearings are influenced by their vertical stiffness, and some by their related bending stiffness. The vertical deflection of a bearing is the sum of the deflections due to rubber shear strain and to rubber volume change, and these two respective stiffnesses are added in series. Thus the overall vertical stiffness is

K z = K z   K z (V) / K z   + K z V



(3.11a)

where Kz(), the vertical stiffness of the bearing without volume change, is given by equations (3.8a) and (3.8c) as 2 K z   = 6 G S A / h ,

(3.11b)

and where Kz(V), the vertical stiffness due to volume change without shear strain, is simply

K z V

where  =

=A

/ h ,

(3.11c)

rubber compression modulus.

Thus 2 2 K z = 6 GS A  /(6 G S +  ) h

69

(3.11d)

Equations (3.11) show that a small shape factor S gives a moderate vertical stiffness which is controlled by shear strain, while a sufficiently large value of S gives a very high vertical stiffness which is controlled by volume change. For a typical bridge-bearing rubber, with G = 1 MPa and  = 2000 MPa, shear strain and volume change make equal contributions to vertical stiffness when S  18. The above discussion neglects the usually small reduction in Kz() which occurs, due to a pressure redistribution in the layers, when rubber compressibility is introduced. When the S-value is high, rubber compressibility reduces considerably the bearing vertical stiffness and the related bending stiffness. However, rubber compressibility causes little change in the other bearing parameters described. 3.5.4

Allowable Seismic Displacement Xb

Displacement Limited by Seismic Shear Strain gs When the rubber shear strain w, due to the vertical load W, is below its maximum allowable value there is a reserve shear strain capacity, say s, to accommodate a horizontal displacement Xb, which is given by (3.12) Xb = h  s where s =

allowable shear strain due to horizontal seismic displacement.

If this displacement is inadequate it may be increased by increasing the rubber height h. In addition, or alternatively, s may be increased if the strain due to weight w is reduced. Displacement Limited by Overlap Factor A¢/A For an isolator bearing, a lower limit to the overlap factor A/A is set by the reducing weight capacity, equation (3.8d), and sometimes by the increasing end moments. Typical lower limits for the overlap factor may be 0.8 for a sustained horizontal displacement and 0.6 for design earthquake displacements. Where possible, such overlap limits should be based on laboratory tests and field experience. The relationship between the overlap factor A/A, the bearing displacement Xb and the bearing dimensions depends somewhat on the shape of the horizontal section of the bearing. For a cylindrical bearing with rubber discs of area A and diameter D:

A  /A = 1 - 2 /    + sin  cos   where sin 

(3.13a)

= Xb/D .

Hence for moderate values of Xb/D

Xb  0.8 D1 - A  /A 

(3.13b)

A  /A  1 - X b B / B - X b C  / C

(3.13c)

Similarly, for a rectangular bearing

where Xb(B) and Xb(C) are the bearing displacements parallel to the sides of lengths B and C respectively. Hence, for displacements parallel to side B,

Xb (B)  B1 - A  /A  70

(3.13d)

When the displacement Xb may be in any direction, a more appropriate displacement limit is

Xb  0.8 B1 - A  /A 

(3.13e)

where B is the shorter side of the bearing. From equations (3.13b) and (3.13e) it is seen that, for a seismic overlap factor A/A = 0.6, the allowable values of Xb are D/3 and B/3 respectively. When the weight per bearing is low, the bearing diameter D or side B may be too short to accommodate the required seismic displacement Xb. If the discrepancy is not great it might be met by increasing the bearing area A and/or by reducing the design-earthquake displacement Xb. The bearing area may be increased, without changing the bearing stiffness ratio Kb/W, if there is a compensating reduction in the rubber shear modulus G and/or an increase in the rubber height h, as required by equation (3.9). Again, the bearing area may be increased if it is possible to design the isolator with fewer bearings and hence with a greater weight W per bearing. Alternatively, the design earthquake displacement Xb may be reduced by increasing the effective isolator damping. If the weight per bearing is so low that the allowable displacement falls well short of the design earthquake displacement, then the allowable displacement may be increased as required, by segmenting the bearing and introducing stabilising plates, as described below. Segmented Bearing for a Low Weight/Displacement Ratio W/Xb When a rubber bearing supports a small weight W it has a small area A, and hence its displacement capacity, as given by equation (3.13b) or (3.13e), is also small. Such a simple bearing may be replaced by an equivalent segmented bearing, as shown in Figure 3.14, which increases the displacement capacity.

Figure 3.14: Segmented bearing formed by rubber segments placed at the corners of common stabilising plates, illustrated by 6 stabilising plates and 20 (multilayer) segments.

Consider the replacement of a simple bearing by an equivalent segmented bearing in which sets of 4 segments are located near the corners of rectangular stabilisation platforms or plates, as shown in Figure 3.14 and illustrated by Skinner (1976). 71

If all the linear dimensions (including the thickness) of the segment rubber layers are half those of the simple bearing layers, and if the number of layers is increased so that the rubber height is unaltered, then both bearings have the same values for the rubber area A and the rubber height h, and the same shape factor S, resulting in the same load capacity and the same horizontal stiffness Kb. For a given rubber and operating conditions, a shape factor which is suitable for a non-segmented bearing is also suitable for the equivalent segmented bearing. Typically each of the cylindrical segments shown in Figure 3.14 will be multilayer, to give the small layer thickness required without the use of more stabilising plates than are necessary to retain the overlap factor required for overall bearing stability. When, as here, the segments have half the horizontal dimensions of the corresponding non-segmented bearing, and there are n segments in each vertical stack (eg, n=5 in Figure 3.14), then a required overlap factor is retained with an increased allowable displacement given by (3.14) Xb (n) = n Xb (1) / 2 Where Xb(1) = allowable displacement for the corresponding non-segmented bearing.

3.5.5

Allowable Maximum Rubber Strains

Allowable Shear Strains gw and gs The allowable rubber shear strains for various loads and displacements are important factors in the performance of rubber bearings, as discussed above. When bearings are used as isolation mounts for compact structures, they must withstand the combined rubber shear strains due to structural weight and seismic displacements. When bearings isolate bridge superstructures, some provision must be made for additional shear strains due to traffic loads and to thermal displacements. In addition to their seismic design, rubber bearing mounts must be checked for their capacity to withstand the more sustained non-seismic loads and displacements. The damaging effect of a given rubber strain increases with its total duration and with the number of times it is reduced or reversed. In particular, rubber strains due to frequent and fluctuating traffic loads are found to be more severe than a corresponding steady strain applied for the life of a bearing. On the other hand, laboratory tests show that the cyclic strains due to seismic displacements are much less severe than corresponding long-duration steady strains, evidently because they involve so few cycles and have such a short duration. The sustainable steady shear strain in a rubber bearing is sometimes given as (Bridge Engineering Standards, 1976) (3.15)  w = 0.2  t where t =

short-duration failure strain in simple tension.

Experiments suggest that corresponding factors for shear strain during earthquakes are 0.4 or more for design earthquakes and say 0.7 for extreme earthquakes. Allowable Negative Pressure Under the combined action of uplift forces and end moments the rubber within isolator bearings may be subjected to large negative pressures. Consider a rubber bearing subject to an uplift force of -Wmax. From equation (3.8) it is found that this gives a small increase in bearing height of h = hw/(6S), and a large central negative pressure of po = -2GSw. For a typical bridge bearing, with G = 1 MPa, h = 0.15 m, S = 10, and -w = -1.0, it follows that h = 2.5 mm and po = -20 MPa. 72

Negative pressures may also arise from bearing end moments, which are generated by relative displacement and tilting of the ends of a bearing. These end moments cause local increases and decreases of the pressure within the bearing discs. A large negative pressure evidently causes a set of small cavities within the bearing rubber, which grow progressively during sustained and cyclic negative pressures. The cavities cause a large reduction in axial stiffness, which may be regarded as resulting from a reduction in the effective shape factor S, but there is little reduction in the horizontal shear stiffness. Figures 3.15(a) and (b) show a vulcanised laminated rubber bearing before and during vertical loading, while Figure 3.15(c) is a stress-strain plot showing both compression and tension. This bearing failed in the rubber at a tensile strain of 350%, though small internal cracks were most probably formed before this strain was reached.

(a)

(b)

(c)

Figure 3.15:

(a) Vulcanised laminated rubber bearing before loading. (Tyler, 1991.) (b) Vulcanised laminated rubber bearing under vertical tension. (Tyler, 1991.) (c) Stress-strain curve for the vulcanised laminated rubber bearing under both compression and tension. (Tyler, 1991.)

73

It is normal practice to design bridge bearing installations so that negative pressures do not occur in the rubber under the combined action of non-seismic loads and motions. It is also appropriate to design isolated structures so that non-seismic actions do not cause negative pressures. However, when seismic actions cause negative pressures in isolator mounts, their duration and frequency are so low that considerable negative pressures might be tolerated (Tyler, 1991). In general, an isolator design should be adopted which avoids very high negative pressures during seismic action. In the particular case of high uplift forces under the corner columns of two-way frame structures, high negative pressures in corner rubber bearings may be avoided by attaching the bearing tops to the bottom beams of the frames designed to allow corner uplift, for example as described by Huckelbridge (1977). 3.5.6

Other Factors in Rubber Bearing Design

In practice the application of laminated-rubber bearings to seismic isolation calls for sophisticated design and specialised manufacturing technology. The rubber must be formulated for long-term stability and resistance to environmental factors, particularly deterioration due to ozone and ultraviolet light. The bonds (vulcanising) between the rubber and the interleaved metal plates must resist the large and varying operating stresses. Bearings must be provided with end and side rubber cover to inhibit corrosion of the metal plates and to remove rubber-surface deterioration from regions of high operating strains. The rubber cover and additional surface materials may be used to increase fire resistance. Interleaved steel plates must have adequate strength to resist rubber shear forces. However, some plate bending may reduce the build-up of rubber tension when large displacements give high end moments. Bearing end-plates must provide for dowels or for other means of preventing end slip under high shear forces. Such shear connections must operate despite end moments and in some cases when uplift occurs. The effect of a fire on the performance of rubber elastomeric bearings and lead rubber bearings has been checked by Miyazaki (1991) in Japan, by heating the outside of bearings to greater than 800oC for more than 100 minutes while carrying a vertical load. After this heating the rubber elastomeric bearings and the lead rubber bearings performed in a satisfactory way without any appreciable change in their force-displacement loops or load bearing capacities. 3.5.7

Summary of Laminated Rubber Bearings

Laminated rubber bearings are already in use in bridges, in order to accommodate thermal expansion. Their modification for the seismic isolation of buildings and bridges is a fairly simple engineering concept, but in practice it requires sophisticated design and specialised manufacturing technology.

3.6

LEAD RUBBER BEARINGS

3.6.1

Introduction

Laminated rubber bearings are able to supply the required displacements for seismic isolation. By combining these with a lead plug insert which provides hysteretic energy dissipation, the damping required for a successful seismic isolation system can be incorporated in a single compact component. Thus one device is able to support the structure vertically, provide the horizontal flexibility together with the restoring force, and provide the required hysteretic damping. 74

The lead rubber bearing was invented in April 1977 by W.H. Robinson when he saw a rubber elastomeric bearing while trying, with little success, to get a cylindrical lead shear damper to operate at large strains. The steel plates in the elastomeric bearing were immediately seen to present a solution to the problem of how to control the shape of the lead during large plastic deformation. A glued elastomeric bearing was drilled out to take a lead plug, as shown in Figure 3.16, and was tested immediately, and the results forwarded to the New Zealand Ministry of Works and Development (MWD). In the next few weeks, the MWD redesigned the isolators for the William Clayton Building (see Chapter 8), replacing the planned design (elastomeric bearings plus steel dampers) with lead rubber bearings, which were substantially less costly to install, and they provided a 650 mm diameter elastomeric bearing for testing with a range of lead plugs. At the same time the Bridge Section of the MWD designed the Toe Toe and Waiotukupuna bridges to take lead rubber bearings. Thus, during a very short and exciting time, lead rubber bearings were invented, tested and used in practical applications. Before describing the lead rubber bearing in detail, it is worthwhile considering the reasons for choosing lead as the material for the insert in the isolators. The major reason is that the lead yields in shear at the relatively low stress of ~10 MPa, and behaves approximately as an elastic-plastic solid. Thus a reasonably sized insert of ~100 mm in diameter is required to produce the necessary plastic damping forces of ~100 kN for a typical 2 MN rubber bearing. Lead is also chosen because, as noted for the lead-extrusion damper, it is 'hot-worked' when plastically deformed at ambient temperature, and the mechanical properties of the lead are being continuously restored by the simultaneous interrelated processes of recovery, recrystallisation and grain growth (Wulff et al (1956); Birchenall (1959) and Van Vlack (1985)). In fact, deforming lead plastically at 20oC is equivalent to deforming iron or steel plastically at a temperature greater than 400oC. Therefore, lead has good fatigue properties during cycling at plastic strains (Robinson & Greenbank ( 1976). Another advantage of lead is that it is used in batteries, and so it is readily available at the high purity of 99.9 per cent required for its mechanical properties to be predictable. An elastomeric bearing, as described in Section 3.5, is readily converted into a lead rubber bearing by placing a lead plug down its centre, Figure 3.16. The hole for the lead plug can be machined through the bearing after manufacture or, if numbers permit, the hole can be made in the steel plates and rubber sheets before they are joined together. The lead is then cast directly into the hole or machined into a plug before being pressed into the hole. For both methods of placing the lead, it is imperative that the lead plug is a tight fit in the hole and that it locks with the steel plates and extrudes a little into the layers of rubber. To ensure that this occurs, it is recommended that the lead plug volume be 1 per cent greater than the hole volume, enabling the lead plug to be firmly pressed into the hole. Thus, when the elastomeric bearing is deformed horizontally, the lead insert is forced by the interlocking steel plates to deform in shear throughout its whole volume.

75

(a)

(b)

(d) (c)

(e) Figure 3.16:

(a) (b) (c) (d)

(e)

Lead rubber bearing which consists of a lead plug inserted into a vulcanised laminated rubber bearing. The form shown here is suitable for applications where there is no applied tension. Lead rubber bearing for William Clayton Building (see Chapter 6). Note the 300 mm rule placed on the bearing. Load capacity 3 MN, stroke + 100 mm. (Robinson, 1982.) Lead rubber bearing under static test. (Robinson, 1982.) Lead rubber bearing for William Clayton Building under dynamic test (1979). The motive force was supplied from the drive of a converted caterpillar tractor: vertical load up to 4 MN, frequency 0.9 Hz, maximum power 100 kW, maximum shear force 400 kN, stroke + 90 mm. (Robinson, 1982.) Lead rubber bearing with top and bottom plates vulcanised to the rubber, suitable for applications requiring applied vertical tension. (Robinson, 1982.)

76

3.6.2

Properties of the Lead Rubber Bearing

Test procedures were designed to measure the load-deflection loops of lead rubber bearings during the horizontal displacements of design earthquakes and extreme earthquakes, while an axial load representing structural weight was applied. These tests were performed at seismic velocities to ensure that the lead strain rates and temperature rises represented those which would apply during the simulated earthquakes. Further load measurements were made at very low velocities to find the reactions to structural dimension changes arising from daily temperature cycling, and also the reactions to the even slower motions associated with the decay of residual isolator displacements after an earthquake (Robinson & Tucker (1977, 1981); Robinson (1982)). The force-displacement hysteresis loop of an elastomeric bearing without a lead plug is shown as the dotted curve in Figure 3.17. This loop, which is for a bearing 650 mm in diameter, is mainly elastic with a rubber shear stiffness, Kb(r) = 1.75 MN/m and a small amount of hysteresis. Also in the figure, is the loop for the same bearing when it contains a lead insert with a diameter of 170 mm. The dashed lines are at the slope of 1.75 MN/m and are a good approximation to the post-yield stiffness. In this case the lead is behaving as a plastic solid which adds ~235 kN to the elastic force required to shear the bearing. Another factor of interest is the initial elastic part of the force-displacement curve for small forces. Thus a reasonable description of the hysteresis loop is a bilinear solid with an initial elastic stiffness of Kb1 followed by a post yield stiffness of Kb2 where

K b1 ~ 10 K b (r) K b 2  K b (r)

(3.16a) (3.16b)

where Kb(r) is given by equation (3.9).

Figure 3.17: Dynamic force-displacement hysteretic loop, for a 650 mm diameter bearing, obtained using equipment shown in Figure 3.16(d), with vertical compression force F(vert) = 3.15 MN, frequency 0.9 Hz, stroke + 90 mm. The dotted line is for the bearing without a lead plug. The solid line is for a lead plug of 170 mm diameter. The slope of the dashed line is K(r) (Robinson, 1982.)

Dependence on the Diameter of the Lead Insert The horizontal force, F, required to cause the bearing to be horizontally sheared can be considered as two forces acting in parallel, the first due to the rubber elasticity and the second due to the plasticity of the lead. The rubber elasticity results in a force which is proportional to the displacement while the plasticity requires a force which is independent of displacement. 77

Thus to a very good approximation

F =  (Pb) A(Pb) + K(r) X

(3.17)

where the shear stress at which the lead yields (Pb) = 10.5 MPa, A(Pb) is the cross-sectional area of the lead, K(r) is the stiffness of the rubber in a horizontal plane, and X is the displacement of the top of the bearing with respect to its base. This fact is illustrated in Figure 3.18 where the maximum shearing force, minus the force due to the elastic stiffness of the rubber, is plotted against the cross-sectional area of the lead insert. The slope of this line is the yield stress of lead, 10.5 MPa (Robinson (1982). Note Qy of a hysteretic damper is given approximately by (Pb)A(Pb).

Figure 3.18: Force due to the lead, F(b) - F(r), as a function of the cross-sectional area of the lead insert. (Robinson, 1982.)

Figure 3.19:

(a) Force-displacement hysteresis loops for a lead rubber bearing used in the William Clayton Building, at 45 and 110mm strokes, with a vertical force of 3.15MN at 0.8Hz. (From Robinson, 1982.). (b) Force-displacement curves for the bearings used in the Wellington Press Building (Chapter 8). (From Robinson & Cousins, 1987 & 1988).

Figure 3.19 contains the force-displacement hysteresis loops for two recent examples, namely the lead rubber bearings for the seismic isolation for (a) the William Clayton Building and (b) the Wellington Press Building. For both of these examples the initial stiffness Kb1~10K(r) while the post-yield stiffness is approximately K(r).

78

Rate Dependence For a number of applications it is necessary to know the behaviour of the lead rubber bearing under creep conditions. For example, if a bridge deck is mounted on the bearings then, during the normal 24 hour cycle of temperature, the bearings will have to accommodate several displacements of ~+3 mm without producing large forces. In order to determine the effect of creep rates of ~1 mm/h, the second lead rubber bearing made, (that is, one with dimensions of 356 x 356 x 140 mm with a 100 mm lead plug) was mounted in the back-to-back reaction frame in the Instron testing machine. The first result was obtained at 6 mm/h, with the force due to the lead alone reaching a maximum after 2.5 h before decreasing slowly. After 6 hours the displacement was held constant and the force due to the lead decreased to one half in about one hour, and continued to fall with time, giving a relaxation time of 1 to 2 h. Another creep test was carried out at 1 mm/h for six hours, when the direction was reversed, giving the hysteresis shown in Figure 3.20. For completeness the force F(R), due to the rubber, is included with its +20 per cent error bar. The shear stress in the lead plug reached a maximum of 3.2 MPa, which is ~30 per cent of the stress of 10.5 MPa for the dynamic tests. The force due to the rubber is great enough to drive the deformed lead, and the structure, back to its original position.

Figure 3.20: Force due to lead during creep of 356 mm2 bearing with 100 mm lead plug, at vertical force of 400 kN. Open points are 6 mm/h, filled points are 1 mm/h and dashed line is F(r). (Robinson, 1982.)

Because of the large errors caused by F(r), it was not possible to determine accurately the rate-dependence of the lead in the lead rubber bearing. To overcome this problem three lead hysteretic dampers, which had been developed earlier to operate in shear without a rubber bearing (Robinson (1982), were tested at various strain rates. These dampers consisted of lead cylinders whose diameters varied parabolically as shown in the insert to Figure 3.21, and whose ends were soldered to two brass plates. The parabolic variation was designed to minimise the effect of bending stresses, which occur away from the neutral axis of the lead, during the application of shearing displacements: in fact, the shear stress near the parabolic surface of the lead remained constant to a first approximation. The rate-dependence of these dampers, with their shear stress normalised to that at = 1 s-1, is shown in Figure .21, by the circled points. This figure also denotes, with the symbol (x), the values obtained for the second lead rubber bearing made, at rates of =10-5 and 3 x 10-1 s-1. These results have a rate-dependence

 (Pb) = a  b

(3.18)

where below = 3 x 10-4 s-1, b = 0.15 and above, b = 0.035. For the lead extrusion damper (Figure 3.10) it was found that, for the two regions, b = 0.14 and 0.03. For slow creep other authors conclude that b = 0.13 (Birchenall (1959), Pugh (1970)). When the experimental errors are taken into account, all of these results are in reasonable agreement.

79

Figure 3.21: Rate dependence of lead cylinders of parabolic section (see insert) in shear, as indicated by the circled points. The crosses indicate the rate dependence of the lead plug in a lead rubber bearing. (Robinson, 1982.)

These results indicate that the lead rubber bearing has little rate-dependence at strain rates of 3 x 10-4 s-1 to 10 s-1, which includes typical earthquake frequencies of 10-1 to 1 s-1. For this range of strain rates, an increase in rate by a factor of ten causes an increase in force of only 8 per cent. Below strain rates of 3 x 10-4 s-1, the dependence of the shear stress on creep rate is greater, with a 40 per cent change in force for each decade change in rate. However, this means that at creep displacements of ~1 mm/h for a typical bearing 100 mm high (that is, at ~ 3 x 10-6 s-1), the shear stress has dropped to 35 per cent of its value at typical earthquake rates, ~ 1 s-1. Fatigue and Temperature The lead rubber bearing can be expected to survive a large number of earthquakes, each with an energy input corresponding to 3 to 5 strokes of +100 mm. For example, the results for a series of dynamic tests on the 650 mm diameter bearing with a 140 mm diameter lead plug are shown in Figure 3.22. The symbols F(a) and F(b) correspond to points such as a and b on Figure 3.17. F(a) and F(b) decreased by 10 and 25 per cent over the first five cycles but recovered some of this decrease in the five-minute breaks between tests.

Figure 3.22: Dynamic tests on lead rubber bearing over seven simulated earthquakes. (Robinson, 1982.)

80

An interval of 12 days between the last two tests did not give a greater recovery than that obtained in 5 minutes. The effect of the 24 cycles is shown more clearly by Figure 3.23, where the outer hysteresis loop is the first, and the inner loop is the twenty-fourth. The area of the twenty-fourth loop is 80 per cent of the first, indicating that the bearing has retained most of its damping capacity over these seven simulated earthquakes.

Figure 3.23: First and 24th hysteresis loops for lead rubber bearing shown in Figure 3.22. The outer loop is the first and the inner loop is the 24th. (Robinson, 1982.)

As a further check on the fatigue performance, the 356 mm bearing was dynamically tested at a shear strain of 0.5 for a total of 215 cycles in a two-day period. This bearing was also subject to 11,000 strokes at +3 mm (0.9 Hz), to demonstrate that it could withstand the daily cycles of thermal expansion which occur in a bridge deck over a period of 30 years. It performed satisfactorily. The 356 mm bearing was also studied with dynamic tests ( ~ 0.5, 0.9 Hz) at temperatures of -35, -15 and +45oC, to ensure its performance in extreme temperature environments. The ratio of the force F(b) to that at 18oC for the first cycle was 1.4, 1.2 and 0.9 at -35, -15 and +45oC respectively, showing that the lead rubber bearing is not strongly temperature-dependent (Robinson (1982). Effect of Vertical Load on Hysteresis As can be seen from the results of Figure 3.20, it is possible to design lead rubber bearings which have little change in their hysteresis loops over a wide range of vertical loads (Tyler & Robinson (1984). On the basis of a simple model, the nominal upper limit of hysteretic force, y(Pb)A(Pb), should be achieved if there is no vertical slippage of the plug sides and no horizontal slippage of the plug ends. Side slip can be made small by using a small spacing between the plates and by ensuring a large confining pressure po. Satisfactory results are achieved with a spacing t less than d/10, and with a pressure po, as given approximately by equation (3.8b) when S is greater than 10. The effect of end slip can be made small by using a lead plug with an adequate height to diameter ratio h/d, say not less than 1.5. Complicating factors include the hysteretic forces due to the lead which is extruded small distances into the spaces between the plates, additional forces which may increase overall hysteretic forces beyond their nominal upper limit. Again the confining pressure is enhanced, beyond that given by the vertical load, by inserting a lead plug whose volume exceeds that of the undeformed cavity in the bearing.

81

Bilinear Parameters for Small Earthquakes When the isolator motions arise from small earthquakes, with displacement spectra reduced by a factor of 2 or more, the bilinear loop parameters change in the same general way as the bilinear loop parameters for an isolator consisting of laminated rubber bearings mounted beside steel-beam dampers, with the same beneficial results. Reduced displacements cause considerable reductions in Qy and considerable increases in Kb2, as shown in Figure 3.24. As a net result, the effective (secant) period, and sometimes the hysteretic damping, falls more slowly, with decreasing earthquake severity, than they would with a fixed-parameter bilinear loop.

Figure 3.24:

(a) (b)

Difference in bilinear loop parameters corresponding to small and large displacements. Load-displacement loops for various strokes of lead rubber bearing used in Press Hall, Petone (see Chapter 6). (Robinson & Cousins, 1987, 1988.)

Summary of Lead Rubber Bearings For strain rates of ~1 s-1, the lead-rubber hysteretic bearing can be treated as a bilinear solid with an initial shear stiffness of ~10 Kb(r) and a post-yield shear stiffness of Kb(r). The yield force of the lead insert can be readily determined from the yield stress of the lead in the bearing, i.e. y(Pb) ~10.5 MPa. Thus the maximum shear force for a given displacement is the sum of the elastic force of the elastomeric bearing and the plastic force required to deform the lead. The actual post-yield stiffness is likely to vary by up to + 40 per cent from Kb(r) but will probably be within + 20 percent of this value. The initial elastic stiffness has only been estimated from the experimental results and may in fact be in the range of 9 Kb(r) to 16 Kb(r). The prediction for the maximum force, F(b), is more accurate and has instead an uncertainty of + 20 percent which is the same as expected for the uncertainty in the shear stiffness of manufactured elastomeric bearings. The actual area of the hysteresis loop formed by this bilinear model is approximately 20 per cent greater than the area of the measured hysteresis loop. The lead-rubber hysteretic bearing provides an economic solution to the problem of seismically isolating structures, in that the one unit incorporates the three functions of vertical support and horizontal flexibility (via the rubber) and hysteretic damping (by the plastic deformation of the lead). Further discussion on lead rubber bearings is contained in Robinson & Cousins (1987, 1988); Skinner et al (1980); Skinner, Robinson & McVerry (1991); Cousins, Robinson & McVerry (1991).

82

3.7

FURTHER ISOLATOR COMPONENTS AND SYSTEMS

A wide range of further isolator components, to provide flexibility and/or damping, have been used or proposed. Some of these isolator components are based on material properties, particularly those which provide flexibility and hysteretic damping forces, as in the cases of the isolator components described above. A second class of isolator components depends on sliding supports and on frictional damping forces. A third class of isolator components depends on geometrical factors such as rocking with uplift, or rolling surfaces, or pendulum action under gravity forces. Representative examples from each class of isolator component are described briefly below.

3.7.1

Isolator Damping Proportional to Velocity

In Chapter 2 it was found that linear isolators, with damping forces proportional to the velocity of isolator deformation, greatly attenuated the higher-mode seismic responses and floor spectra of the isolated structures. In contrast, it was found that high isolator damping, which departs severely from linear velocity dependence, gives smaller reductions in the seismic responses of higher modes. When small higher-mode seismic responses, or low floor spectra, are a design requirement then the benefits of high isolator damping can still be obtained by increasing the velocity-dependent damping. Bearings with High-Loss Rubber Velocity-dependent damping may be obtained using high-loss elastomers, or pitch-like substances, or hydraulic dampers with viscous liquids. The rubber bearings, which may be required for horizontally flexible supports, may use specially formulated and manufactured rubbers which give an effective isolator damping of about 15% of critical. These high damping rubbers are both very amplitude dependent and history dependent, for example, at a strain amplitude of 50% in the rubber during the first cycle of operation, the 'unscragged' state, the modulus is approximately 1.5 times that for the third and subsequent cycles, when 'scragged'. The original unscragged properties return in a few hours to days. The reduction of modulus between the unscragged and scragged state decreases as the strain amplitude increases. Future improvements in the energy absorption of rubbers are to be expected, but at present problems arise with creep under sustained loads, with non-linearity and temperature dependence of the damping forces, and with change of shape of the bearing at large displacements, giving rise to amplitude-dependent damping. Hydraulic Dampers It should be possible to develop effective velocity dampers, of adequate linearity, for a wide range of seismic isolator applications by utilising the properties of existing high-viscosity silicone liquids. In principle, the development of a velocity-dependent silicone-based hydraulic damper is straightforward. A double-acting piston might be used to drive the silicone liquid cyclically through a parallel set of tubular orifices, designed to give high fluid shears and hence the required velocity damping forces. By using a sufficient working volume of silicone fluid to limit the temperature rise to 40oC, during a design-level earthquake, the corresponding reduction in damper force is limited to about 25%. For comparison the thermal capacity, per unit volume, for silicone fluid is comparable to that for lead, or about 40% of that for iron. 83

The development of practical linear hydraulic dampers is complicated by a number of factors including the increase in silicone liquid volume with temperature, about 10% for a 100oC temperature rise, and also the tendency of the silicone liquid to cavitate under negative pressure. 3.7.2

PTFE Sliding Bearings

Non Lubricated PTFE Bearings The weight of a structure may be supported on horizontally moving bearings consisting of blocks of PTFE (polytetrafluoroethylene) sliding on plane horizontal stainless-steel plates. Starting about 1965, such bearings were used to provide low-friction supports for parts of many bridge superstructures. The coefficient of friction of a PTFE bridge bearing is typically of the order of 0.03, when operating at the very low rates arising from temperature cycling of the bridge superstructure. However, it is found that the coefficient of friction is very much higher, and is dependent on pressure and sliding velocity, when the operating velocity is typical of that which occurs in an isolator during a design-level earthquake, and when the operating pressure is typical of that adopted for PTFE bridge bearings (Tyler, 1977). For operating conditions typical of seismic isolator actions during design-level earthquakes, the frictional coefficients ranged from about 0.10 to 0.15 or more. Consider a set of the above PTFE bearings used as a seismic isolator. The first isolator period Tb1 arises from foundation flexibility only, and is typically very short. The second isolator period Tb2 tends to infinity and therefore provides no centring force to resist displacement drift. The yield ratio Qy/W is given by the bearing coefficient of friction and is therefore rather large and variable. The approximately-rectangular force-displacement loop gives very high hysteretic damping. However, absence of a centring force may result in large displacement drift if seismic inertia forces are substantially greater than the bearing frictional forces. Also high initial stiffness leads energy into higher modes, providing strong floor spectra of high frequencies. An isolator with a wider range of applications is obtained if part of the weight of the structure rests on PTFE bearings, while the remainder of the weight rests on rubber bearings. The reduced sliding weight reduces the yield ratio Qy/W, while the rubber bearings can be used to give an appropriate value for the centring force, as indicated by the second isolator period Tb2, which should usually be in the range between 2.0 and 4.0 seconds. Problems arising from a very short first period Tb1 may be removed by mounting the PTFE bearings on rubber bearings, as described below. Lubricated PTFE Bearings Lubricated PTFE bearings have quite small coefficients of friction, usually less than 0.02 (Tyler, 1977), for the pressures and velocities which they would encounter as seismic isolator mounts. When an isolator has low-friction load-support bearings, then components to provide centring and damping forces need not support weights. For example, approximately linear centring and damping forces could be provided by blocks of high-loss elastomer, for which creep is not a problem without sustained loads. If higher linear damping is required, hydraulic dampers could be added. However, since almost every isolator application is tolerant of at least a moderate degree of non-linearity, it should usually be possible to provide some of the centring and damping forces by non-linear components, such as weight-supporting lead rubber bearings. For high reliability, lubricated PTFE bearings should be serviced regularly. However, for high-technology applications, for example nuclear power plant isolation, maintenance should not present a serious problem. 84

3.7.3

PTFE Bearings Mounted on Rubber Bearings

In Chapter 2 it was found that a bilinear isolator with a short first period Tb1 results in relatively large higher-mode seismic accelerations and floor spectra. In Chapter 4 it is shown that these higher-mode seismic responses may be substantially reduced by increasing the first bilinear period Tb1 to exceed the first period of the unisolated structure T1(U). A compound isolator component developed in France (Plichon, et al, 1980) consisted of a sliding bearing mounted on top of a rubber bearing. Initially the bearings were made of lead-bronze blocks sliding on stainless steel, while later designs replaced the lead-bronze blocks by PTFE blocks. The flexibility of the laminated rubber components of the compound bearing can be chosen to give a first bilinear period Tb1 which exceeds T1(U), the first structural period. As in the previous section, the second bilinear period Tb2 may be limited to a value which prevents excessive displacement drift by supporting part of the structural weight directly on rubber bearings. This also reduces the value of Qy/W for the isolator. 3.7.4

Tall Slender Structures Rocking with Uplift

The seismic design loads and deformations of tall slender structures are normally associated with high overturning moments at the base level. If the narrow base of such a structure is allowed to rock with uplift, then the base moment is limited to that required to produce uplift against the restraining forces due to gravity. This base moment limitation will usually reduce substantially the seismic loads and deformations throughout the structure. The feet of a stepping structure are supported by pads which allow some rotation of the weightsupporting feet, while the overall structure rocks with uplift of other feet. Laminated rubber or lead slabs have been used to allow this rotation. These feet pads also accommodate small irregularities and slope mismatches between the feet and the supporting foundations. The stepping feet move in vertical guides which prevent 'walking', which would give horizontal or rotational displacements of the base of the structure. Rocking with stepping is particularly effective in reducing the seismic loads and deformations of top-heavy slender structures such as tower-supported water tanks (where the tanks should be slender or contain baffles to prevent large long-period sloshing forces during major earthquakes). Another top-heavy structure is a bridge with tall slender piers. The piers may be permitted to rock in a direction transverse to the axis of the superstructure, providing the superstructure can accommodate the resulting deformations. The seismic responses of a slender rocking structure are related in some ways to the responses of a structure with an approximately rigid-plastic horizontally-deforming isolator, but there are also major differences. For mode-1 seismic responses a rigid rocking structure may be assumed, with forces and displacements expressed as horizontal actions at the height of the centre of gravity. The cyclic force-displacement curve is then almost vertical for all forces below the uplift force (which corresponds to Qy with bilinear hysteresis) and almost horizontal for all displacements during uplift. The force-displacement curve is essentially bilinear elastic. An effective period may be derived using the secant stiffness for maximum seismic displacement. The effective damping will arise from any energy losses during structural and foundation deformations together with the contribution of any added dampers. The effective period and damping may then be used to relate the maximum seismic displacement to the earthquake displacement spectra, as in the case of any other non-linear isolator.

85

Since stepping isolation is a very non-linear constraint, and since the equivalent first isolator period Tb, is substantially less than the first period of the unisolated structure, the maximum seismic acceleration responses of the higher isolated modes are expected to be relatively large. With stepping the higher mode periods and shapes may be derived by assuming a zero base moment, instead of the zero base shear force assumed when the isolator acts horizontally. With rocking isolation there is always a substantial centring force, which is given by the uplift force. This centring force ensures that there is little drift displacement to add to the spectral displacement. The substantial centring force, and the high first stiffness, of the rocking isolator also ensure that there is very little residual displacement after an earthquake, even when substantial hysteretic dampers have been introduced. An early application of rocking with uplift, to increase the seismic resistance of a tall slender structure, is contained in a design study by Savage (1939). The 105 meter piers of the proposed Pit River road-rail bridge were designed with their bases free to rock with uplift under severe along-stream seismic loads. A New Zealand railway bridge at Mangaweka, over the Rangitikei River, with 69 meter piers, was designed and built with the pier feet free to uplift during severe along-stream seismic loads (see Chapter 8). A tall rocking chimney structure, built at Christchurch New Zealand, is described by Sharpe & Skinner (1983). 3.7.5

Further Components for Isolator Flexibility

Tall Columns and Free Piles Horizontal flexibility can be provided by tall first-storey columns or by free-standing piles. Such flexible columns must have adequate length to avoid Euler instability under combined gravity earthquake loads, while providing adequate horizontal flexibility. With tall columns, the end moments may be severe despite relatively low horizontal shears. With deep free-standing piles it is usually convenient to provide dampers and stops or buffers at the pile tops since it is usually practical to anchor them at this level. This approach has been used in Union House, Auckland, which uses steel cantilever dampers, and the Wellington Central Police Station, which uses lead-extrusion dampers (see Chapter 8). If tall columns are used to isolate a tower block it would be possible to anchor dampers to a surrounding high stiffness highstrength mezzanine structure. In both the above cases where isolation was provided by tall free-standing piles, the tall piles were required to support the structure on a high-strength soil which underlay a low-strength soil layer. The tall piles were made free-standing by surrounding them with clearance tubes. Basement boxes, supported on shorter piles and embedded in the surface layer, were used to provide anchors for the hysteretic dampers and the buffers. Hanging Links and Cables It is possible to provide horizontal flexibility by supporting a structure with hanging hinged links or with hanging flexible cables (Newmark & Rosenblueth, 1971). Effective pendulum lengths of 1.0 and 2.25 meters would give isolator periods of 2.0 and 3.0 seconds respectively. The necessary overlap of the supports and the structure can certainly be provided but in most cases this would be somewhat inconvenient and probably expensive, particularly for the longer links required for the longer isolator periods. When isolation is required for a relatively small item within a structure it would sometimes be appropriate to suspend it from anchors at a higher structural level.

86

Rollers, Balls and Rockers An object can be supported on rollers or balls, between hardened steel surfaces, to provide a very low resistance to horizontal displacement. Again the object may be supported on rockers with rolling contact on plane or curved upper and lower surfaces, with the curvatures of the 4 contacting surfaces chosen to give a gravity centring action. While simple in principle, the use of hard rolling surfaces to provide horizontally flexible isolator supports presents practical problems. These may include load sharing between the rolling components and the low load capacity of rolling units, particularly when only parts of the contacting surfaces are worked during the intervals between substantial earthquakes. It is therefore likely that rolling supports will normally be restricted to the isolation of special components of low or moderate weight.

3.7.6

Buffers to Reduce the Maximum Isolator Displacement

Isolator Maximum Displacement Isolators are normally designed to accommodate a travel greater than that which would occur during design earthquakes. However, during extreme low-probability earthquakes there is a possibility that the base of the structure will arrive at the end of the isolator design displacement when the structure still has considerable kinetic energy. If a stiff structure encounters a rigid base stop with considerable kinetic energy the ductility demand on the structure may be high, and may even substantially exceed the structure's design deformation capacity. The use of a resilient or energy-absorbing buffer can considerably increase the acceptable base impact velocity. There are two components of structural shear strain when its base impacts a stiff buffer. One is a transient shear pulse which travels up the structure, with attenuation, and is reflected successively at the top and base. This transient shear pulse can be attenuated substantially by having a buffer stiffness which is substantially less than the inter-storey stiffness. The other component is an overall shear deformation, which can be substantially reduced by having a buffer stiffness lower than the overall structural stiffness. This is not practical in all cases. During a low-probability extreme earthquake it is acceptable to permit much greater damage than is accepted for design-level earthquakes. The principal requirement is to prevent casualties and particularly to avoid the extreme hazard of structural collapse. Typically a seismic gap and buffer system should be designed to ensure that a structure does not collapse for a base displacement which would be from 50% to 100% greater (in the absence of a buffer), than that provided to accommodate design-level earthquakes. Omni Directional Buffers using Rubber in Shear Consider a structure mounted on laminated rubber bearings which have a maximum horizontal rubber shear strain of 100% under design earthquakes. Under earthquakes of twice this severity the bearings would deform to a strain of approximately 200%, and store 4 times the elastic energy. Suppose that the earthquake energy is not reduced by the presence of buffers (in fact it is likely to be reduced by 20% or 30%). The energy to be stored or absorbed in the buffers is three times that stored in the bearings on buffer impact. If stiff rubber shear buffers are used they will be required to store almost 3 times the energy in the bearings. For a shear strain of 3 in the rubber buffers the energy density is 9 times that of the bearings and hence the rubber volume required for the buffers is a third of that in the bearings. The stiffness of the buffers may be based on the maximum base shear acceptable for the structure under extreme earthquake conditions. 87

Omni Directional Buffers using Tapered Steel Beams Steel-beam buffers can be made omni directional in the same way as rubber buffers can. They may be designed to yield at a level which limits the base shear on the structure to an acceptable level. They may be of lower cost but more costly to install than equivalentcapacity rubber buffers. Operationally they are superior because of their yield-limited resistance force and because of the capacity to absorb most of the energy put into them. Buffer Anchors For many structures it will be difficult to provide buffer anchors of the desired strength. If the buffer anchors deform in a controlled way with an appropriate level of resistance, they may themselves function as buffers and greatly reduce the demands on a buffer device or even remove the need for added buffers. The basement box which provides stops for base displacement of the New Zealand Central Police Station has a level of soil and of pile resistance which allows it to provide considerable buffer action. Because the basement box is comparable in mass to a building storey, it is necessary to have a base-to-basement deformable interaction which has lower stiffness than the interstorey members, to attenuate impact shear pulses. Such a deformable interaction is provided by lead collars, around the columns near their tops, which may impact basement stops during extreme earthquakes. 3.7.7

Active Isolation Systems

Active Control of Isolator Parameters When it is necessary to control the floor accelerations accurately during frequent moderate earthquakes, it should be possible to exercise a large measure of control over isolator parameters by including a set of double-acting hydraulic dampers with their coefficient of velocity damping force under the direct control of electrical signals, which are a function of the measured floor accelerations and base displacements. In the event of control system failure or for large earthquakes, the isolator should revert to an essentially passive system, effective for severe earthquakes. It should be possible to check on the performance of this system by applying an artificial floor acceleration signal or by monitoring the response of the isolator by measuring its effect on ground micro tremors. Active Forces on Isolated Structures Where a very low level of vibration is important it would be possible, in principle, to use an active system to ensure a very low level of building horizontal vibrations. For example, the building could be supported on lubricated PTFE mounts and the active drive would only have to provide the low frictional losses in the mounts. In practice some additional power would be necessary to provide some centring action. The displacements required to accommodate such an isolator would be large during a major earthquake. The system would be most practical if it was only required to provide a high degree of isolation during frequent moderate earthquakes. To resist wind loads it would be necessary to provide some clamping system whenever wind loads exceed the force capacity of the isolator actuators. Alternatively the structure could be enclosed by wind shields, in special cases. A more practical system for many applications is likely to be a linear isolator which provides sufficient attenuation of the first mode(s) and an active system to further attenuate some of the small higher-mode responses, if necessary. 88

CHAPTER 4: 4.1

ENGINEERING PROPERTIES OF ISOLATORS

SOURCES OF INFORMATION

The plain rubber, high damping rubber and lead rubber isolators are all based on elastomeric bearings. The following sections describe the properties of these types of bearing manufactured from natural rubber with industry standard compounding. High damping rubber bearings are manufactured using proprietary compounds and vary from manufacturer to manufacturer. Some examples are provided of high damping rubber but if you wish to use this type of device you should contact manufacturers for stiffness and damping data. Examples of properties of devices in this chapter are from specific manufacturers and may vary with manufacturer. The properties show general characteristics but manufacturers literature should be consulted for specific values.

4.2

ENGINEERING PROPERTIES OF LEAD RUBBER BEARINGS

Lead rubber bearings under lateral displacements produce a hysteresis curve which is a combination of the linear-elastic force-displacement relationship of the rubber bearing plus the elastic-perfectly plastic hysteresis of a lead core in shear. The lead core does not produce a perfectly rectangular hysteresis as there is a “shear lag” depending on the effectiveness of the confinement provided by the internal steel shims. This is discussed further in the chapter on design procedures.

Actual Hysteresis

SHEAR FORCE

Bi-Linear Approximation

SHEAR DISPLACEMENT

Figure 4.1: Lead Rubber Bearing Hysteresis

The resultant hysteresis curve, as shown in Figure 4.1, has a curved transition on unloading and reloading. For design and analysis an equivalent bi-linear approximation is defined such that the area under the hysteresis curve, which defines the damping, is equal to the measured area. It is possible to model the bearing with a continuously softening element but this is not often used.

89

4.2.1

Shear Modulus

Elastomeric and lead rubber bearings are usually manufactured using rubber with a shear modulus at 100% strain ranging from about 0.40 MPa to 1.20 MPa. Typically, the rubber used for LRBs has only a slight dependence on applied strain, unlike the high damping rubber bearing, which is specifically formulated to have a high dependence on strain. Figure 4.2 shows the variation in shear modulus with shear strain for a rubber with a nominal shear modulus of 0.40 MPa. The shear modulus is about 10% higher than the nominal values for strains of 50%. Above 250% shear strain the rubber stiffens such that at 400% shear strain the modulus is 30% above the nominal value.

SHEAR MODULUS, G (MPa)

0.60 0.50 0.40 0.30

0.4 MPa Rubber 10 MPa Vertical Stress

0.20 0.10 0.00 0%

50%

100% 150% 200% 250% 300% APPLIED SHEAR STRAIN (%)

Figure 4.2:

350%

400%

Rubber Shear Modulus

As for all elastomeric bearings, the shear modulus has some dependence on vertical load. However, unless the vertical load is very high, the variation with vertical load is low, generally less than 10% and most often less than 5%.

4.2.2

Rubber Damping

Many technical publications on elastomer properties refer to the loss angle. The rubber loss angle, , is defined as the phase angle between stress and strain and is used in rubber technology to define the loss factor (or loss tangent) which is defined as the ratio between the loss modulus and the storage modulus:

G" tan   ' G where G" is the out-of-phase shear modulus and G' the in-phase shear modulus. This is a measure of the damping in the material. The materials standards ASTM D2231-94 provides Standard Practice for Rubber Properties in Forced Vibration but this is not generally used in structural engineering applications as it relates to smaller strain levels than are used for seismic isolation. To obtain damping properties for elastomeric bearings, it is usual to use the results from full size bearing tests rather than single rubber layers as specified in ASTM D2231. This is because factors such as flexing of the steel shims affect the total energy loss of the system. Damping is calculated from these tests using the ratio of the area of the hysteresis loop (analogous to the loss modulus) to the elastic strain energy (analogous to the storage modulus). 90

Most lead rubber bearings use a medium- to low-modulus natural rubber which is not compounded to provide significant viscous damping by hysteresis of the rubber material. All damping is assumed to be provided by the lead cores.

4.2.3

Cyclic Change in Properties

For lead rubber bearings the effective stiffness and damping are a function of both the vertical load and the number of cycles. There is a more pronounced effect on these quantities during the first few cycles compared to elastomeric bearings without lead cores. Test results from dynamic tests with varying load levels and shear strains to quantify these effects. Figures 4.3 and 4.4 show the variation in hysteresis and loop area versus cycle number for 380 mm (15") diameter lead rubber bearings. The test results plotted are for 100% shear strain and a vertical load of 950 KN (211 kips), corresponding to a stress of 9 MPa (1.3 ksi).

HYSTERESIS LOOP AREA (kip-in)

180 160

Test Frequency 0.01 hz

140

Test Frequency 0.10 hz Test Frequency 0.40 hz

120 100 80 60 40 20 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16

CYCLE NUMBER

Figure 4.3: Variation In Hysteresis Loop Area

10 Test Frequency 0.01 hz Test Frequency 0.10 hz Test Frequency 0.40 hz

EFFECTIVE STIFFNESS (kip/inch)

9 8 7 6 5 4 3 2 1 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

CYCLE NUMBER

Figure 4.4: Variation in Effective Stiffness

At slow loading rates there is a relatively small drop in loop area, Ah, and effective stiffness, Keff, with increasing cycles. For faster loading rates, the values at the first cycles are higher but there is a larger drop off. The net effect is that the average values over all cycles are similar for the different loading rates.

91

The design procedures and prototype test requirements are such that the design hysteresis loop area and effective stiffness are required to be matched by the average of three cycle tests at the design displacement. This test is considered to best match the likely earthquake demand on the bearings. The maximum reduction in loop area will be about 1% per cycle for the first 10 cycles but then the hysteresis loop stabilizes. The actual maximum reduction in loop area is a function of the dimensions of the isolator and lead core and the properties of the elastomer. There appears to be a size dependence on the variation in effective stiffness and hysteresis loop area with increasing number of cycles when bearings are tested at the actual expected frequency of response. For practical reasons, there are few test results of large isolation bearings which have been subjected to multiple cycles of the design displacement at the actual expected frequency of loading. One example is tests of large isolators with very large lead cores, approaching the maximum size likely to be used for LRBs. As such, the measured changes with increasing cycles are probably the extreme which might be experienced with this type of isolator.

Diameter (mm)

Height (mm)

820 870 1020 1020

332 332 332 349

Type 1 Type 2 Type 2M Type 3

Core Size (mm) 168 184 188 241

Applied Displacement (mm) 254 305 305 280

Shear Strain 139% 167% 167% 163%

Table 4.1: Isolator Dimensions

Figure 4.5 plots the ratio of hysteresis loop area (EDC = Energy Dissipated per Cycle) measured from each cycle to the requirement minimum loop area in the specification. Values are plotted for each of 15 cycles, which were applied at a frequency of 0.5 hz (corresponding to the isolation period of 2 seconds). 240% 220% Type 1 0 Deg Type 2 0 Deg Type 2M 0 Deg Type 3 0 Deg

200%

EDC / EDC Minimum

180% 160% 140% 120% 100% 80% 60% 40% 1

2

3

4

5

6

7

8

9

10

11

12

13

CYCLE

Figure 4.3: Cyclic Change in Loop Area

92

14

15

Figure 4.5 shows that the initial loop area is well above the specified minimum and remains higher for between 6 and 8 cycles. By the end of the 15 cycles the EDC has reduced to about 60% of the specified value. Figure 4.5 plots the ratios from the 1st and 15th cycles and the mean ratios over all cycles. This shows that the mean value is quite close to the specified minimum. The reduction in loop area is apparently caused by heat build up in the lead core and is a transient effect. This is demonstrated by the results in Figure 4.6 as each isolator was tested twice, once at zero degrees and the bearing was then rotated by 90 degrees and the test repeated. As the figure shows, the initial EDC for the Cycle 1 of the second test was similar to the 1st cycle of the preceding test, not the 15th cycle. This indicates that most of the original properties were recovered and it is likely than total recovery would have occurred with a longer interval between tests. 250%

Cycle 1 Cycle 15 Average

TEST EDC / EDC Min

200%

150%

100%

50%

Type 3 90 Deg

Type 3 0 Deg

Type 2M 90 Deg

Type 2M 0 Deg

Type 2 90 Deg

Type 2 0 Deg

Type 1 90 Deg

Type 1 0 Deg

0%

Figure 4.4: Mean Cyclic Change in Loop Area

Actual earthquakes would rarely impose anything like 15 cycles at the design displacements. Most time history analyses show from 1 to 3 cycles at peak displacements and then a larger number of cycles at smaller displacements. If there are near fault effects there is often only a single cycle at the peak displacement. Figure 4.5 shows that the LRBs will provide at least the design level of damping for this number of cycles. 4.2.4

Age Change in Properties

The rubber tests on compounds used for LRBs show an increase in hardness by up to 3 Shore A after heat aging. This increase in hardness is equivalent to an increase in shear modulus of 10%. The increase in shear modulus would have a lesser effect on the total bearing stiffness as the lead core yield force is stable with time. In service, the change in hardness for bearings would be limited to the outside surface since the cover layer prevents diffusion of degradants such as oxygen into the interior. Therefore, average effects would be less than the 10% value. For unprotected natural rubber in service over 100 years (for example, Rail Viaduct in Melbourne, Australia) the deterioration was limited to approximately 1.5 mm (0.06 inches) from the exposed surface. 93

There is not much information on direct measurement of the change in stiffness properties with time of loaded elastomeric bearings. One example was machine mountings manufactured in 1953 and in service continuously in England. In 1983, after 30 years, two test bearings which had been stored with the machine were tested again and were found to have increased in stiffness by 15.5% and 4.5%. A natural rubber bearing removed from a freeway bridge in Kent showed an increase in shear stiffness of about 10% after 20 years service. Since the time that the bearings above were manufactured, considerable advances have been made in environmental protection of the bearings. It is predicted that changes in stiffness of the elastomer will be no more than 10% over the design life of the isolators. The net effect on isolator effective stiffness at seismic displacements would be about one-half this value. Damping would not be effected by aging of LRBs as the rubber damping is negligible compared to that provided by the lead core.

4.2.5

Design Compressive Stress

The design procedures used to calculate vertical load capacity are based on a rated load (limiting strain) approach, as incorporated in codes such as AASHTO and BS5400. The effective allowable compressive stress is a function of (1) the ultimate elongation of the rubber (2) the safety factor applied to the ultimate elongation (3) the bearing plan size (4) the bearing shape factor and (5) the applied shear strain. For long term gravity loads (displacement = 0) a factor of 1/3 is applied to the elongation at break. For short term seismic loads (displacement > 0) a factor of 0.75 is applied to the elongation for DBE loads and 1.0 for MCE loads. Additional rules are used based on experience to ensure that the bearings will perform satisfactorily. For example, it is generally required that the effective bearing area (area of overlap between top and bottom plates) be at least 20% of the gross area at maximum displacement. The result of this procedure is that the allowable compressive stress is a function of the bearing size and the applied displacement. Ultimate compressive stresses are calculated by the same procedure as for allowable stresses except that a factor of 1.0 is applied to the elongation at break to obtain the load capacity.

4.2.6

Design Tension Stress

Elastomeric based bearings such as LRBs and HDR bearings have in the past been designed such that tension does not occur. This is because there is little design information for rubber bearings under this type of load. As successive code revisions have increased seismic loads, it has provided very difficult to complete isolation designs such that no tension occurs and some designs do permit tension on the isolators. Provided high quality control is exercised during manufacture, elastomeric bearings can resist a high tension without failure. Bearings (without lead cores) have been tested to a tensile strain of 150% at failure, as shown in Figure 4.7. The tension stiffness is approximately elastic to a stress of 4 MPa at a strain of approximately 15%. The stiffness then reduces as cavitation occurs and remains at a low stiffness to a strain of 150%.

94

The rubber used for the bearing in Figure 4.7 has a shear modulus G = 1.0 MPa. The isolator design procedures permit an ultimate compression stress of 3G, which would permit a tensile stress of 3 MPa (30 kgf/cm2) for this bearing. As shown in Figure 4.7, this level of stress provides an adequate factor of safety before cavitation occurs.

Figure 4.5: Tension Test on Elastomeric Bearing

The tests above were for plain bearings under pure tension. Lead rubber bearings for the have also been tested under combined shear and tension at close to the design limit (2.4G versus 3G limit) to a shear strain of 225% (Table 8-2). The bearings were undamaged under these conditions. The maximum uplift displacement was approximately 12 mm ( ½”).

Type A 920

Type B 970

Tension Force (KN) Tension Stress (MPa)

549 0.89 (2.4G)

608 0.88 (2.4G)

Displacement (mm) Shear Strain

686 225%

686 225%

Diameter (mm)

Table 4.2: Combined Shear and Tension Tests

4.2.7

Maximum Shear Strain

As discussed above for allowable vertical compressive stresses, the load capacity is calculated based on a total strain formulation where the strain due to compression and the applied shear strain are combined and required to be less than a specified fraction of the elongation at break.

95

The converse applies for ultimate shear strain, where the maximum shear strain that can be applied depends on the concurrent vertical strain. Although the formulas produce a maximum shear strain based on concurrent vertical loads, empirical limits are also applied to the shear strain based on experimental evidence. Generally, the limiting shear strain is taken as 150% for DBE loads and 250% for MCE loads, unless the design formulas provide a lower limit. Testing of lead rubber bearings at high shear strain levels have shown that failure in lead rubber bearings occurs between 300% and 350% shear strain. The bearings without lead cores can survive imposed shear strains of 400%. Table 4.3 summarizes test results for lead rubber bearings (LRB), high damping rubber bearings (HDR) and LRBs without the lead core (R).

BEARING

HITEC 150 kip HITEC 500 kip HITEC 750 kip

LRB LRB LRB

Diam. D0 (mm) 450 620 620

PEL

HDR

450

8.8

305

340%

0.22

762% (2)

R R R R R R R

350 350 500 500 500 500 500

-5.5 -2.7 2.5 7.5 10.0 15.0 20.0

84 140 250 250 400 250 250

155% 250% 250% 250% 400% 250% 250%

Vert 0.61 0.40 0.40 0.11 0.40 0.40

Strain (3) 363% (4) 282% (5) 347% 854% 444% 509%

JQT Tension JQT Shear/Tens JQT Shear/Comp.

Type

Vert Stress (MPa) 4.7 8.0 12.0

Max. Disp (mm) 335 434 381

Shear Strain

Effect. Area

320% 339% 190%

0.11 0.16 0.24

Total Strain 925% (1) 795% (1) 614% (2)

Table 4.3: High Shear Test Results

Notes to Table 4.1: 1. The 150 kip and 500 kip HITEC specimens were tested to failure. 2. The 500 kip HITEC bearing was cycled to 15” displacement but the equipment was not sufficient to perform the failure test. The 18” bearing in the PEL test was cycled to 340% strain without failure. 3. The Japanese Tension test was to failure under pure tension at an ultimate tensile strain of 155%. 4. The Japanese combined shear/tension test was for 5 cycles at 150% and 5 cycles at 250% shear strain. Failure did not occur. 5. Failure did not occur in any of the Japanese combined shear/compression tests 6. LRB indicates Lead Rubber Bearing, HDR indicates high damping rubber bearings, R indicates LRB without lead core.

96

4.2.8

Bond Strength

The bond strength defines the adhesion between the rubber layers and the internal steel shims. Specifications typically require that the adhesive strength between the rubber and steel plates be at least 40 lb/inch when measured in the 90 peel test specified by ASTM D429, Method B. Failure is required to be 100% rubber tear. All compounds used for LRBs should meet this requirement.

4.2.9

Vertical Deflections

The initial vertical deflections under gravity loads are calculated from standard design procedures for elastomeric bearings. For bearings with a large shape factor the effects of bulk modulus are important and are included in the calculation of the vertical stiffness on which deflection calculations are based. Elastomeric bearings are stiff under vertical loads and typical deflections under dead plus live load are usually of the order of 1 mm to 3 mm (0.04 to 0.10 inches).

Long Term Vertical Deflection Creep is defined as the increase in deformation with time under a constant force and so is the difference between short term and long term deflection. In rubber, creep consists of both physical creep (due to molecular chain slippage) and chemical creep (due to molecular chain breakage). For structural bearings the physical deformation is dominant. Chemical effects, for example oxidation, are minimal since the bulk of the bearing prevents easy diffusion of chemicals into the interior. Therefore, chemical effects can be ignored. Natural rubber generally offers the greatest resistance to creep compared to all other rubbers. The actual values depend on the type and amount of filler as well as the vulcanization system used. Creep usually does not exceed more than 20% of the initial deformation in the first few weeks under load and at most a further 10% increase in deformation after a period of many years. The maximum long term deflections for design purposes are conservatively taken to be 1.5 times the short term values. A detailed case study has been made of a set of bearings over a 15 year period. The building, Albany Court in London, was supported on 13 bearings of capacity from 540 KN to 1800 KN (120 kips to 400 kips). Creep was less than 20% of the original deflection after 15 years.

Vertical Deflection Under Lateral Load Under lateral loads there will be some additional vertical deflections as the bearing displaces laterally. Generally, this deformation is relatively small. Figure 4.8 is an example of a combined compression shear test in which vertical deformations were measured.

97

The bearing is displaced to a shear displacement of 508 mm (20”) under a vertical load of 2500 KN (550 kips). The initial vertical deflection when the load is applied is 2.5 mm (0.1”) which increases to a maximum of approximately 4.6 mm (0.18”) at the 508 mm lateral displacement. The most severe total vertical deflection measured was 12.4 mm (0.49”) at a lateral displacement of 686 mm (27”). Based on these results, allowance in design should be made for about 15 mm (0.6”) vertical downward movement at maximum displacements. SHEAR FORCE vs DISPLACEMENT (per Bearing) A2h10 150

100

kip

Force

50

0

-50

Actual T heoretical

-100

-150 -30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

Dis plac ement inch

COMPRESSION LOAD an d D ISPL ACEMEN T A2h 10 570

0.050

560 0.000

-0.050

L oad Displacement

530

-0.100

520

inch

kip

Axial Load

540

Displ acement

550

510 -0.150 500

490 -30.00

-0.200 -20.00

-10.00

0.00

10.00

20.00

30.00

Shear Di spl acement inch

Figure 4.6: Combined Compression and Shear Test

Wind Displacement For LRBs, resistance to wind loads is provided by the elastic stiffness of the lead cores. Typical wind displacements for projects have ranged from 3.5 mm (0.14”) under a wind load of 0.01W to 11 mm (0.43”) under a load of 0.03W. The cores are usually sized to have a yield level at least 50% higher than the maximum design wind force.

Comparison of Test Properties with Theory The discussions above, and the design procedures in Chapter 5, are based on theoretical formulations for LRB design. A summary of test results from nine projects in Table 4.4 compares the theoretical values with what can be achieved in practice:

98

Project

Plan Size mm

 Mm

Design KEFF KN/mm

Design EDC KN-mm

Test KEFF KN/mm

Test EDC KN-mm

KTEST / KDESIGN

EDCTEST / EDC DESIGN

1.

662

264

1.42

115720

1.41

143425

99%

124%

2.

875

58.2

11.51

640

12.02

741

104%

116%

3.

420 365 1100 1000

158 104 113 125

0.91 0.91 9.51 11

220 90 1240 1790

0.922 1.008 10.336 11.406

286 117 1712 2381

101% 111% 109% 104%

130% 130% 138% 133%

4.

686 686

76 76

6.00 6.85

511 407

5.04 6.00

542 397

84% 88%

106% 98%

5.

686 686 686

206 185 261

12.69 15.09 12.57

127102 136246 202082

14.17 14.65 12.11

184823 167792 266662

112% 97% 96%

145% 123% 132%

6.

500

169

1.27

81870

1.20

97425

94%

119%

7.

813 864 1016 1016

254 305 305 279

13.28 14.14 19.63 28.76

166764 233058 240030 369989

13.97 14.32 20.44 29.44

201625 303581 346672 554355

105% 101% 104% 102%

121% 130% 144% 150%

8.

1219

406

13.95

500748

13.43

482803

96%

96%

9.

914 965

508 508

6.81 7.45

240259 241059

7.16 7.89

294894 307124

105% 106%

123% 127%

Table 4.1: LRB Test Results

Of the 19 isolators tested in Table 4.4, the effective stiffness in 13 was within 5% of the design value and a further 3 were within 10%. One test produced a stiffness 12% above the design value and two were respectively –12% and –16% lower than the design values. These last two were for the same project (Project 4) and were the result of a rubber shear modulus lower than specified. Specifications generally require the stiffness to be within 10% for the total system and allow 15% variation for individual bearings. The hysteresis loop area (EDC) exceeded the design value for 17 of the 19 tests. Three tests were lower than the design value, by a maximum of 4%. Specifications generally require the EDC to be at least 90% of the design value, with no upper limit.

99

4.3 ENGINEERING PROPERTIES OF HIGH DAMPING RUBBER ISOLATORS

SHEAR FORCE

High damping rubber bearings are made of specially compounded elastomers which provide equivalent damping in the range of 10% to 20%. The elastomer provides hysteretic behavior as shown in Figure 4.9.

SHEAR DISPLACEMENT

Figure 4.9: High Damping Rubber Hysteresis

Whereas the properties of lead rubber bearings have remained relatively constant over the last few years, there have been continuous advances in the development of high damping rubber compounds. These compounds are specific to manufacturers as they are a function of both the rubber compounding and the curing process. Although the technical literature contains much general information on HDR, there is not a lot of technical data specific enough to enable a design to be completed. The information in these sections relates to a specific compound developed for a building project. This can be used for a preliminary design. In terms of currently available compounds it is not a particularly high damping formulation, so design using these properties should be easily attainable. If you wish to use HDR, the best approach is probably to issue performance based specifications to qualified manufacturers to get final analysis properties.

4.3.1

Shear Modulus

The shear modulus of a HDR bearing is a function of the applied shear strain as shown in Figure 4.10. At low strain levels, less than 10%, the shear modulus is 1.2 MPa or more. As the shear strain increases the shear modulus reduces, in this case reaching a minimum value of 0.4 MPa for shear strains between 150% and 200%. As the shear strain continues to increase the shear modulus increases again, for this compound increasing by 50% to 0.6 MPa at a strain of 340%. The initial high shear modulus is a characteristic of HDR and allows the bearings to resist service loads such as wind without excessive movement. The increase in shear stiffness as strains increases beyond about 200% can be helpful in controlling displacements at the MCE level of load, which may cause strains of this magnitude. However, they have the disadvantage of increasing force levels and complicating the analysis of an isolated structure on HDR bearings.

100

14

1.4 1.2 Damping Shear Modulus

10

1.0

8

0.8

6

0.6

4

0.4

2

0.2

0 0

50

100

150

200

250

300

Shear Modulus MPa

Equivalent Viscous Damping %

12

0.0 350

Shear Strain %

Figure 4.10: HDR Shear Modulus and Damping

4.3.2

Damping

Although the majority of the damping provided by HDR bearings is hysteretic in nature there is also a viscous component which is frequency dependent. These viscous effects may increase the total damping by up to 20% and, if quantified, can be used in design. Viscous damping is difficult to measure across a full range of displacements as the power requirements increase as the displacements increase for a constant loading frequency. For this reason, viscous damping effects are usually quantified up to moderate displacement levels and the results used to develop a formula to extrapolate to higher displacements. Figure 4.11 shows the equivalent viscous damping for a load frequency of 0.1 hz, a slow loading rate at which viscous effects can be assumed to be negligible. For strains up to 100%, the tests used to develop these results were also performed at a loading rate of 0.4 hz (period 2.5 seconds), an average frequency at which an isolation system is designed to operate. The damping at 0.4 hz was higher than that at 0.1 hz by a factor which increased with strain. At 25% the factor was 1.05 and at 100% the factor was 1.23. The frequency dependency indicates the presence of viscous (velocity dependent) damping in the elastomer. The velocity increases proportionately to the frequency and so the high frequency test gives rise to higher viscous damping forces. The tests at various strain levels are performed at the same frequencies and so the velocity increases with strain. The velocities are four times as high at 100% strain as at 25%. This is why the factor between the 0.4 hz and 0.1 hz damping increases. The added viscous damping adds approximately 20% to the total damping for strains of 100% or greater, for this compound increasing the damping from 8% to 9.6%.

101

Equivalent Viscous Damping %

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Extrapolated Data

0.1 hz Damping 0.4 hz Damping 1.2 x 0.10 hz Damping

0

20

40

60

80

100

120

140

160

180

200

Shear Strain %

Figure 4.11: Viscous Damping Effects in HDR

4.3.3

Cyclic Change in Properties

The properties of a HDR bearing will change under the first few cycles of loading because of a process known as “scragging”. When a HDR bearing is subjected to one or more cycles of large amplitude displacement the molecular structure is changed. This results in more stable hysteresis curves at strain levels lower to that at which the elastomer was scragged. Partial recovery of unscragged properties is likely. The extent of this recovery is dependent on the compound.

12

0.5

10

0.4

8

0.3

6

0.2

4

Shear Modulus Equivalent Damping

0.1

2

0

EQUIVALENT DAMPING %

SHEAR MODULUS (psi)

VARIATION WITH REPEATED CYCLES STRAIN = 100% 0.6

0 1

2

3

4

5

6

7

8

9

10

LOADING CYCLE NUMBER

Figure 4.12: Cyclic Change in Properties for Scragged HDR

When HDR bearings are specified the specifications should required one to three scragging cycles at a displacement equal to the maximum test displacement. You should request information from each manufacturer as to scragging effects on a particular compound to enable you to decide on just how many scragging cycles are needed. Once a HDR bearing has been scragged the properties are very stable with increased number of cycles, as shown in Figure 4.12.

102

4.3.4

Age Change in Properties

Although most HDR compounds have a more limited service record than other natural rubber formulations the same additives to resist environmental degradation are used as for other elastomers and there is no reason to suspect that they will have a shorter design life. However, as the compounds are so specific to particular manufacturers you should request data from potential suppliers. The specifications will require the same accelerated (heat) aging tests as for lead rubber bearings.

4.3.5

Design Compressive Stress

HDR bearings are generally designed using the same formulas as for LRBs and so the comments in the sections on LRBs also apply.

4.3.6

Maximum Shear Strain

The maximum shear strains for LRBs usually have an empirical limit which may restrict the shear strain to a lesser value than permitted by the design formulas. These limits are related to performance of the lead core and so do not apply to HDR bearings. The maximum shear strain is based on the limiting strain formulas and may approach 300% for MCE loads, compared to a 250% limit for LRBs. The higher shear strain limits for HDR bearings may result in a smaller plan size and lower profile than a LRB, for a smaller total volume. However, this also depends on the levels of damping as the displacements may differ between the two systems. 4.3.7

Bond Strength

The bond strength requirements are the same as for LRBs previously.

4.3.8

Vertical Deflections

The vertical stiffness, and so deflections under vertical loads, is governed by the same formulas as for LRBs and so will provide similar deflections for similar construction although the specific elastomer properties may cause more differences.

Long Term Vertical Deflections HDR bearings are cured differently from LRBs and have higher creep displacements. The compression set (after 22 hours at 158F) may be as high as 50%, compared to less than 20% for low damping rubber compounds. This may cause an increase in long term deflections and you should seek advice from the supplier on this design aspect.

103

4.3.9

Wind Displacements

HDR bearings generally rely on the initially high shear modulus to resist wind loads and do not require a supplemental wind restraint. The wind displacement can be calculated using compound-specific plots of shear modulus versus shear strain. This may require an iterative procedure to solve for a particular lateral wind load. There have been no reported instances of undue wind movements in buildings isolated with HDR bearings.

4.4 ENGINEERING PROPERTIES OF SLIDING TYPE ISOLATORS Most specifications for sliding bearings require that the sliding surface be a self-lubricating polytetrafluoroethylene (PTFE) surface sliding across a smooth, hard, non-corrosive mating surface such as stainless steel. There are two types of sliding isolators commonly used: 1.

Curved slider bearings (the Friction Pendulum System) providing the total isolation system.

2.

Sliding bearings in parallel with other devices, usually with HDR or LRB.

The former application uses proprietary products and the detailed information on the sliding surfaces, construction etc. will be provided by the supplier. The information supplied should provide the information described here for other sliding devices. Most applications which have used sliding bearings to provide part of the isolation system have been based on “pot” bearings, a commercially available bearing type which has long been used for non-seismic bridge bearings. For light loads, such as under stairs, a simpler sliding bearing can be constructed by bonding the PTFE to an elastomeric layer. Pot-type bearings have a layer of PTFE bonded to the base of the "pot" sliding on a stainless steel surface. The "pot" portion of the bearing consists of a steel piston, inside a steel cylinder, bearing on a confined rubber layer. The pot allows rotations of typically up to at least 0.20 radians. Figure 4.13 shows a schematic section of the bearing.

Slide Plate

Recessed PTFE Confined Elastomer

Pot

Cylinder

Figure 4.7: Section through Pot Bearings

104

Stainless Steel Sliding Surface

The pot bearing in Figure 4.13 is oriented with the slide plate on top. The bearing can also be oriented with a reversed orientation and the slide plate at the bottom. The option of the slide plate on the top has the advantage that debris will not settle on the stainless steel slide surface but the disadvantage that under lateral displacements the eccentricity will cause secondary moments in the structure above the isolation plane. With the slide plate on the bottom the moments due to eccentricity will be induced in the foundation below the isolator which will often be better able to resist these moments. In this case, either wipers or a protective skirt may be required to prevent debris settling on the slide plate. The reason for selecting pot bearings rather than simply PTFE bonded to a steel plate is that in many locations some rotational capability is required to ensure that during earthquake displacements the load is evenly distributed to the PTFE surface. This may be achieved by bonding the PTFE to a layer of rubber or other elastomer. However, the advantage of a pot bearing is that the elastomer is confined and so will not bulge or extrude under high vertical pressures. In this condition, the allowable pressure on the rubber is at least equal to that on the PTFE and so more compact bearings can be used than would otherwise be required. Methods of protecting the sliding surface should be considered as part of supply. Pot bearings which have been installed on isolation projects previously have used wipers to clear debris from the sliding surface before it can damage the PTFE/stainless steel interface.

4.4.1

Dynamic Friction Coefficient

The coefficient of friction of PTFE depends on a number of factors, of which the most important are the sliding surface, the pressure on the PTFE and the velocity of movement. Data reported here is that developed for pot bearings based on tests of bearings used for a building project. For this project tests showed that the minimum dynamic coefficient for a velocity < 25 mm/sec (1 in/sec) ranged from 2.5% to 8% depending on pressure. These results were from a wide range of bearing sizes and pressures. The mean coefficient of friction at low speeds was 5% at pressures less than 13.8 MPa (2 ksi) decreasing to 2% at pressures exceeding 69 MPa (10 ksi). The high load capacity test equipment used for the full scale bearings was not suitable for high velocity tests and so the maximum dynamic friction coefficient was obtained from two sources: 1. A series of tests were performed at the University of Auckland, New Zealand (UA), using bearing sizes of 10 mm, 25 mm and 50 mm (3/8”, 1” and 2”) diameter. The effect of dynamic coefficient friction versus size was determined from these tests. 2. Additional data was obtained from State University of Buffalo tests performed on 254 mm (10”) bearings using the same materials (Technical Report NCEER-88-0038). This data confirmed the results from the UA tests.

105

COEFFICIENT OF FRICTION

0.14 0.12 0.10 0.08 0.06 p = 7 Mpa (1 ksi)

0.04

p = 14 Mpa (2 ksi) p = 21 Mpa (3 ksi)

0.02

p = 45 Mpa (6.5 ksi)

0.00 0

100

200

300

400

500

600

VELOCITY (mm/sec)

Figure 4.14: Coefficient of Friction for Slider Bearings

Figure 4.14 plots the coefficient of friction for 254 mm (10") bearings. The test results from the UA series of tests showed some size dependence, as the maximum dynamic coefficient of friction for velocities greater than 500 mm/sec (20 inch/sec) was approximately 40% higher for 50 mm (2 inch) diameter bearings compared to 254 mm (10 inch) bearings.

4.4.2

Static Friction Coefficient

On initiation of motion, the coefficient of friction exhibits a static or breakaway value, B, which is typically greater than the minimum coefficient of sliding friction. This is sometimes termed static friction or stiction. Table 4.5 lists measured values of the maximum and minimum static friction coefficient for bearing tests from 1000 KN (220 kips) to 36,500 KN (8,100 kips). These values are plotted in Figure 4.15 with a power "best fit" curve. As for the dynamic coefficient, the friction is a function of the vertical stress on the bearing. At low stresses (10 MPa) the static coefficient of friction is about 5% and the maximum sticking coefficient almost two times as high (9%). At high pressures (70 MPa) the static coefficient is approximately 2% and the sticking coefficient up to 3%. The ratio of the maximum to minimum depends on the loading history. A test to ultimate limit state overload invariably causes a high friction result immediately after.

106

Type

Vertical Vertical Sticking Minimum Load Stress Friction Speed (kips) (ksi) Coefficient Friction % Coefficient % 36500KN 2028 1.51 4.92 4.30 8100 kip 4056 3.01 3.40 2.96 8111 6.03 3.00 2.60 11333 8.42 2.70 2.44 23500KN 5200 kip

1306 2611 5222 7833

1.51 3.03 6.06 9.09

5.48 3.90 3.00 2.22

4.58 3.40 2.68 1.94

7800KN 3900 kip

989 1978 3956 5933

1.48 2.96 5.91 8.86

6.28 4.36 2.62 2.34

5.10 3.50 2.42 2.04

15400KN 3400 kip

856 1711 3422 5133

1.46 2.94 5.87 8.81

7.00 4.54 2.90 2.22

5.74 3.94 2.52 1.96

9100KN 2000 kip

506 1011 2022 3033

1.70 3.39 6.78 10.17

6.38 4.98 3.32 2.66

5.54 3.96 2.92 2.40

3000KN 670 kip

167 333 667 1067

1.48 2.96 5.91 9.46

7.18 3.90 2.88 2.30

5.52 3.02 2.50 1.92

1000KN 220 kip

56 111 222 356

1.49 3.00 5.99 9.58

7.16 4.74 3.22 2.80

6.04 4.24 2.72 2.26

Table 4.2 : Minimum/Maximum Static Friction

107

10 9

Sticking Friction Slow Speed Friction Best Fit (Slow Speed) Best Fit (Sticking)

Coefficient of Friction %

8 7 6 5 4 3 2 1 0 0

10

20

30

40

50

60

70

80

Vertical Stress (MPa) Figure 4.8: Static and Sticking Friction

4.4.3

Effect of Static Friction on Performance

An isolation system which was formed of a hybrid of flat sliding and high damping rubber bearings was studied extensively to assess the effect of static friction on the forces transmitted into the superstructure. The sliding friction element used for the study has a sliding force which is a function of the velocity and pressure on the element. The coefficient of friction is continually updated during the time history analysis as either of these parameters change. The element also has a sticking factor where the initial coefficient of friction is factored by a sticking factor which reduces exponentially over a specified travel distance. For this project the response with a sticking factor of 2.0 was assessed. 60,000

FRICTION FORCE (KN)

40,000 20,000 0 0

1

2

3

4

5

-20,000 -40,000 -60,000

No Sticking Sticking Factor 2.0

-80,000 TIME (seconds)

Figure 4.9: Time History with Sticking

108

6

Figure 4.16 shows the effect of the sticking factor on the time history of friction force. The structure has a weight of 400,000 KN on the sliding bearings, a static coefficient of friction of 4% and a maximum coefficient of friction of 10%. The maximum coefficient of friction produces a sliding force of 40,000 KN. Because the sticking initially occurred at the lower coefficient of friction, the sticking factor of 2.0 increased the maximum force by a lesser factor, increasing the force by 50% to 60,000 KN. Figure 4.17 shows the force-displacement function over the same time period shown in Figure 4.16. 60,000

FRICTION FORCE (KN)

40,000 20,000 0 -100 -20,000

-50

0

50

100

150

200

250

-40,000 No Sticking Sticking Factor 2.0

-60,000 -80,000

DISPLACEMENT (mm)

Figure 4.10: Hysteresis with Sticking

The isolation system comprises sliding bearings supporting 35% of the seismic weight and high damping rubber bearings supporting the remaining 65%. Figure 4.18 plots the hysteresis curves for each of these isolator components and the total hysteresis for the combined system.

FRICTION FORCE (KN)

150,000 TFE Bearings HDR Bearings Total Force

100,000 50,000 0 -150

-100

-50

0

50

100

150

200

250

300

-50,000 -100,000 DISPLACEMENT (mm)

Figure 4.11

Combined Hysteresis with Sticking

The effects of the static breakaway friction are dissipated over relatively small displacements and after displacements of 50 mm or more the effects are negligible. The HDR bearings provide a force which increases with increasing displacement and so the sticking force is not as high as the force which occurs at maximum displacement when the maximum HDR force is added to the friction force at maximum velocity.

109

This type of evaluation can be used on projects which contain sliding bearings as one component to determine the maximum weight which can be supported on sliders such that the breakaway friction does not govern maximum forces.

4.4.4

Check on Restoring Force

The UBC requires systems without a restoring force to be designed for a displacement equal to three times the design displacement. This has a large impact on P- forces, the size of the separation gap and the cost of separating services and components. Wherever possible, systems should be designed to provide a restoring force. The definition of a restoring force is that the force at the design displacement is at least 0.025W greater then the force at one-half the design displacement. Calculations for the restoring force for the example described above are listed in Table 8-6. This design just achieves the UBC definition of a system containing a restoring force. As this system had 35% of the weight on sliders, an upper limit of 30% should be used for preliminary design to ensure that the restoring force definition is achieved.

Design Displacement Force at Design Displacement, FDD

245 mm 121,915 KN = 0.107W

½ Design Displacement Force at ½ Design Displacement, F0.5DD

122 mm 93,859 KN = 0.082W

FDD – F0.5DD = 0.107W – 0.082W

0.025W  0.025 W Ok

Table 4.3: Calculation of Restoring Force

The restoring force requirement is absolute, not earthquake specific, and so may cause problems in low seismic zone when total forces, as a fraction of seismic weight, are low. For such zones it may not be possible to use sliders as part of the isolation system and still comply with the UBC requirement for a restoring force. However, in low seismic zones it may be practical to design and detail for three times the computed seismic displacement anyway.

4.4.5

Age Change in Properties

PTFE is about the best material known to man for corrosion resistance, which is why there is difficulty in etching and bonding it. For base isolation use, the PTFE is dry/non lubricated and any changes over the design life will be minor. Tests confirm little change in friction over several thousand cycles such as occurs in a bridge with daily and seasonal movements due to thermal stresses.

110

4.4.6

Cyclic Change in Properties

As the PTFE slides on the stainless steel surface under high pressure and velocity there is some flaking of the PTFE and these flakes are deposited on the stainless steel surface. As the total travel distance increases (over 2 meters) a thin film of PTFE will build up on the stainless steel. This will result is some reduction of the coefficient of friction. A maximum MCE displacement would be about 12 m (assuming 10 cycles, 1200 mm travel per cycle). At the frequency of an isolation system  would probably decrease about 10% over this travel. Extreme testing performed at the University of Sydney measured a heat build up in TFE of about 250F after 250 cycles at  100 mm amplitude and 0.8 hz frequency. After 100 cycles of this load (approximately 40 m travel) the coefficient of friction had reduced to approximately one-half the original value.

4.4.7

Design Compressive Stress

Typical allowable bearing stresses for service loads are 45 MPa (6.5 ksi) for virgin PTFE and 60 MPa (8.7 ksi) for glass filled PTFE.

4.4.8

Ultimate Compressive Stress

The ultimate bearing stress is 68 MPa (9.85) ksi for virgin TFE and 90 MPa (13.0 ksi) for glass filled TFE.

4.5 DESIGN LIFE OF ISOLATORS Most isolation systems are based on PFTE and natural rubber bearings which have a long record of excellent in-service performance. As part of prototype testing, rubber tests including ozone testing and high temperature tests to simulate accelerated aging are performed to ensure the environmental resistance and longevity of the system. All steel components of the elastomeric based bearings are encased in a protective cover rubber except for the load plates. These plates are usually coated with a protective paint. The protective coating system adopted for the Museum of New Zealand, which had a specified 150 year design life, was a deposited metal paint system.

4.6 FIRE RESISTANCE Isolation bearings are generally required to achieve a fire rating equivalent to that required for the vertical load carrying assemblies. One of two approaches can be used to provide acceptable fire rating with the method used decided on depending on specific project needs: 1. Design surrounding flexible protective "skirts" for the bearings as was done for Parliament Buildings. 2. Rate the resistance of rubber itself based on vertical load, dimensions and fire loading to determine whether it is more economical to provide the fire rating by providing extra cover rubber to the bearing. 111

4.7 EFFECTS OF TEMPERATURE ON PERFORMANCE Elastomeric bearings are usually compounded from natural rubber and so are subjected to temperature constraints typical to this material. The upper operating range of service temperature for natural rubber, without special compounding, is 60C (140F) and so the upper limit of the design temperatures for most projects will not cause any problems. The stiffness of natural rubber is a function of temperature but within the range of -20C to 60C (-5F to 140F) the effect is slight and not significant in terms of isolation performance. Below -20C the stiffness gradually increases as the temperature is lowered until at about – 40C (-40F) it is double the value at 20C (68F). The variation in stiffness is reversible as temperature is increased. As an example of the assessment of the effect of extreme low temperatures, the base isolation properties for a bridge project in a cold region were calculated assuming the shear modulus was increased by a factor of 2. Figure 4.19 illustrates the effect on maximum pier and bent forces in the longitudinal direction.

LONGITUDINAL BENT FORCE (KN)

1000 900 800 700

No Base Isolators

600

With Base Isolators at 20F With Base Isolators at -40C

500 400 300 200 100 0 Bent 2

Pier 3

Bent 4

Figure 4.19: Effect of Low Temperatures

The Pier 3 longitudinal force increased by 25%. The transverse Pier 3 force increased by 18%. Bent 2 and 4 forces were essentially unchanged as the force was determined by the elastic stiffness which is only a weak function of rubber shear modulus. For this project, if a design earthquake occurred at temperatures below -20C the pier forces could increase, with a maximum increase of about 25% at the extreme low temperature. The probability of a design level earthquake occurring while temperatures are below -20C is probably low, although this depends on the temperature distribution at the bridge site. If the probability was considered significant, and the increased forces could lead to substructure damage, the isolators could be modified to ensure that the forces at minimum temperature did not exceed target values.

4.8 TEMPERATURE RANGE FOR INSTALLATION For bridge isolation projects, base isolators are designed to resist the maximum seismic displacements plus the total R+S+T (creep, shrinkage and thermal) displacements. Therefore, the temperature of installation does not matter from a technical perspective. For aesthetic reasons it is desirable to install the bearings at as close to mean temperature as possible so that the bearings are not in a deformed configuration for most of their service life. 112

CHAPTER 5: ISOLATION SYSTEM DESIGN

5.1 INTRODUCTION This Chapter describes a design procedure for seismic isolation systems. Many isolation systems use a combination of elastomeric bearings types (lead-rubber, high damping rubber and plain rubber) which are designed specifically for the applied loads and displacements. Other isolation solutions, such as sliding systems and the friction pendulum system, are based on devices which are designed by the supplier for the particular application. The design procedures here are used to design elastomeric bearing types and perform a preliminary assessment of the performance of an isolation system which incorporates one or more types of device. The procedure is suitable for design office use to select the types and properties of devices which will achieve the desired performance. The design characteristics developed by the procedure are used as input to a detailed analysis and evaluation of the isolated structure. Because of the complexity of hardware design, and empirical aspects of design for most types of isolators, it is usual to obtain assistance from manufacturers. As base isolation technology has evolved, manufacturers have realized that structural engineers do not have the skills to design hardware and so will provide this assistance. There are codes available (U.S, British and Australian) which provide design rules for devices used in isolation, such as elastomeric bearings and Teflon sliding bearings. However, most of these codes are for non-seismic bridge applications and need to be adapted to use for seismic isolation applications.

5.1.1

Assessing Suitability

Not all structures are suited for seismic isolation and the first stage in the design procedure is to check suitability. The checks should examine the need for isolation, the suitability of the site and the suitability of the particular structure. Table 5.1 lists some of the items which should be assessed prior to commencing any detailed design. Some structures are more suited than others to isolation, as listed in Table 5.2. Most examples of isolated buildings fall into one or more of these categories. This does not exclude other building types, but most projects will have one or more of (1) requirements for continuing operation (2) low ductility (3) historic merit or (4) valuable contents.

113

Item 1. Need for Isolation Level of Earthquake Risk

Checks

Seismic Design Requirements 2. Site Suitability Geologic Conditions

Is Earthquake Design Required?. Seismic isolation is best suited for moderate and high seismic areas. If seismic design adds to costs significantly, then isolation is likely to be more effective. Potential for resonance effects may rule out isolation (e.g. Mexico City). Stiff Soil is best for isolation. As site conditions become softer, isolation becomes less effective and more expensive. Near fault motions may add to the response at the isolated periods. If the distance to the nearest active fault is small isolation displacements may be excessive.

Site Subsoil Conditions Distance to Fault

3. Structure Suitability Weight of the Structure

Heavy structures tend to be the most cost effective to isolate. Generally, the period of the non-isolated structure should be less than 2 seconds, although there are exceptions. Isolators are usually placed in a crawl space or basement. If a slag-on-grade is planned, this will need to be replaced with a suspended floor. Large aspect ratio of the structural system (height to width ratios) may cause overturning problems. For bridges, tall piers may make the period too long. For retrofit, assess how difficult to separate the structure from the ground.

Period of the Structure Structural Configuration

Table 5.1: A Suitability Check List

Type of Building Essential Facilities Health Care Facilities Old Buildings Museums Manufacturing Facilities

Reasons for Isolating Functionality High Importance Factor, I Functionality High Importance Factor, I Preservation Low R Valuable Contents Continued Function High Value Contents

Table 5.2: Most Suitable Buildings for Isolation

114

5.1.2

Design Development for an Isolation Project

If a project appears to be a suitable candidate for isolation, the level of design of the isolation system depends on the procurement strategy to be adopted for the isolation system. Specifications will be either prescriptive or performance based on some combination of the two, as listed in Table 5.3. A prescriptive specifications provides details of the devices to be supplied (materials, dimensions etc.) as for other structural components such as steel frames, concrete walls etc. A performance specification states the performance to be achieved and requires the suppliers to design devices to meet this performance (such as for a design-and-build contract). Each of these approaches has advantages and disadvantages and in most cases a combined specification is most effective. In this case, the engineer would supply properties of a complying system (e.g. effective stiffness and damping for HDR devices) but also supply the expected performance of this system to allow vendors of other systems to design and bid systems with at least equal performance.

Description Specify detailed device characteristics, including stiffness and damping. May specify sizes.

Specify performance requirements of the isolation system (period, displacement, and damping).

Advantages Prescriptive Specification. Structural engineer retains control.

Disadvantages Requires the structural engineer to be expert in isolation design.

Simple to evaluate bids.

Limits potential bidders. May not be optimal system. Performance Based Specification Does not require expertise Difficult to evaluate bids. in device design. Wider range of bidders.

Vendors design devices.

May need to check analysis of a large number of systems.

Less engineering effort at design stage. Combined Prescriptive / Performance Specification Specify a complying Widest range of bidders. Requires design expertise. system as for prescriptive approach. List performance of this system and allow other devices that can match this.

Most likely to attract optimal design.

Table 5.3: Procurement Strategies

115

Difficult to evaluate bids. May need to check analysis of a large number of systems.

5.2 DESIGN EQUATIONS FOR ELASTOMERIC BEARING TYPES 5.2.1

Codes

The vertical load capacity of elastomeric isolation bearings has traditionally been based on a limiting strain formulation as implemented in the British codes BS 5400 and BE 1/76. These codes were intended for non-seismic applications where lateral forces are from sources such as traffic loads and thermal movements in bridges. The U.S. AASHTO bridge code provides rules for vertical load capacity of elastomeric bearings subjected to earthquake induced displacements. This code adjusts the factors of safety from the British codes to be more appropriate for short duration, infrequently occurring loads.

5.2.2

Empirical Data

For lead rubber bearings some of the procedures are based on empirical data, in particular the effective yield stress of the lead core and the elastic (unloading) stiffness. The values reported here are typical of those used by manufacturers, based on a database of test results for this type of bearing assembled from projects from 1978 to the present. The values used have been shown to give an accurate estimate of force levels and hysteresis loop areas. However, specific manufacturers may recommend different data for their bearings. 5.2.3

Definitions

The symbols and definitions used in engineering design and in codes sometimes differ from the scientific terminology used in earlier chapters of this book. In this chapter, the symbols have the meaning defined below. Ab Ag

= =

Gross area of bearing, including side cover

Ah

=

Area of hysteresis loop (Also termed EDC = energy dissipated per

Apl Ar

=

cycle) Area of Lead core

=

Reduced rubber area

= = = = = = = = = =

Overall plan dimension of bearing Bonded plan dimension of bearing Elastic modulus of rubber 3.3 to 4.0 G depending on hardness Buckling Modulus Effective Compressive Modulus Bulk Modulus Factor applied to elongation for load capacity 1 / (Factor of Safety) Force in bearing at specified displacement

= = = = = =

Acceleration due to gravity Shear modulus of rubber (at shear strain ) Height free to buckle Moment of Inertia of Bearing Material constant (0.65 to 0.85 depending on hardness) Yielded stiffness of lead rubber bearing = Kr

B Bb E Eb Ec E f

Fm

g G Hr I k Kd

Bonded area of rubber

116

Keff

=

Kr

=

Lateral stiffness after yield

Ku

=

Elastic Lateral stiffness

Kv Kvi

=

Vertical stiffness of bearing

=

Vertical stiffness of layer i

n p P Pcr P Qd

= = = = = =

Si ti

=

Number of rubber layers Bonded perimeter Applied vertical load Buckling Load Maximum rated vertical load Characteristic strength (Force intercept at zero displacement) Shape factor for layer i

=

Rubber layer thickness

tsc

=

Thickness of side cover

=

Thickness of internal shims

Tpl Tr

=

Thickness of mounting plates

=

Total rubber thickness

W

=

Total seismic weight

 m y  c sc sh sr u

= = = = = = = = =

Applied lateral displacement Maximum applied displacement Yield displacement of lead rubber bearing Equivalent viscous damping Compressive Strain Shear strain from applied vertical loads Shear strain from applied lateral displacement Shear strain from applied rotation Minimum elongation at break of rubber

 y

= =

Applied rotation Lead yield stress

tsh

5.2.4

Effective Stiffness

Range of Rubber Properties

Rubber compounds used for isolation are generally in the hardness range of 37 to 60, with properties as listed in Table 5.4. As compounding is a continuous process intermediate values from those listed are available. As seismic demands have increased over the last 10 years the softer rubbers tend to be used more often. The lowest stiffness rubber has a shear modulus G of about 0.40 MPa although some manufacturers may be able to supply rubber with G as low as 0.30 MPa. There is uncertainty about the appropriate value to use for the bulk modulus, K, with quoted values ranging from 1000 to 2000 MPa. The 1999 AASHTO Guide Specifications provide a value of 1500 MPa and this is recommended for design.

117

Hardness IRHD2

37 40 45 50 55 60

Young’s Modulus E (MPa) 1.35 1.50 1.80 2.20 3.25 4.45

Table 5.4:

5.2.5

Shear Modulus G (MPa) 0.40 0.45 0.54 0.64 0.81 1.06

Material Constant k 0.87 0.85 0.80 0.73 0.64 0.57

Elongation at Break Min, % 650 600 600 500 500 400

Vulcanized Natural Rubber Compounds

Vertical Stiffness and Load Capacity

The dominant parameter influencing the vertical stiffness, and the vertical load capacity, of an elastomeric bearing is the shape factor. The shape factor of an internal layer, Si, is defined as the loaded surface area divided by the total free to bulge area:

Si 

B 4t i

for square and circular bearings

for lead rubber bearings, which have a hole for the lead core,

Si 

5.2.6

A b  A pl

(5.1a)

(5.1b)

πB b t i

Vertical Stiffness

The vertical stiffness of an internal layer is calculated as:

K vi 

Ec A r ti

(5.2)

where the compressive modulus, Ec, is a function of the shape factor and material constant as follows:



E c  E 1  2kS 2i



(5.3)

In the equation for vertical stiffness, a reduced area of rubber, Ar, is calculated based on the overlapping areas between the top and bottom of the bearing at a displacement, , as follows (see Figure 5.1):

  A r  A b 1   Bb

  

for square bearings

118

(5.4a)

   A r  0.5B 2 sin 1   Bb  where



B

2 b

 2



        for circular bearings

(5.4b)

Shaded = Overlap Area

ELEVATION

RECTANGULAR

CIRCULAR

Figure 5.1: Effective Compression Area

When the effective compressive modulus, Ec, is large compared to the bulk modulus E then the vertical deformation due to the bulk modulus is included by dividing Ec by 1 + (Ec /E) to calculate the vertical stiffness. Bulk modulus effects are included when the vertical stiffness is used to calculate vertical deformations in the bearing but not the shear strains due to vertical load. The 1999 AASHTO Guide Specifications are an exception to this – see below.

5.2.7

Compressive Rated Load Capacity

The vertical load capacity is calculated by summing the total shear strain in the elastomer from all sources. The total strain is then limited to the ultimate elongation at break of the elastomer divided by the factor of safety appropriate to the load condition. The shear strain from vertical loads, sc , is calculated as 119

 sc  6S i  c

(5.5)

where

c 

P

(5.6)

K vi t i

If the bearing is subjected to applied rotations the shear strain due to this is

B   sr  b 2t i Tr 2

(5.7)

The shear strain due to lateral loads is

 sh 

 Tr

(5.8)

For service loads such as dead and live load the limiting strain criteria are based on AASHTO 14.5.1P

f u   sc

where f = 1/3 (Factor of safety 3)

(5.9a)

And for ultimate loads which include earthquake displacements

f u   sc   sh where f = 0.75

(Factor of safety 1.33)

(5.9b)

Combining these equations, the maximum vertical load, P, at displacement  can be calculated from:

P 

K vi t i f u   sh  6S i

(5.10)

Codes used for buildings and other non-bridge structures (e.g. UBC) do not provide specific requirements for calculating elastomeric bearing load capacity. Generally, the total strain formulation from AASHTO is used with the exception that the Maximum Considered Earthquake (MCE) displacement is designed using f = 1.0.

5.2.8

AASHTO 1999 Requirements

The 1999 AASHTO Guide Specifications generally follow these same formulations but make two adjustments: 1. The total strain is a constant value for each load combination, rather than a function of ultimate elongation. Using the notation of this section, AASHTO defines a strain due to non-seismic deformations, s,s and a strain due to seismic displacements, s,eq. The limits are then:  sc  2.5 (5.11a)

 sc   s ,s   sr  5.0

(5.11b)

 sc   s ,eq  0.5 sr  5.5

(5.11c) 120

2. The shear strain due to compression, sc, is a function of the maximum shape factor:

 sc 

3SP 2 Ar G (1  2kS 2 )

For S  15, or

 sc 

3P(1  8GkS 2 / E  ) 4GkSAr

For S > 15.

(5.12a)

(5.12b)

Equation (5.12a) for S  15 is a re-arranged form of the Equation (5.5) with the approximation that E = 4G. The formula for S > 15 has approximated (1+2kS2)  2kS2 and adjusted the vertical stiffness for the bulk modulus effects. There is no universal agreement regarding the inclusion of bulk modulus effects in load capacity calculations and it is recommended that the 1999 AASHTO formulas be used only if the specifications specifically require this (see Section 4.3 for discussion).

5.2.9

Tensile Rated Load Capacity

For bearings under tension loads, the stiffness in tension depends upon the shape of the unit, as in compression, but limited available data suggests that the stiffness under tension is much less than the compression stiffness. Due to lack of definitive data, the same equations are used as for compressive loads as tension except that the strains are the sum of absolute values. When rubber is subjected to a hydrostatic tension of the order of 3G, cavitation may occur. This will drastically reduce the stiffness. Although rubbers with very poor tear strength may rupture catastrophically once cavitation occurs, immediate failure does not generally take place. However, the subsequent strength of the component and its stiffness may be affected. Therefore, the isolator design should ensure that tensile stresses do not exceed 3G under any load conditions. Because of the low tension strength relative to compressive strength, and the uncertainty about tensile stiffness, elastomeric based bearings should not be used in locations where there may be significant tensions. In practice, design should be such as to avoid all tension loads under the design basis earthquake but permit limited tensions, up to 3G, for the maximum earthquake.

5.2.10 Bucking Load Capacity For bearings with a high rubber thickness relative to the plan dimension the elastic buckling load may become critical. The buckling load is calculated using the Haringx formula as follows: The moment of inertia, I is calculated as 4

B I b 12 B 4 I b 64

for square bearings

(5.13a)

for circular bearings

(5.13b) 121

The height of the bearing free to buckle, that is the distance between mounting plates, is

H r  (nt i )  (n  1)t sh

(5.14)

An effective buckling modulus of elasticity is defined as a function of the elastic modulus and the shape factor of the inner layers:

E b  E(1  0.742S 2i )

(5.15)

Constants T, R and Q are calculated as:

Hr Tr R  K rHr

T  E bI

Q

(5.16) (5.17)



(5.18)

Hr

From which the buckling load at zero displacement is:

 R 4TQ 2  1 P   1 2  R  0 cr

(5.19)

For an applied shear displacement the critical buckling load at zero displacement is reduced according to the effective "footprint" of the bearing in a similar fashion to the strain limited load:

Pcr  Pcr0

Ar Ag

(5.20)

The allowable vertical load on the bearing is the smaller of the rated load, P, or the buckling load.

5.2.11 Lateral Stiffness and Hysteresis Parameters for Bearing Lead rubber bearings, and elastomeric bearings constructed of high damping rubber, have a nonlinear force deflection relationship. This relationship, termed the hysteresis loop, defines the effective stiffness (average stiffness at a specified displacement) and the hysteretic damping provided by the system. A typical hysteresis for a lead rubber bearing is as shown in Figure 5.2.

122

Figure 5.2: Lead Rubber Bearing Hysteresis

For design and analysis this shape is usually represented as a bilinear curve with an elastic (or unloading) stiffness of Ku and a yielded (or post-elastic) stiffness of Kd. The post-elastic stiffness Kd is equal to the stiffness of the elastomeric bearing alone, Kr. The force intercept at

zero displacement is termed Qd, the characteristic strength, where:

Q d   y A pl

(5.21)

The theoretical yield level of lead, y, is 10.5 MPa (1.5 ksi) but the apparent yield level is generally assumed to be 7 MPa to 8.5 MPa (1.0 to 1.22 ksi), depending on the vertical load and lead core confinement. The post-elastic stiffness, Kd, is equal to the shear stiffness of the elastomeric bearing alone:

Kr 

G A r

(5.22)

Tr

The shear modulus, G, for a high damping rubber bearing is a function of the shear strain , but is assumed independent of strain for a lead rubber bearing manufactured from natural rubber and with standard cure. The elastic (or unloading) stiffness is defined as: Ku  Kr for elastomeric bearings

 12 A pl K u  6.5K r 1  Ar  or

K u  25K r

   

(5.23a) (5.23b)

for lead rubber bearings (5.23c)

For lead rubber bearings, the first formula for Ku was developed empirically in the 1980’s to provide approximately the correct stiffness for the initial portion of the unloading cycle and to provide a calculated hysteresis loop area which corresponded to the measured areas. The bearings used to develop the original equations generally used 12.7 mm (½”) rubber layers and doweled connections. By the standard of bearings now used, they were poorly confined. Test results from more recent projects have shown that the latter formula for Ku provides a more realistic estimate for many configurations of LRBs. 123

The shear force in the bearing at a specified displacement is:

Fm  Q d  K r 

(5.24)

from which an average, or effective, stiffness can be calculated as:

K eff 

Fm 

(5.25)

The sum of the effective stiffness of all bearings allows the period of response to be calculated as:

Te  2

W gK eff

(5.26)

Seismic response is a function of period and damping. High damping and lead rubber bearings provide hysteretic damping. For high damping rubber bearings, the hysteresis loop area is measured from tests for strain levels, , and the equivalent viscous damping  calculated as given below. For lead rubber bearings the hysteresis area is calculated at displacement level m as:



A h  4Q d  m   y



(5.27)

from which the equivalent viscous damping is calculated as:



1 2

 Ah   K 2  eff

   

(5.28)

The isolator displacement can be calculated from the effective period, equivalent viscous damping and spectral acceleration as: 2

S T  m  a 2e 4 B

(5.29)

where Sa is the spectral acceleration at the effective period Te and B is the damping factor, a function of  which is obtained from the appropriate code. The Eurocode EC8 provides a formula for the acceleration at damping  relative to the acceleration at 5% damping as:

 (T , )   ( t ,5)

7 2 

(5.30)

Where  is expressed as a percent of critical damping. UBC and AASHTO provide tabulated B coefficients, as listed in Table 5.5. FEMA-356 provides a different factor for short and long periods but generally the factor Bl would apply for all isolated structures. This has the same values as the UBC and AASHTO. In Table 5.5 the reciprocal of the EC8 value is listed alongside the equivalent factors from FEMA-356. EC8 provides for a greater reduction due to damping than the other codes and seem to relate to the short period values, Bs, from FEMA-356. 124

Effective Damping  % of Critical

50

B Factor FEMA 356 (Periods > To) AASHTO UBC 0.8 1.0 1.2 1.5 1.7 1.9 2.0

Eurocode EC8

0.75 1.00 1.31 1.77 2.14 2.45 2.73

Table 5.5: Damping Coefficients

The formula for m includes Te and B, both of which are themselves a function of m. Therefore, the solution for maximum displacement includes an iterative procedure. 5.2.12 Lead Core Confinement The effect of inserting a lead core into an elastomeric bearing is to add an elastic-perfectly plastic component to the hysteresis loop as measured for the elastomeric bearings. The lead core will have an apparent yield level which is a function of the theoretical yield level of lead, 10.5 MPa, (1.58 ksi) and the degree of confinement of the lead. As the confinement of the lead increases the hysteresis of the lead core will move more towards an elasto-plastic system as shown in Figure 5.3. Confinement is provided to the lead core by three mechanisms: 1

The internal shims restraining the lead from bulging into the rubber layers.

2

Confining plates at the top and bottom of the lead core.

3

Vertical compressive loads on the bearings.

The confinement provided by internal shims is increased by decreasing the layer thickness, which increases the number of shims providing confinement. Earlier lead rubber bearings used doweled and then bolted top and bottom mounting plates. Current practice is to use bonded mounting plates, which provides more effective confinement than either of the two earlier methods.

Figure 5.3: Effect of Lead Confinement

125

The degree of confinement required also increases as the size of the lead core increases. Smaller diameter cores, approximately B/6, tend to have a higher apparent yield level than cores near the maximum diameter of B/3. The effective stiffness and loop area both reduce with the number of cycles. The effective stiffness is essentially independent of axial load level but the loop area varies proportional to vertical load. During an earthquake some bearings will have decreased loop area when earthquake induced loads act upwards. However, at the same time instant other bearings will have increased compressive loads due to earthquake effects and so an increased loop area. The net effect will be little change in total hysteresis area based on an average dead load. Lead core confinement is a complex mechanism as the lead is flowing plastically during seismic deformations and the elastomer must be considered to be a compressible solid. These features preclude explicit calculations of confinement forces. Manufacturers generally rely on their databases of prototype and test results plus manufacturing experience to ensure that the isolators have adequate confinement for each particular application. This is then demonstrated by prototype tests. For long term loads, lead will creep and the maximum force in the core will be less than the yield force under suddenly applied loads. For structures such as bridges where non-seismic displacements are applied to the bearings this property will affect the maximum force transmitted due to creep, shrinkage and temperature effects. Tests at slow loading rates have shown that for loads applied over hours or days rather than seconds the stress relaxation in the lead is such that the maximum force in the lead will be about one-quarter the force for rapid loading rates. Therefore, for slowly applied loads the maximum lead core force is assumed to be F = 0.25 Qd.

5.3 BASIS OF AN ISOLATION SYSTEM DESIGN PROCEDURE

3.00

45%

2.50

40%

2.00

35%

1.50

30%

1.00

25%

Effective Period Equivalent Damping

0.50

20%

0.00 0

50

100

150

200

250

300

ISOLATOR DISPLACEMENT (mm)

Figure 5.4: Isolator Performance

126

350

15% 400

EQUIVALENT VISCOUS DAMPING

EFFECTIVE PERIOD (Seconds)

Most isolation systems produce hysteretic damping. Both the effective period and damping are a function of displacement, as shown in Figure 5.4 for a lead rubber bearing. Similar curves can be developed for other types of device.

Because of this displacement dependence, the design process is iterative. A further complication arises for elastomeric types of bearing in that, as well as period and damping, the minimum plan size of the bearing is also a function of displacement. 5.3.1

Elastomeric Based Systems

For elastomeric based systems, the iterative process involves the size and properties of the devices. Initial bearing plan sizes are determined, based on maintaining a factor of safety of at least 3 under maximum vertical loads in the undeformed configuration. The number of rubber layers, and the lead core sizes if any, is then set by a trial-and-error procedure to achieve the required seismic performance. As the damping is a function of displacement, this requires an iterative procedure which can be implemented using standard design office tools. The iterative procedure can be automated, for example, by using spreadsheet macros, but there is no guarantee that convergence will be achieved as there are limits on effective periods and damping using practical isolators. Generally, the higher the vertical load on an elastomeric bearing the easier it will be to achieve long effective periods. 5.3.2

Sliding and Pendulum Systems

Both flat and curved sliding systems can be designed using the same procedure as outlined above but is generally simpler in that the device properties are not a function of dimensions. The isolation system properties are defined by two parameters: 1. The characteristic strength, defined as W where  is the coefficient of friction for the sliding surface and W is the total seismic weight. 2. The post-yielded stiffness is defined as zero for a flat slider or W/R for a spherical slider. The steps above are then used to iterate to solve for the isolated displacement. 5.3.3

Other Systems

The design procedure can be used for any type of isolation system which can be approximated with a softening bi-linear hysteresis loop, that is, the yielded stiffness is less than the elastic stiffness, or for which tabulated values of damping and stiffness versus displacement are available. For devices that do not have these characteristics, special design procedures may need to be developed.

5.4 STEP-BY-STEP IMPLEMENTATION OF A DESIGN PROCEDURE This section describes the step-by-step implementation of a design procedure, which can be performed manually but is best automated using design tools such as Excel or MathCad. The procedure is based on the manual selection of, and adjustment to, isolator sizes. It is difficult to develop an automatic optimization routine because of constraints imposed by practical bearing sizes and properties. Example spreadsheets with this procedure implemented for bridges and buildings are supplied with this book. These spreadsheets are described later with the bridge and building isolation design examples. 127

Figure 5.5 illustrates the steps in implementing the isolation system design procedure. Many of the steps relate to calculations involving the properties and capacities of elastomeric devices and so the procedure is simplified for sliding and FPS types of isolators.

1. Define Seismic Input (e.g. UBC, NZS 1170, AASHTO) 2. Define bearing types (e.g. LRB, HDR, PTFE), material properties and load data 3. Set assumed bearing dimensions (plan size, height, core size)

Elastomeric based systems only

4. Calculate bearing properties for assumed sizes

Elastomeric based systems only

5. Calculate seismic performance for DBE and MCE 6. Calculate load capacity under maximum displacements for a. Gravity b. DBE c. MCE

Elastomeric based systems only

7. Assess factors of safety and performance at DBE and MCE levels. 8. If necessary, adjust bearing sizes in Step 3. above.

Elastomeric based systems only

Figure 5.5: Design Procedure Flow Chart

5.4.1

Example to Illustrate Calculations

The design procedure is illustrated using numerical values for a simplified design of a health facility as shown in Figure 5.6. This building has a lateral load system comprising perimeter concrete moment frames and internal steel chevron braces. The internal steel columns have high axial loads, and the potential for uplift. The isolation system selected for this building is a combination of 27 lead rubber bearings at the perimeter and 4 flat slider bearings, one under each internal steel column. The flat sliding bearings are PTFE on stainless steel. To permit rotations due to possible uplift, pot type bearings would be used at these internal locations. 128

Figure 5.6: Example Building

5.4.2

Design Code

The example provided in this section is based on design to 1997 UBC requirements. Designs based on other codes follow the same general principles. The main differences between different codes are in specification of the seismic input. UBC, in common with most codes, has a constant velocity for isolation periods (periods, T, greater than 1 second). A constant spectral velocity simplifies design as the acceleration is inversely proportional to T and the displacement is directly proportional to T. However, the procedure can be adjusted if necessary to calculate response for design spectra which are not based on constant spectral velocity. The design procedures used for elastomeric based bearings such as lead rubber and high damping rubber are derived from the AASHTO 1991 Guide Specifications. These could be relatively simply modified to incorporate changes in the AASHTO 1999 Guide Specifications although these seem to be conservative relative to other codes. Building codes do not specify the design methods for individual bearings but rather require prototype tests which are in the nature of proof tests. Experience has shown that design to 1991 AASHTO, rather than the more conservative 1999 AASHTO, produces designs which can demonstrate stability in proof tests.

5.4.3

Units

The example calculations here are in the SI units of kN and mm. The procedure will work with any consistent set of units. Care must be taken to ensure that parameters such as the gravitational constant, g, are in the correct units. Also, properties generally expressed as MPa, such as E and G, must be converted to kN, mm.

129

5.4.4

Seismic and Building Definition

The project definition parameters for the example building are listed in Table 5.6. The information provided defines the seismic loads and the structural data required in terms of the UBC requirements for evaluating performance. Other codes define the seismic input differently and may have differing requirements for torsion. 1. The seismic information is extracted from UBC tables for the particular site. This requires the zone, soil type and fault information. For UBC design, the parameters are used to derive coefficients CV and CVM which define the spectral acceleration for a given period. These are for the two levels of load defined in the UBC, respectively DBE (Design Basis Earthquake) and MCE (Maximum Capable or Maximum Considered Earthquake). For other codes, equivalent formulations of these coefficients will be defined. 2. The isolated lateral force coefficient, RI is the factor by which isolated elastic design forces are reduced. For UBC design, the response modification coefficient, R, and importance factor, I, for an equivalent fixed base building are required as they form a limitation on base shear. Note that, for base isolated structures, the importance factor is assumed to be unity for all structures in the UBC. As for the seismic coefficients, other codes may specify different response modification factors and the procedure for developing design forces from the elastic response may need to be adjusted. 3. Building dimensions are required to estimate the torsional contribution to the total isolation system displacement. The formula listed in Table 5.6 is that provided by the UBC. The project definition information is specific to a project and, once set, does not need to be changed as different isolation systems are assessed and design progresses.

130

Seismic Zone Factor, Z Soil Profile Type Seismic Coefficient, CA

0.4 SB 0.400

Table 16-I Table 16-J Table 16-Q

Seismic Coefficient, CV

0.480

Table 16-R

Near-Source Factor Na

1.000

Table 16-S

Near-Source Factor Nv

1.200

Table 16-T

MCE Shaking Intensity MMZNa

0.484

Calculated

MCE Shaking Intensity MMZNv

0.581

Calculated

Seismic Source Type Distance to Known Source (km) MCE Response Coefficient, MM

A 10.0 1.21

Table 16-U From site seismology Table A-16-D

Lateral Force Coefficient, RI

2.0

Table A-16-E

Fixed Base Lateral Force Coefficient, R 5.5 Importance Factor, I 1.0 Seismic Coefficient, CAM 0.484

Table 16-N Table 16-K Table A-16-F

Seismic Coefficient, CVM

0.581

Table A-16-G

Eccentricity, e Shortest Building Dimension, b Longest Building Dimension, d Dimension to Extreme Isolator, y DTD/DD = DTM/DM

3.50 32.00 70.00 35.0 1.248

5% of d or d Building size From geometry 1 y

12e b  d2 2

Table 5.6: Seismic and Building Definition

5.4.5

Material Definition

Material definition requirements for design are device specific. The parameters required for various devices are listed in Table 5.7. This is the basic information used for the design process and includes parameters for lead rubber bearings and sliding bearings. The range of properties available for rubber is restricted and some properties are related to others, for example, the ultimate elongation, material constant and elastic modulus are all a function of the shear modulus (see Table 5.4 earlier in this Chapter). Designers should check with manufacturers for values outside the range given in Table 5.4. As for the rubber, the PTFE properties used for sliding bearings are supplier-specific. Values listed in Table 5.7 are suited for evaluating alternative designs but manufacturers will need to be consulted for final specification.

131

Parameter

Symbol

Value

Comment

Shear Modulus

G

0.0004

Ultimate Elongation Material Constant Elastic Modulus Bulk Modulus Damping Lead Yield Strength Teflon Coefficient of Friction Gravity

u k E E  Y 

Shear modulus of rubber. See Table 5.1. (Note units are kN, mm) 6.5 From Table 5.1 for shear modulus used. 0.87 From Table 5.1 for shear modulus used. 0.00135 From Table 5.1 for shear modulus used. 1.5 Typical value for natural rubber. 0.05 5% used for plain rubber bearings 0.008 Consult manufacturer, usually 7 to 8.5 MPa. 0.10 Use high velocity value for design

g

9810

Set gravitation constant in current units

TFE Properties Vertical Stiffness Lateral Stiffness

5000 2000

These are required for analysis only (e.g. ETABS) Generally, use a high value High initial lateral stiffness for sliding bearings

 Low Velocity  High Velocity Coefficient a

0.04 0.10 0.90

These are typical values, consult manufacturer

Table 5.7: Material Properties Used For Design

High damping rubber is the most variable of the common isolator materials as each manufacturer has specific properties for both stiffness and damping. The design procedure can be adapted to interpolate from tabulated values of the shear modulus and equivalent damping. The damping values tabulated may include viscous damping effects if appropriate. An example of HDR stiffness and damping properties versus shear strain is listed in Table 5.8. These are for a relatively low damping rubber formulation and so any design based on these properties should be easily achievable from a number of manufacturers. As such, they should be conservative for preliminary design.

Shear Strain Shear Modulus Equivalent Damping G   % MPa % 10 1.21 12.72 25 0.79 11.28 50 0.57 10.00 75 0.48 8.96 100 0.43 8.48 125 0.40 8.56 150 0.38 8.88 175 0.37 9.36 200 0.35 9.36 Table 5.8: High Damping Rubber

132

5.4.6

Isolator Types and Load Data

The isolator types and load data are defined as shown in Table 5.9. See Chapter 7 for assistance on selecting the device types and the number of variations in type. For most projects, there will be some iteration as the performance of different types and layouts is assessed. 1. The procedure here is based on equivalent viscous damping in linear or bi-linear systems. As such, the types of isolators which can be included in this procedure are lead rubber bearings (LRB), high damping rubber bearings (HDR), elastomeric bearings (ELAST, equivalent to an LRB with no lead core), flat sliding bearings (TFE) and curved sliding bearings (FPS). 2. For each isolator type, vertical load conditions must be defined. The average DL + SLL is used to assess seismic performance. The maximum and minimum load combinations are used to assess the isolator capacity. The latter values are generally available only after analysis has been performed. For preliminary design, a conservative estimate is generally to assume a maximum vertical load of two times the maximum dead load and a minimum load of zero. These can be adjusted as more accurate loads become available. If minimum loads are tensile, you will have to consult manufacturers to ensure that the tension stresses are not excessive. Tension loads cannot be resisted by sliding bearings and uplift may occur at these locations if a tension is indicated. Nonlinear analysis can quantify uplift, if any. 3. The total wind load on the isolators may form a lower limit on the design shear forces. This does not govern for most buildings. 4. Most building projects will not have a non-seismic displacement or rotation; these are more common on bridge projects. High rotations (greater than about 0.003 radians) will severely limit the capacity of the elastomeric types of isolator (LRB, HDR and ELAST). If there are high rotations in particular locations, the pot-bearing type of slider may be a better solution. For most projects, the data in this section will be changed as variations of isolation system are examined. Often, the isolator type will be varied and sometimes variations in the number of each type of isolator will be considered, for example, to vary the seismic weight ratio between LRB and TFE bearings.

133

Type Number of Bearings Average DL + SLL, Pd Max DL + LL Max DL + SLL + E Min DL – E Seismic Weight Wind Load / Isolator Non-Seismic Displacement NS Non-Seismic Rotation, NS Seismic Rotation, E

Lead Rubber LRB

Flat Sliders TFE

Total

27 3782

4 4986

31

4948 8358 0 102114

5216 11170 0 19944

122058

50

50

1550

Comment Options can be LRB HDR, TFE, ELAST From building weight take-off. Estimate for preliminary design Number of bearings x average DL+LL Usually only for bridges

Table 5.9: Isolator Types & Load Data

5.4.7

Isolator Dimensions

This procedure provides specific design for the elastomeric types of isolator (LRB, HDR and ELAST). For other types (TFE and FPS) the design procedure evaluates the performance using the devices but does not provide design details. For these types of bearings you will need to provide the load and design conditions to manufacturers for detailed design. The isolators are defined by the plan size and rubber layer configuration (elastomeric based isolators) plus lead core size (lead rubber bearings) or radius of curvature (curved slider bearings). For curved slider bearings the radius defines the post-yielded slope of the isolation system and the period of response. Table 5.10 lists the parameters required for design. The plan size and rubber layer configuration is inter-related to the seismic performance and so values entered at this stage of the design procedure will need to be adjusted depending on results from the later stages of the procedure.

134

Plan Dimension, B

LRB 870

Depth (optional), D Layer Thickness, ti Number of Layers, N Lead Core Size, dpl Shape

10 21 175 C

Side Cover, tsc Internal Shim Thickness, tsh Load Plate Thickness, Tpl Total Rubber Thickness, Tr Total Height, H Radius of Curvature, R

10 3.0 40.0 210 350

TFE Comment 500 Use nominal dimension for sliders, not used in design Rectangular bearings may be used for bridges Usually, use same for all elastomeric types Vary as part of design process Vary as part of design process May include equations for square (S), circular (C) or rectangular isolators (R). Typically 10 mm Typically 3 mm Required to get total height N tI = Nti+ (N-1)tsh + 2Tpl Required for FPS isolators only R

Total Yield Level of System (summed over all types)

5.89%

gT 2 4 2

Calculated using Qd from Table 5.7 as: Qd  W

 Q xNumberofBearings d

W

Table 5.10: Isolator Dimensions

1. The minimum plan dimensions for the elastomeric isolators are those required for the maximum gravity loads. The gravity factor of safety (F.S.), at zero displacement, should be at least 3 for both the strain and buckling limit states. The design procedure requires a plan dimension such that this factor of safety is achieved. In practice, the seismic demands are usually such that the gravity F.S. is larger than 3. A good starting point for high seismic regions is a strain factor of safety of 5 under maximum DL + LL. For metric dimensions, an increment of 50 mm in plan sizes is generally used with sizes in the sequence of 570 mm, 620 mm etc. This is based on mold sizes in 50 mm increments plus 20 mm side cover rubber. Manufacturers may have specific recommendations. 2. The rubber layer thickness is generally a constant at 10 mm. This thickness provides good confinement for the lead core and is sufficiently thin to provide a high load capacity. If vertical loads are critical the load thickness may be reduced to 8 mm or even 6 mm although you should check with manufacturers for these thin layers. Thinner layers add to the isolator height, and also cost, as more internal shims are required. The layer thickness should not usually exceed 10 mm for LRBs but thicker layers may be used for elastomeric or HDR bearings (up to 15 mm). The load capacity drops off rapidly as the layer thickness increases.

135

3. The number of layers defines the flexibility of the system. This needs to be set so that the isolated period is within the desired range and so that the maximum shear strain is not excessive. This is set by trial and error. The aim is generally to keep strain below 150% under maximum displacements (200% for HDR) and so the total rubber thickness should be in the range of estimated total displacement divided by 1.5 or 2. An increase in the number of layers will decrease the buckling load and so as the number of layers is increased an increase in plan size may be needed. As for the strain F.S, it is recommended that the buckling Factor of Safety under maximum gravity loads be in the range of 4 to 5. 4. The size of the lead core for LRBs defines the amount of damping in the system. The ratio of QD/W is calculated for guidance. This ratio usually ranges from 3% in low seismic zones to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level for a given seismic zone. As for the number of rubber layers, the lead core is sized by trial and error. 5. Plan shapes are usually circular but may be square (plus rectangular for bridges). Most building projects use circular bearings as it is considered that these are more suitable for loading from all horizontal directions. Square and rectangular bearings are more often used for bridges as these shapes may be more space efficient.

The procedure for fine tuning dimensions is to set initial values, solve for the isolation performance and change the configuration to achieve the improvements you need. At each step, the effect of the change is evaluated by assessing the isolation system performance.

5.4.8

Calculate Bearing Properties

The device dimensions defined in the preceding section are used to calculate the bearing properties listed in Table 5.11. For elastomeric based bearings many of the properties are a function of plan shape and formulas are listed for both circular and square bearings. The stiffness and strength properties are a function of the type of device. Formulas are listed in Table 5.11 for LRB, TFE and FPS devices. HDR bearing design is based on tables of shear modulus and effective damping versus applied shear strain and so a design procedure requires a method to lookup the appropriate values, for example, the Excel LOOKUP function.

136

LRB 594468

Gross Area, Ag Bonded Dimension, Bb Bonded Depth (R only), Db Bonded Area, Ab

850 567450

Plug Area, Apl Net Bonded Area, Abn Total Rubber Thickness, Tr Bonded Perimeter, p

24053 543397 210 2670

Shape Factor, SI Characteristic Strength, Qd

20.3 192.4

Shear Modulus (50%) 50

0.0004

Yielded Stiffness Kr

1.09

For LRB c1, Coefficient on Kr c2, Coefficient on Apl/Ab

6.50 12.00

Elastic Stiffness Ku

10.81

Yield Force, Fy Yield Displacement, y Moment of Inertia, I Buckling Factors Height Free to Buckle, Hr Buckling Modulus, Eb Constant T Constant R Constant Q

TFE

Equation B2 (Square) (Circular) B2/4 B – 2tsc D – 2tsc Bb 2 (Square) (Circular) Bb2/4 dpl2/4 Ab - Apl N tI Bb (Circular) (Square) 4Bb Abn / ( tI p) 498.6 yApl (LRB) (TFE or FPS) Pd 0.0 (HDR) G (LRB) Need to LOOKUP from table of G vs Strain for HDR 0.00 G(Ag-Apl)/Tr (LRB, HDR) 0 (TFE) (FPS) Pd/R Typical values, see discussion in Section 4.2.11

0.00 c1Kr (1 – c2Apl/Abn) (LRB) 0 (TFE or FPS) (HDR) = Kr 213.9 498.6 Qd/(1 – Kr/Ku) (LRB) (TFE or FPS) Qd 19.78 0.00 Fy / Ku (LRB) 0 (TFE or FPS) 2.56e10 Bb4 / 64 (Circular) (Square) Bb4/ 12 Elastomeric Types only 270.0 Tr + tsh (N – 1) 0.416 E (1 + 0.742 Si2) 1.37e10 EbIHr / Tr 293.4 KrTr 0.0116  / Hr

Table 5.11: Bearing Properties

137

5.4.9

Gravity Load Capacity

For elastomeric bearing types the gravity load capacity is calculated prior to assessing earthquake performance. If necessary, plan sizes and layer configurations are adjusted to ensure that the bearings have adequate factors of safety under maximum dead plus live loads. The vertical stiffness is also calculated. Table 5.12 lists the calculations required for this phase of the design procedure. As discussed above, for high seismic zones it is recommended that the starting point of the design be such that there are factors of safety of 4 to 5 at zero displacement under maximum dead plus live loads. This is achieved by limiting  to the range of 0.2u to 0.25u and ensuring Pcr > 4 or 5 PDL+LL. These factors can be adjusted by changing the plan size, layer thickness and / or number of layers. The design procedure in Table 5.12 includes an empirical adjustment to the yielded stiffness, Kr, as a function of the ratio of applied load to the buckling load. This has been incorporated as a result of observed stiffness from prototype tests as the vertical load is varied. Manufacturers may be able to provide alternate functions to account for vertical loads on the bearings. The vertical stiffness is not used directly as part of the design and evaluation procedure but is required for analysis. It can also be used to calculate vertical deflections in the bearings at the time of installation.

138

Factor f on u Applied Vertical Load, PDL+LL Applied Displacement Applied Rotation Shape Factor, Si Constant k Elastic Modulus, E Compressive Modulus, Ec Reduced Area, Ar

LRB 0.33 4948 0.000 0.000 20.35 0.87 0.0014 0.974 567450

TFE

Comment / Equations Factor of safety 3 for gravity Maximum DL + LL Non-Seismic Displacement NS Non-Seismic Rotation, NS From properties From material properties From material properties E (1 + 2kSi2)   A b 1  NS Bb 

   

(Square)

         0.5B2 sin 1     Bb  where

 

Vertical Stiffness, Kvi Compressive Strain, c Compressive Shear Strain, sc Displacement Shear Strain, sh Rotational Shear Strain, sr Total Strain,  Allowable Strain Buckling Load, Pcr

Status Adjusted Shear Modulus Adjusted Stiffness Kr* Vertical Stiffness Calculation Kvi Kv Bulk Modulus E Vertical Stiffness, Kv

55273 0.009 1.09 0.00 0.00 1.09 2.17 23188

B

2 b

 2NS



(Circular)

EcAr / tI (per layer) P / Kviti 6Sic NS / Tr Bb2NS / (2 ti Tr ) c + sc + sr u / f   R 4TQ 2 A 1  1 r  AG 2 R  

OK

Satisfactory if   u/f and Pcr > PDL + LL G (1 – PD / Pcr) Kr (1 – PD / Pcr)

0.00033 0.91 55273 2632 1.5 1596

calculated above Kvi / N From material properties Kv / (1 + Ec/E)

Table 5.12: Gravity Load Capacity

5.4.10 Calculate Seismic Performance For design to UBC, the seismic performance must be assessed for two levels of earthquake load, termed DBE and MCE. Tables 5.13 and 5.14 detail the procedure to assess maximum response for these two levels of load. The steps involved are: 1.

A displacement, , is assumed (the total rubber thickness provides a convenient starting point).

2.

The maximum force in each bearing, F, is calculated at this displacement. 139

3.

The effective stiffness of each bearing at this displacement is calculated as F/. The total system effective stiffness is the summation of the individual device stiffness times the number of each type.

4.

The effective period is calculated using the total seismic mass and the effective stiffness.

5.

The equivalent viscous damping is calculated from the area of the hysteresis loop. For HDR, the damping and shear modulus are interpolated from tabulated values of these quantities versus shear strain.

6.

The damping factor, B, is calculated for the calculated level of equivalent viscous damping.

7.

The spectral displacement is calculated from the acceleration response spectrum at the effective period, modified by the damping factor B.

8.

This displacement is compared with the displacement assumed in Step 1. above. If the difference exceeds a preset tolerance, the calculated displacement defines a new starting displacement and the procedure is repeated until convergence is achieved.

The seismic performance is evaluated for both the design level and the maximum seismic events. For UBC design the spectral acceleration is calculated as SA = displacement as SD =

g 4

C 2 V

CV and the spectral BTE

gT 2 TE (which is equivalent to S A e2 ). For other codes, there will B 4

be different formulas for SA (often defined as the seismic coefficient, C). Provided SA can be defined, SD can be calculated directly from this. The procedure in Tables 5.13 and 5.14 is developed for LRB, TFE and FPS bearings. For HDR bearings the properties are extracted from tabulated properties of shear modulus and damping versus shear strain as follows: 1.

Shear strain is calculated as  =  / Tr.

2.

The effective stiffness is calculated as Ke = GAb/Tr where G is the shear modulus at strain .

3.

The damping, , at strain  is used to calculate the equivalent hysteresis loop area as: Ah = 2Ke2.

(5.31)

NOTE: The equivalent hysteresis area is only required if HDR bearings are used with other bearing types. If all bearings are HDR then  can be used to calculate the B factor directly. The iteration procedure can be automated using design office tools such as spreadsheets. Figure 5.7 provides an example of a subroutine written in VBA which can be used in Excel spreadsheets. This relies on named ranges in the spreadsheet: 1.

The cell containing total rubber thickness is named, in this example as Trmax, which is the maximum rubber thickness in any bearing. 140

2.

The assumed displacement is named as dbe1 and mce1 for the two levels of earthquake load respectively.

3.

The calculated spectral displacement is named as dbe2 and mce2 for the two levels of earthquake load respectively.

A button can be added to the spreadsheet to run the subroutine as a macro. (Named ranges are shown bolded in Tables 5.13 and 5.14).

DBE Performance Number of Isolators

LRB

TFE

Total

Comment

27

4

31

Elastic Stiffness, Ku Yielded Stiffness, Kr* Yield Displacement, y Characteristic Strength, Qd Seismic Displacement, DD

10.81 0.91 19.78 192.4

0.00 0.00 0.00 498.6

Number of each type of isolator Bearing parameters calculated from bearing properties above

Bearing Force, F Effective Stiffness, Ke Seismic Weight, W Seismic Mass, M Effective Period, TE

357.2 1.97

498.6 2.75

181.3 Assume a displacement, “dbe1” adjust until SD/DD = 1.0 Qd+DDKr* 64.22 F/DD 122058 Sum of dead loads 12.44 W/g 2.77 M 2

Loop Area, Ah Damping,

124286 30.55%

361500 63.66%

Ke

4801722 4QD(DD1 Ah 36.22%

y)

2 2 K e DD

Damping Factor, B Spectral Acceleration, SA

1.82 0.095

Spectral Displacement, SD

UBC Table A-16-C CV BTE

g T 181.25 CV E B “dbe2” 4 2 1.00 SD/ m

Check Convergence

Table 5.13: Seismic Performance for DBE

141

MCE Performance Number of Isolators Elastic Stiffness, Ku Yielded Stiffness, Kr* Yield Displacement, y Characteristic Strength, Qd Seismic Displacement, Dm Bearing Force, F Effective Stiffness, Ke Seismic Weight, W Seismic Mass, M Effective Period, TE Loop Area, Ah Damping, Damping Factor, B Spectral Acceleration, SA Spectral Displacement, SD

LRB

TFE

Total

27 10.81 0.91 19.78 192.4

4 0.00 0.00 0.00 498.6

31

252.42 “mce1” 421.9 1.672

498.6 1.975

179058 26.76%

503423 63.66%

Check Convergence

53.035 122058 12.442 3.04 6848245 32.26% 1.74 0.110 252.43 “mce2” 1.00

Table 5.14: Seismic Performance for MCE Sub SolveDisp() tol = 0.0001 ds = Range("Trmax") i=0 Range("dbe1") = ds Do Until Abs(1 - (Range("dbe1") / Range("dbe2"))) < tol i=i+1 ds = Range("dbe2") Range("dbe1") = ds If i > 200 Then Call MsgBox("Cannot Solve DBE") Exit Sub End If Loop ds = Range("Trmax") i=0 Range("mce1") = ds Do Until Abs(1 - (Range("mce1") / Range("mce2"))) < tol i=i+1 ds = Range("mce2") Range("mce1") = ds If i > 200 Then Call MsgBox("Cannot Solve MCE") Exit Sub End If Loop End Sub

Figure 5.7: Subroutine to Solve for Displacement

142

Comment

See Table 5.9 for Formulas

5.4.11 Seismic Load Capacity For elastomeric based bearings the vertical load carrying capacity is a function of applied shear displacement and so the capacity must be checked using the same procedures as were used for gravity loads (Table 5.12) with adjustments to acceptance criteria to reflect the lower frequency of seismic loads. Table 5.15 lists the calculations for maximum DBE displacements. The center of mass displacements calculated above are factored by the torsional factor (in this example, by 1.248). The equivalent calculations for MCE are listed in Table 5.16. As the MCE seismic load has a long return period the minimum factor of safety is reduced to 1.0 for these displacements.

Factor f on Eu Applied Vertical Load, PDL+SLL+E DBE Displacement Factor on Displacement Applied Displacement Applied Rotation Shape Factor, SI Constant k Elastic Modulus, E Compressive Modulus, Ec Reduced Area, Ar

LRB 0.75 8358 181.3 1.248 226.2 0.000 20.35 0.87 0.0014 0.974 377451

TFE

Comment / Equations Factor of safety 1.33 for DBE Maximum DL + SLL + E DBE Displacement DD DTD/DD DTD Seismic Rotation, E From properties From material properties From material properties E (1 + 2kSi2)  D  A b 1  TD  Bb  

(Square)

         0.5B2 sin 1  B    b where

 

Vertical Stiffness, Kvi Compressive Strain, c Compressive Shear Strain, sc Displacement Shear Strain, sh Rotational Shear Strain, sr Total Strain,  Allowable Strain Buckling Load, Pcr

Status

36766 0.023 2.78 1.08 0.00 3.85 4.88 15424

B

2 b

2  DTD



EcAr / tI (per layer) P / Kviti 6Sic NS / Tr Bb2NS / (2 ti Tr ) c + sc + sr u / f   R 4TQ 2 A 1  1 r   2 R A   G

OK

Satisfactory if   u/f and Pcr > PDL + LL

Table 5.15: Load Capacity at DBE

143

(Circular)

Factor f on Eu Applied Vertical Load, PDL+SLL+E MCE Displacement Factor on Displacement Applied Displacement Applied Rotation Shape Factor, SI Constant k Elastic Modulus, E Compressive Modulus, Ec Reduced Area, Ar Vertical Stiffness, Kvi Compressive Strain, c Compressive Shear Strain, sc Displacement Shear Strain, sh Rotational Shear Strain, sr Total Strain,  Allowable Strain Buckling Load, Pcr Status

LRB 1.00 8358 252.4 1.248 315.1 0 20.35 0.87 0.0014 0.974 305911 29797 0.028 3.42 1.50 0.00 4.93 6.50 12501 OK

TFE

Comment/Equations Factor of safety 1.0 for MCE Maximum DL + SLL + E MCE Displacement DM DTM/DM DTM Seismic Rotation, E See Table 5.12

Satisfactory if   u/f and Pcr > PDL + LL

Table 5.16: Load Capacity at MCE

5.4.12 Assess Factors of Safety and Performance Tables 5.9 to 5.16 have developed bearing properties, isolation system performance and load capacities. Key response parameters are extracted from these tables to provide a summary list for evaluation of factors of safety and seismic performance. Factors of Safety The values in Table 5.17 are used to ensure that the demands on the bearings are within acceptable limits: 1.

The gravity factor of safety should exceed 3.0 for both strain and buckling. For high seismic zones it will generally be higher as performance is governed by seismic limit states.

2.

The DBE factor of safety should be at least 1.5 and preferably 2.0 for both strain and buckling.

3.

The MCE factor of safety should be at least 1.25 and preferably 1.5 for both strain and buckling.

4.

The ratio of reduced area to gross area should not go below 25% and should preferably be at least 30%.

144

5.

The maximum shear strain for LRBs should not exceed 200% and preferably be less than 150%. For HDR bearings higher strains are acceptable, up to 250% but preferably less than 200%.

The limit states are governed by both the plan size and the number of rubber layers. An adjustment to either of both these parameters may be required to achieve a design within the limitations above. At each change, a check will also be required to ensure that the seismic performance is achieved.

Gravity Strain F.S. Buckling F.S DBE Strain F.S Buckling F.S MCE Strain F.S Buckling F.S Reduced Area / Gross Area Maximum Shear Strain

LRB 5.95 4.69 1.69 1.85 1.32 1.50 53.9% 150%

TFE

Comment u/ = 6.50 / 1.09 Pcr/P = 23188/4948 u/ = 6.50 / 3.85 Pcr/P = 15424/8358 u/ = 6.50 / 4.93 Pcr/P = 12501/8358 at MCE = Ar / Ab at MCE = sh

Table 5.17: Summary of Demand on Elastomeric Bearings

Seismic Performance The performance of the isolated structure is summarized for the DBE and MCE levels in Table 5.18. These are extracted from earlier stages of the design process. Performance indicators to assess are: 1. The isolated period. Most isolation systems have an effective period in the range of 1.50 to 2.50 seconds for DBE, with the longer periods tending to be used for high seismic zones. It may not be possible to achieve a period near the upper limit if the isolators have light loads. 2. The displacements and total displacements. The displacements are estimated values at the center of mass and the total displacements, which include an allowance for torsion. The latter values, at MCE loads, define the separation required around the building. 3. The force coefficient Vb/W is the maximum base shear force that will be transmitted through the isolation system to the structure above. This is the base shear for elastic performance but is necessarily the design base shear. 4. The design base shear coefficient is defined by UBC as the maximum of four cases: a). The elastic base shear reduced by the isolated response modification factor VS = VB/RI. b). The yield force of the isolation system factored by 1.5. c). The base shear corresponding to the wind load.

145

d). The coefficient required for a fixed base structure with a period equal to the isolated period. For this example, the second condition governs, 1.5 times the isolation yield level. 5. The performance summary also lists the equivalent viscous damping of the total isolation system and the associated damping reduction factor, B. Design should always aim for at least 10% damping at both levels of earthquake and preferably 15%.

Effective Period TD TM Displacement DD DM Total Displacements DTD DTM Force Coefficient Vb / W Force Coefficient Vs / W 1.5 x Yield Force / W Wind Force / W Fixed Base V at TD Base Shear Force

DBE 2.77 181.2 226.2 0.095 0.048 0.088 0.013 0.070 10,785

Damping eff Damping Coefficients BD BM

36.2% 1.82

MCE Comment 3.04 From Seismic 252.4 Performance 315.1 0.110 SA SA / RI FY/ W Fw / W From UBC MAX(Vs,Vy, Vw, VF) x W (at DBE) 32.3% From Seismic Performance 1.74

Table 5.17: Summary of Seismic Performance

There is quite an art to the selection of final isolation design parameters. For example, in this case damping is very high and could be decreased by reducing the lead core sizes in the LRBs. If the cores are reduced from 175 mm to 150 mm then the design shear force is reduced from 0.088 to 0.071, approximately equal to the fixed base limit of 0.070. However, the maximum MCE displacement is increased from 315 mm to 363 mm. The designer must assess whether the decrease in design shear justifies the increased seismic displacement, with associated increases in separation gap and connection design forces.

5.4.13 Properties for Analysis The properties developed as part of the design procedure are used to derive the stiffness properties for analysis. Table 5.19 shows the calculations to provide properties as defined by the ETABS computer program. Values are calculated for both the effective stiffness and nonlinear methods of analysis.

146

LRB First Data Line: ID ITYPE KE2 KE3 DE2 DE3 Second Data Line: K1 K2 K3 FY2/K11/CFF2 FY3/K22/CFF3 RK2/K33/CFS2 RK3/CFS3 A2 A3 R2 R3

TFE

1 Isolator1 1.67 1.67 0.218 0.218

2 Isolator2 1.98 1.98 0.587 0.587

Identification Number Biaxial Hysteretic/Linear/Friction Spring Effective Stiffness = Kr* + Qd / DD Spring Effective Damping Ratio =  - 0.05

1595.8 10.64 10.64 210.41 210.41 0.09 0.09

5000.0 2000.00 2000.00 0.10 0.10 0.04 0.04 0.90 0.90 0.000 0.000

Spring Stiffness along Axis 1 (Axial) Initial Spring Stiffness = Ku Yield Force = Fy for LRB =  High Velocity for TFE Post-Yield Stiffness Ratio = Kr*/Ku for LRB = Low Velocity for TFE Coefficient controlling friction = Coefficient a Radius of Contact = R for FPS devices

Table 5.19: Analysis Properties for ETABS

5.4.14 Hysteresis Properties The design properties can also be used to develop the bi-linear hysteresis curve for each type of device. Table 5.20 lists the calculations for each point on the hysteresis curves, which are plotted in Figure 5.8. Force

Yield Displacement, Y Design Displacement, DD Yield Force, FY

Disp 19.78 252.4 210.4

Disp 0.00 252.4 498.6

Origin Point A

0 19.8

0 213.9

0 0.0

Point B

252.4

421.9

252.4

Point C

212.9

-5.88

252.4

Point D

-252.4

-421.9

-252.4

Point E

-212.9

5.88

-252.4

Point A

19.8

213.9

0.00

Force

0 Start of Plot 498.6  = Y F = FY 498.6  = DD F = QD + DDKr* -498.6  = DD – 2 Y F = QD + DDKr* - 2FY -498.6  = - DD F = - QD - DDKr* 498.6  = - DD + 2 Y F = - QD - DDKr* + 2FY 498.6  = Y F = FY

Table 5.20: Points on Hysteresis

147

Comment Bearing Properties DBE Performance Bearing Properties

600

SHEAR FORCE (KN)

Lead Rubber Slider

B

400 A 200

E -300

-200

0 -100

0

100

-200

D

-400

-600 SHEAR DISPLACEMENT (mm)

Figure 5.8: Hysteresis Curves

148

200

C

300

CHAPTER 6: EFFECT OF ISOLATION ON BUILDINGS

As discussed earlier, there are a number of types of isolation systems which provide the essential elements of (1) flexibility (2) damping and (3) rigidity under service loads. Other systems provide some of these characteristics and can be used in parallel with other components to provide a complete system. To provide some guidance in selecting systems for a particular project, three prototype buildings have been used to examine the response under seismic loads of five types of system, each with variations in characteristics. An example is then provided of parametric studies that are performed to refine the system properties for a particular building.

6.1 PROTOTYPE BUILDINGS The evaluations of prototype buildings in this section are intended to provide overall response characteristics of each system type. The buildings used were assumed linear elastic and the evaluation was not fully code compliant. The evaluation procedure used was consistent for all buildings and isolation systems and so provides a reasonable comparison between systems. However, it is not intended to provide final design displacements and forces for this particular seismic zone. Factors such as three-dimensional analysis, eccentricity and MCE factors would need to be included in a final design. 6.1.1

Building Configuration

Three simple shear buildings as shown in Figure 6.1 were used for the evaluation. Each building was assumed to have a total seismic weight of 5000 KN, distributed equally over all floors including the base floor. The assumption of equal total seismic weight allowed the same isolation systems to be used for all buildings. The buildings were also assumed to have equal storey stiffness at all levels. For each building, the storey stiffness was adjusted to provide a target fixed base period:



Two variations of the three storey building were used, with periods of 0.20 and 0.50 seconds respectively. The shorter period corresponds approximately to historic unreinforced masonry (URM) type buildings that tend to have large wall areas and storey stiffness. A three storey building with a 0.50 second period would correspond to a stiff frame or perhaps a wall structural system.



The periods for the five storey building were defined as 0.20, 0.50 and 1.00 seconds. This is the range of periods which would be encountered for this height of building for construction ranging from URM (0.2 seconds) to a moment frame (1.0 seconds).

149

3A T = 0.20 Seconds 5A T = 0.20 Seconds 3B T = 0.50 Seconds 5B T = 0.50 Seconds 5C T = 1.00 Seconds

8A T = 0.50 Seconds 8B T = 1.00 Seconds

Figure 6.1: Prototype Buildings



The eight storey building was modeled with periods of 0.50 and 1.00 seconds, corresponding respectively to a stiff URM type building and a stiff moment frame, braced frame or structural wall building.

The height and period range of the prototypes have been restricted to low to mid-rise buildings with relatively short periods for their height. This is the type of building that is most likely to be a candidate for base isolation.

6.1.2

Design of Isolators

A total of 32 variations of five types of isolation system were used for the evaluation. The designs were completed using the Holmes UBC Template.xls spreadsheet which implements the design procedures described later in these guidelines. For most systems the solution procedure is iterative; a displacement is assumed, the effective period and damping is calculated at this displacement and the spectral displacement at this period and damping extracted. The displacement is then adjusted until the spectral displacement equals the trial displacement.

Force

Each system was designed to the point of defining the required stiffness and strength properties required for evaluation, as shown in Figure 6.2.

K2 fy

K1

Deformation

Figure 6.2: System Definition

150

Acceleration (g)

The design basis for the isolation system design was a UBC seismic load using the factors listed in Table 6.1. The site was assumed to be in the highest seismic zone, Z = 0.4, within 10 kms of a Type A fault. This produced the design spectrum shown in Figure 6.3. The UBC requires two levels of load, the Design Basis Earthquake (DBE) which is used to evaluate the structure and the Maximum Capable Earthquake (MCE, formerly the Maximum Credible Earthquake) which is used to obtain maximum isolator displacements. 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

UBC MCE UBC DBE

0.00

1.00

2.00 3.00 PERIOD (Seconds)

4.00

Figure 6.3: UBC Design Spectrum

Each system, other than the sliding bearings, was defined with effective periods of 1.5, 2.0, 2.5 and 3.0 seconds, which covers the usual range of isolation system period. Generally, the longer period isolation systems will be used with flexible structures. The sliding system was designed for a range of coefficients of friction.

Seismic Zone Factor, Z Soil Profile Type Seismic Coefficient, CA Seismic Coefficient, CV Near-Source Factor Na Near-Source Factor Nv MCE Shaking Intensity MMZNa MCE Shaking Intensity MMZNv Seismic Source Type Distance to Known Source (km)

0.4 SC 0.400 0.672 1.000 1.200 0.484 0.581 A 10.0

MCE Response Coefficient, MM 1.21 Lateral Force Coefficient, RI 2.0 Fixed Base Lateral Force 3.0 Coefficient, R 1.0 Importance Factor, I Seismic Coefficient, CAM 0.484 Seismic Coefficient, CVM 0.813 Table 6.1: UBC Design Factors

151

Table 16.I Table 16.J Table 16.Q Table 16.R Table 16.S Table 16.T

Table 16.U Table A-16.D Table A-16.E Table 16.N Table 16.K Table A-16.F Table A-16.G

1. The ELASTIC system is an elastic spring with no damping. This type of system is not practical unless used in parallel with supplemental dampers as displacements will be large and the structure will move under service loads. However, it serves as a benchmark analysis to evaluate the effect of the damping in the other systems. This is modeled as a linear elastic spring with the yield level set very high. 2. The LRB is a lead rubber bearing. Variations were designed with three values of Qd, corresponding to 0.05W, 0.075W and 0.010W. Qd is the force intercept at zero displacement and defines the yield level of the isolator. For this type of bearing the effective damping is a function of period and Qd and ranges from 8% to 37% for the devices considered here.

4.0 3.6 3.2 2.8 2.4 2.0 1.6

20 18 16 14 12 10 8

Shear Modulus Damping

1.2 0.8 0.4 0.0

6 4 2 0 0

50

100

150

200

EQUIVALENT DAMPING (%)

SHEAR MODULUS (MPa)

3. HDR is a high damping rubber system. There are a large number of high damping formulations available and each manufacturer typically provides a range of elastomers with varying hardness and damping values. The properties are a function of the applied shear strain. The properties used for this design were as plotted in Figure 6.4.

250

SHEAR STRAIN (%)

Figure 6.4: HDR Elastomer Properties

These properties represent a mid-range elastomer with a shear modulus of approximately 3 MPa at very low strains reducing to 0.75 MPa for a strain of 250%. The damping has a maximum value of 19% at low strains, reducing to 14% at 250% strain. Most elastomeric materials have strain-stiffening characteristics with the shear modulus increasing for strains exceeding about 250%. If the bearings are to work within this range then this stiffening has to be included in the design and evaluation. The strain-dependent damping as plotted in Figure 6.4 is used to design the bearing. For analysis this is converted to an equivalent hysteresis shape. Although complex shapes may be required for final design, the analyses here used a simple bi-linear representation based on the approximations from FEMA-273. A yield displacement, y, is assumed at 0.05 to 0.10 times the rubber thickness and the intercept, Q, calculated from the maximum displacement and effective stiffness as:

Q

 eff 2 2(   y )

152

The damping for these bearings varies over a narrow range of 15% to 19% for the isolator periods included here. 4. PTFE is a sliding bearing system. Sliding bearings generally comprise a sliding surface of a self-lubricating polytetrafluoroethylene (PTFE) surface sliding across a smooth, hard, noncorrosive mating surface such as stainless steel. (Teflon © is a trade name for a brand of PTFE). These bearings are modeled as rigid-perfectly plastic elements (k1 = , K2 = 0). A range of coefficients of friction, m, was evaluated. The values of  = 0.06, 0.09, 0.12 and 0.15 encompass the normal range of sliding coefficients. Actual sliding bearing coefficients of friction are a function of normal pressure and the velocity of sliding. For final analysis, use the special purpose ANSR-L element that includes this variability. For this type of isolator the coefficient of friction is the only variable and so design cannot target a specific period. The periods as designed are calculated based on the secant stiffness at the calculated seismic displacement. The hysteresis is a rectangle that provides optimum equivalent damping of 2/ = 63.7%. 5. FPS is a patented friction pendulum system, which is similar to the PTFE bearing but which has a spherical rather than flat sliding surface. The properties of this type of isolator are defined by the radius of curvature of the bowl, which defines the period, and the coefficient of friction. Two configurations were evaluated, using respectively, coefficients of friction of 0.06 and 0.12. Bowl radii were set to provide the same range of periods as for the other isolator types. Equivalent viscous damping ranged from 9% to 40%, a similar range to the LRBs considered. These bearings are modeled as rigid-strain hardening elements (k1 = , K2 > 0). As for the PTFE bearings, the evaluation procedure was approximate and did not consider variations in the coefficient of friction with pressure and velocity. A final design and evaluation would need to account for this. Table 6.2 lists the variations considered in the evaluation and the hysteresis shape parameters used for modeling.

153

System

Variation

NONE ELASTIC ELASTIC ELASTIC ELASTIC

Isolated Period (Seconds) 0.0 1.5 2.0 2.5 3.0

 (%)

 (mm)

0% 5% 5% 5% 5%

0 250 334 417 501

C

k1 (KN/mm)

k2 (KN/mm)

fy

0.447 0.336 0.269 0.234

100000 8.94 5.03 3.22 2.34

0 8.94 5.03 3.22 2.34

100000 100000 100000 100000 100000

LRB LRB LRB LRB

Qd=0.050

1.5 2.0 2.5 3.0

8% 11% 15% 20%

230 272 310 342

0.417 0.273 0.199 0.153

62.83 32.82 19.87 12.82

7.98 4.10 2.40 1.49

287 287 287 287

LRB LRB LRB LRB

Qd=0.075

1.5 2.0 2.5 3.0

13% 20% 26% 31%

194 229 262 295

0.349 0.227 0.168 0.134

60.52 28.94 15.96 9.81

7.05 3.30 1.77 0.96

426 426 426 426

LRB LRB LRB LRB

Qd=0.100

1.5 2.0 2.5 3.0

20% 28% 33% 37%

167 203 240 276

0.299 0.206 0.156 0.128

55.10 24.72 11.56 6.83

5.96 2.60 1.14 0.41

562 562 562 562

1.5 2.0 2.5 3.0

15% 16% 17% 19%

186 242 303 348

0.184 0.140 0.110 0.094

45.28 20.06 10.34 9.02

7.62 4.28 2.60 1.74

514 462 414 414

HDR HDR HDR HDR PTFE PTFE PTFE PTFE

=0.06 =0.09 =0.12 =0.15

5.6 3.7 2.8 2.2

64% 64% 64% 64%

467 312 234 187

0.060 0.090 0.120 0.150

500 500 500 500

0 0 0 0

300 450 600 750

FPS FPS FPS FPS

=0.06

1.5 2.0 2.5 3.0

9% 13% 17% 21%

200 231 253 269

0.417 0.292 0.223 0.180

500 500 500 500

8.94 5.03 3.22 2.24

300 300 300 300

FPS FPS FPS FPS

=0.12

1.5 2.0 2.5 3.0

21% 28% 34% 40%

135 150 159 164

0.359 0.270 0.222 0.193

500 500 500 500

8.94 5.03 3.22 2.24

600 600 600 600

Table 6.2: Isolation System Variations

154

Figure 6.5 plots the hysteresis curves for all isolator types and variations included in this evaluation. The elastic isolators are the only type which have zero area under the hysteresis curve, and so zero equivalent viscous damping. The LRB and HDR isolators produce a bilinear force displacement function with an elastic stiffness and a yielded stiffness. The PTFE and FPS bearings are rigid until the slip force is reached and the stiffness then reduces to zero (PTFE) or a positive value (FPS). It is important to note that these designs are not necessarily optimum designs for a particular isolation system type and in fact almost surely are not optimal. In particular, the HDR and FPS bearings have proprietary and/or patented features that need to be taken into account in final design. You should get technical advice from the manufacturer for these types of bearing. The UBC requires that isolators without a restoring force be designed for a displacement three times the calculated displacement. A system with a restoring force is defined as one in which the force at the design displacement is at least 0.025W greater than the force at 0.5 times the design displacement. This can be checked from the values in Table 6.2 as R = (k2 x 0.5)/W. The only isolators which do not have a restoring force are the LRB with Qd = 0.100 and an isolated period of 3 seconds and all the sliding (PTFE) isolation systems.

LEAD RUBBER BEARINGS Qd = 0.05

3000

3000

2000

2000 FORCE (KN)

FORCE (KN)

ELASTIC ISOLATORS

1000 0 -600

-400

-200

-1000

0

200

-2000

400

T=1.5

T=2.0

T=2.5

T=3.0

600

1000 0 -400

-200

2000

1500

1500

1000

1000

FORCE (KN)

FORCE (KN)

T=1.5

T=2.0

T=2.5

T=3.0

LEAD RUBBER BEARINGS Qd = 0.010

2000

500 0 -100-500 0

400

DISPLACEMENT (mm)

LEAD RUBBER BEARINGS Qd = 0.075

-200

200

-3000

DISPLACEMENT (mm)

-300

0

-2000

-3000

-400

-1000

100

200

300

-1000

T=1.5

T=2.0

-1500

T=2.5

T=3.0

400

-2000

500 0 -400

-300

-200

-100-500 0

100

200 T=1.5

T=2.0

-1500

T=2.5

T=3.0

-2000

DISPLACEMENT (mm)

DISPLACEMENT (mm)

155

300

-1000

400

PTFE SLIDING BEARINGS

-400

2500 2000 1500 1000 500 0 -500 0 -1000 -1500 -2000 -2500

-200

200

400

T=1.5

T=2.0

T=2.5

T=3.0

FORCE (KN)

FORCE (KN)

HIGH DAMPING RUBBER BEARINGS

-600

1000 800 600 400 200 0 -200 -200 0 -400 -600 -800 -1000

-400

FRICTION PENDULUM BEARINGS m = 0.06

0

100

200

300

FORCE (KN)

FORCE (KN)

0

-2000

m=0.09

m=0.12

m=0.15

1500

1000

-1000

m=0.06

2000

2000

-100

600

FRICTION PENDULUM BEARINGS m = 0.12

3000

-200

400

DISPLACEMENT (mm)

DISPLACEMENT (mm)

-300

200

1000 500 0 -200

-100

-500 0

100

200

T=1.5

T=2.0

-1000

T=1.5

T=2.0

T=2.5

T=3.0

-1500

T=2.5

T=3.0

-3000

-2000

DISPLACEMENT (mm)

DISPLACEMENT (mm)

Figure 6.5: Isolation System Hysteresis

6.1.3

Evaluation Procedure

As discussed later, the procedures for evaluating isolated structures are, in increasing order of complexity, (1) static analysis, (2) response spectrum analysis and (3) time-history analysis. The static procedure is permitted for only a very limited range of buildings and isolation systems and so the response spectrum and time-history analyses are the most commonly used methods. There are some restrictions on the response spectrum method of analysis that may preclude some buildings and/or systems although this is unusual. The time-history method can be used without restriction. As the same model can be used for both types of analysis it is often preferable to do both so as to provide a check on response predictions. In theory, the response spectrum analysis is simpler to evaluate as it provides a single set of results for a single spectrum for each earthquake level and eccentricity. The time-history method produces a set of results at every time step for at least three earthquake records, and often for seven earthquake records. In practice, our output processing spreadsheets produce results in the same format for the two procedures and so this is not an issue. Also, the response spectrum procedure is based on an effective stiffness formulation and so is usually an iterative process. The effective stiffness must be estimated, based on estimated displacements, and then adjusted depending on the results of the analysis.

156

The evaluations here are based on both the response spectrum and the time-history method of analysis, respectively termed the Linear Dynamic Procedure (LDP) and the Non-Linear Dynamic Procedure (NDP) in FEMA-273. Response Spectrum Analysis The response spectrum analysis follows the usual procedure for this method of analysis with two modifications to account for the isolation system:

SHEAR FORCE

1. Springs are modeled to connect the base level of the structure to the ground. These springs have the effective stiffness of the isolators. For most isolator systems, this stiffness is a function of displacement – see Figure 6.6.

Isolator Hysteresis Effective Stiffness

SHEAR DISPLACEMENT

Figure 6.6: Effective Stiffness

2. The response spectrum is modified to account for the damping provided in the isolated modes. Some analysis programs (for example, ETABS) allow spectra for varying damping to be provided, otherwise the 5% damped spectrum can be modified to use a composite spectra which is reduced by the B factor in the isolated modes – see Figure 6.7.

ACCELERATION (g)

1.2 5% Damped Sa

1.0 0.8

Isolated Period

0.6 0.4

Sa B

0.2 0.0 0.0

1.0

2.0

3.0

PERIOD (Seconds)

Figure 6.7: Composite Response Spectrum

157

4.0

More detail for the response spectrum analysis based on effective stiffness and equivalent viscous damping is provided in Chapter 10 of these guidelines. Time History Analysis Each building and isolation system combination was evaluated for three earthquake records, the minimum number required by most codes. The record selection was not fully code compliant in that only a single component was applied to a two-dimensional model and the records selected were frequency scaled to match the design spectrum, as shown in Figure 6.8. The frequency scaled records were chosen as these analyses are intended to compare isolation systems and analysis methods rather than obtain design values. The time history selection procedure specified by most codes results in seismic input which exceeds the response spectrum values and so would produce higher results than those reported here.

1.400

1.200

El Centro Seed

1.000

Olympia Seed

0.800

Taft Seed Design Spectrum

0.600

ACCELERATION (g)

ACCELERATION (g)

1.400

0.400 0.200 0.000 0.000

1.000

2.000

3.000

4.000

1.200 1.000

Envelope

0.800

Design Spectrum

0.600 0.400 0.200 0.000 0.000

PERIOD (Seconds)

1.000

2.000

3.000

4.000

PERIOD (Seconds)

Figure 6.8: 5% Damped Spectra of 3 Earthquake Records

Each building model and damping system configuration was analyzed for the 20 second duration of each record at a time step of 0.01 seconds. At each time step the accelerations and displacements at each level were saved as were the shear forces in each storey. These values were then processed to provide isolator displacements and shear forces, structural drifts and total overturning moments. 6.1.4

Comparison with Design Procedure

The isolator performance parameters are the shear force coefficient, C, (the maximum isolator force normalized by the weight of the structure) and the isolator displacement, . The design procedure estimates these quantities based on a single mass assumption – see Table 6.2.

158

Response Spectrum Analysis The response spectrum results divided by the design estimates are plotted in Figure 6.9. These values are the average over all buildings. Numerical results are listed in Table 6.3. A value of 100% in Figure 6.9 indicates that the analysis matched the design procedure, a value higher than 100% indicates that the time history provided a higher value than the design procedure. The response spectrum analysis displacements and shear coefficients were consistently lower than the design procedure results with one exception. The results were lower by a relatively small amount. Both the shear coefficients and the displacements were generally from 0% to 10% lower than the predicted values. An exception was type H (High Damping Rubber) where the differences ranged from +10% to –20%. This is because the design for these types was based on tabulated viscous damping whereas the analysis was based on an equivalent hysteresis shape. 120%

100%

80%

60%

Average Response Spectrum Displacement/Design Value

40%

Average Response Spectrum Shear Coefficient/Design Value 20%

F 2 T=3.0

F 2 T=2.0

F 1 T=2.5

F 1 T=1.5

P T=5.6

P T=2.8

H T=2.5

H T=1.5

L 3 T=3.0

L 3 T=2.0

L 2 T=2.5

L 2 T=1.5

L 1 T=3.0

L 1 T=2.0

E T=2.5

E T=1.5

0%

Figure 6.8: Isolator Results from Response Spectrum Analysis Compared to Design

159

Design Procedure System

Variation

NONE ELAST ELAST ELAST ELAST

Period (Seconds)

 (mm)

C

1.5 2.0 2.5 3.0

250 334 417 501

0.447 0.336 0.269 0.234

Response Spectrum Analysis C  (mm) 0 0.678 236 0.423 323 0.325 409 0.263 483 0.225

Time History Maximum of 3 Earthquakes C  (mm) 1.551 309 0.552 369 0.371 434 0.279 528 0.247

LRB LRB LRB LRB

Qd=0.050

1.5 2.0 2.5 3.0

230 272 310 342

0.417 0.273 0.199 0.153

206 256 295 325

0.379 0.260 0.192 0.148

144 213 269 344

0.280 0.225 0.180 0.153

LRB LRB LRB LRB

Qd=0.075

1.5 2.0 2.5 3.0

194 229 262 295

0.349 0.227 0.168 0.134

175 212 248 278

0.322 0.216 0.164 0.130

140 195 258 332

0.272 0.204 0.167 0.141

LRB LRB LRB LRB

Qd=0.100

1.5 2.0 2.5 3.0

167 203 240 276

0.299 0.206 0.156 0.128

152 190 226 258

0.282 0.199 0.153 0.127

140 197 269 384

0.267 0.203 0.163 0.137

1.5 2.0 2.5 3.0

186 242 303 348

0.184 0.140 0.110 0.094

206 212 270 279

0.366 0.254 0.202 0.165

148 177 269 320

0.277 0.225 0.202 0.179

HDR HDR HDR HDR PTFE PTFE PTFE PTFE

=0.15 =0.12 =0.09 =0.06

2.2 2.8 3.7 5.6

187 234 312 467

0.150 0.120 0.090 0.060

177 225 305

0.149 0.120 0.090

204 223 309 430

0.150 0.120 0.090 0.060

FPS FPS FPS FPS

=0.06

1.5 2.0 2.5 3.0

200 231 253 269

0.359 0.270 0.222 0.193

179 216 239 259

0.328 0.255 0.213 0.188

124 160 199 228

0.280 0.221 0.188 0.162

FPS FPS FPS FPS

=0.12

1.5 2.0 2.5 3.0

135 150 159 164

0.328 0.255 0.213 0.188

117 135 145 152

0.381 0.277 0.214 0.176

103 111 122 130

0.301 0.231 0.198 0.178

Table 6.3: Isolation System Performance (Maximum of All Buildings, All Earthquakes)

160

The close correlation between the two methods is not surprising as they are both based on the same concepts of effective stiffness and equivalent viscous damping. The main difference is that the design procedure assumes a rigid structure above the isolators whereas the response spectrum analysis includes the effect of building flexibility. 120% 100% 80% 60% 40%

Response Spectrum Displacement/Design Value

20%

Response Spectrum Shear Coefficient/Design Value

0% 3 3 5 5 5 8 8 STORY STORY STORY STORY STORY STORY STORY T=0.2 T=0.5 T=0.2 T=0.5 T=1.0 T=0.5 T=1.0

Figure 6.9: Spectrum Results for LRB1 T=1.5 Seconds

The effect of building flexibility is illustrated by Figure 6.10, which plots the ratio of response spectrum results to design procedure values for the lead rubber bearing (LRB 1) with a period of 1.5 seconds. Figure 6.9 shows that the average ratio for this system is 90% of the design values. However, Figure 6.10 shows that the ratio actually ranges from 97% for buildings with a period of 0.2 seconds to 77% for the building with a 1.0 second period. As the building period increases the effects of building flexibility become more important and so the response spectrum values diverge from the design procedure results. The effects shown in Figure 6.10 tend to be consistent in that for all systems the base displacement and base shear coefficient was lower for the buildings with longer periods. The only exception was for the sliding systems (PTFE) where the shear coefficient remained constant, at a value equal to the coefficient of friction of the isolators. Time History Analysis The ratios of the displacements and shear coefficients from the time history analysis to the values predicted by the design procedure are plotted in Figure 6.11. Two cases are plotted (a) the maximum values from the three time histories and (b) the average values from the three time histories. In each case, the values are averaged over the 7 building configurations. The time history results varied from the design procedure predictions by a much greater amount than the response spectrum results, with discrepancies ranging from +40% to -40% for the maximum results and from +20% to –42% for the mean results. For the elastic systems the time history analysis results tended to be closer to the design procedure results as the period increased but this trend was reversed for all the other isolation system types. As the elastic system is the only one which does not use equivalent viscous damping this suggests that there are differences in response between hysteretic damping and a model using the viscous equivalent.

161

As the period increases for the hysteretic systems, the displacement also increases and the equivalent viscous damping decreases. The results in Figure 6.11 suggest that the viscous damping formulation is more accurate for large displacements than for small displacements.

160% 140% 120% 100% 80% 60% Maximum Time History Displacement/Design Value

40%

Maximum Time History Shear Coefficient/Design Value 20%

F 2 T=3.0

F 2 T=2.0

F 1 T=2.5

F 1 T=1.5

P T=5.6

P T=2.8

H T=2.5

H T=1.5

L 3 T=3.0

L 3 T=2.0

L 2 T=2.5

L 2 T=1.5

L 1 T=3.0

L 1 T=2.0

E T=2.5

E T=1.5

0%

Figure 6.10: Isolator Results from Time History Analysis Compared to Design (A) Maximum From Time History Analysis

140% Average Time History Displacement/Design Value 120%

Average Time History Shear Coefficient/Design Value

100% 80% 60% 40% 20%

(B) Mean From Time History Analysis

162

F 2 T=3.0

F 2 T=2.0

F 1 T=2.5

F 1 T=1.5

P T=5.6

P T=2.8

H T=2.5

H T=1.5

L 3 T=3.0

L 3 T=2.0

L 2 T=2.5

L 2 T=1.5

L 1 T=3.0

L 1 T=2.0

E T=2.5

E T=1.5

0%

Figure 6.12 plots the ratios based on the maximum values from the three earthquakes compared to the design procedure values for the lead rubber bearing (LRB 1) with a period of 1.5 seconds (compare this figure with Figure 6.10 which provides the similar results from the response spectrum analysis). Figure 6.12 suggests that results are relatively insensitive to the period of the structure above the isolators. However, Figure 6.12, which plots the results for the individual earthquakes, shows that for EQ 1 and EQ 3 the results for the 1.0 second period structures are less than for the stiffer buildings, as occurred for the response spectrum analysis. However, this effect is masked by EQ 2 which produces a response for the 1.0 second period structures which is much higher than for the other buildings. This illustrates that time history response can vary considerably even for earthquake records which apparently provide very similar response spectra. 100% 90% 80% 70% 60% 50% 40%

Time History Displacement/Design Value

30%

Time History Shear Coefficient/Design Value

20% 10% 0% 3 3 5 5 5 8 8 STORY STORY STORY STORY STORY STORY STORY T=0.2 T=0.5 T=0.2 T=0.5 T=1.0 T=0.5 T=1.0

Figure 6.11: Time History Results for LRB1 T=1.5 Sec

100% 90% 80% 70% 60% 50% 40% 30% 20%

EQ 1 Displacement Ratio EQ 2 Displacement Ratio EQ 3 Displacement Ratio

10% 0% 3 3 5 5 5 8 8 STORY STORY STORY STORY STORY STORY STORY T=0.2 T=0.5 T=0.2 T=0.5 T=1.0 T=0.5 T=1.0

Figure 6.12: Variation Between Earthquakes

The mean time history results show that the design procedure generally provided a conservative estimate of isolation system performance except for the elastic isolation system, where the design procedure under-estimated displacements and shear forces, especially for short period isolation systems.

163

6.1.5

Isolation System Performance

The mean and maximum results from the three time histories were used above to compare displacements and base shear coefficients with the design procedure and the response spectrum procedure. For design, if three time histories are used then the maximum rather than the mean values are used. (Some codes permit mean values to be used for design if at least 7 earthquakes are used). Table 6.3 listed the average isolation response over the 7 building configurations for each system. These results are plotted in Figures 6.14 and 6.15, which compare respectively the shear coefficients and displacements for each isolation system for both the response spectrum method and the time history method. 

The plots show that although both methods of analysis follow similar trends for most isolation systems, the response spectrum results are higher in many cases. This is consistent with the comparisons with the design procedure discussed earlier, where the time history tended to produce ratios that were lower than the response spectrum.



For all isolation systems, the base shear coefficient decreases with increasing period and the displacement increases. This is the basic tradeoff for all isolation system design.



The PTFE (sliding) bearings produce the smallest shear coefficients and the smallest displacements of all systems except the FPS. However, as these bearings do not have a restoring force the design displacements are required to be increased by a factor of 3. With this multiplier the PTFE displacements are higher than for all other isolator types.



There are relatively small variations between the three types of Lead Rubber Bearings (LRB). For these systems the yield force is increased from 5% W to 7.5% W to 10% W for systems 1, 2 and 3 respectively. The LRB systems produce the smallest shear coefficients after the PTFE sliders.



The two Friction Pendulum Systems (FPS) variations are the values of the coefficient of friction, 0.06 for Type 1 and 0.12 for Type 2. The increased coefficient of friction has little effect on the base shear coefficients but reduces displacements. The FPS with  = 0.12 produces the smallest displacements of any system.

There is no one optimum system, or isolated period, in terms of minimizing both base shear coefficient and displacement. This isolator performance in only one aspect in selecting a system, the performance of the structure above is usually of at least equal performance. This is examined in the following sections and then well-performing systems are identified in terms of parameters that may be important depending on project objectives.

164

165

Figure 6.14: Isolator Performance : Isolator Displacements

400

300

200

100

0 FPS 1 T = 2.5

FPS 1 T = 1.5

PTFE T = 5.6

PTFE T = 2.8

HDR T = 2.5

HDR T = 1.5

LRB 3 T = 3.0

LRB 3 T = 2.0

LRB 2 T = 2.5

FPS 2 T = 3.0

Response Spectrum Time History

FPS 2 T = 3.0

600 FPS 2 T = 2.0

Figure 6.13: Isolator Performance: Base Shear Coefficients

FPS 2 T = 2.0

FPS 1 T = 2.5

FPS 1 T = 1.5

PTFE T = 5.6

PTFE T = 2.8

HDR T = 2.5

HDR T = 1.5

LRB 3 T = 3.0

LRB 3 T = 2.0

LRB 2 T = 2.5

500 LRB 2 T = 1.5

LRB 1 T = 3.0

LRB 1 T = 2.0

ELAS T = 2.5

ELAS T = 1.5

BASE SHEAR COEFFICIENT 0.50

LRB 2 T = 1.5

LRB 1 T = 3.0

LRB 1 T = 2.0

ELAS T = 2.5

ELAS T = 1.5

ISOLATOR DISPLACEMENT (mm)

0.60

Response Spectrum Time History

0.40

0.30

0.20

0.10

0.00

6.1.6

Building Inertia Loads

The isolation system response provides the maximum base shear coefficient that is the maximum simultaneous summation of the inertia forces from all levels above the isolator plane. The distribution of these inertia forces within the height of the structure defines the design shears at each level and the total overturning moments on the structure. Response Spectrum Analysis The inertia forces are obtained from the response spectrum analyses as the CQC of the individual modal responses, where modal inertia forces are the product of the spectral acceleration in that mode times the participation factor times the mass. Figure 6.16 plots these distributions for three building configurations, each for one isolator effective period. The combinations of building period and isolator period have been selected as typical values that would be used in practice. Figure 6.16 shows that the inertia force distributions for the buildings without isolation demonstrate an approximately linear increase with height, compared to the triangular distribution assumed by most codes for a uniform building with no devices. Note that the fixed base buildings have an inertia force at the base level. This is because a rigid spring was used in place of the isolation system for these models and the base mass was included. As all modes were extracted this spring mode has acceleration equal to the ground acceleration and so generates an inertia force. All isolation systems exhibit different distributions from the non-isolated building in that the inertia forces are almost constant with the height of the building for all buildings. Some systems show a slight increase in inertia force with height but this effect is small and so for all systems the response spectrum results suggest that a uniform distribution would best represent the inertia forces. As the following section describes, the results from the time history analysis were at variance with this assumption.

166

5 Story Building T = 0.5 Seconds Ti = 2.5 Seconds

3 Story Building T = 0.2 Seconds Ti = 2.0 Seconds F5

F3 F4

FPS 2 FPS 1 PTFE HDR LRB 2

F2

F1

F2 F1

LRB 1 Elastic No Devices

F0

0

500

1000

1500

FPS 2 FPS 1 PTFE HDR LRB 2 LRB 1 Elastic No Devices

F3

F0

2000

0

200

400

600

800

1000

1200

INERTIA FORCE (KN)

INERTIA FORCE (KN)

8 Story Building T = 1.0 Seconds Ti = 3.0 Seconds F8 F7 F6 F5 F4

FPS 2 FPS 1 PTFE HDR LRB 2 LRB 1 Elastic No Devices

F3 F2 F1 F0 0

100

200

300

400

500

600

INERTIA FORCE (KN)

Figure 6.15: Response Spectrum Inertia Forces

Time History Analysis As discussed above, for a fixed base regular building most codes assumed that the distribution of inertia load is linear with height, a triangular distribution based on the assumption that first mode effects will dominate response. This distribution has an effective height at the centroid of the triangle, that is, two-thirds the building height above the base for structures with constant floor weights. A uniform distribution of inertia loads would have a centroid at one-half the height. The effective height was calculated for each configuration analyzed by selecting the earthquake which produced the highest overturning moment about the base and calculating the effective height of application of inertia loads as Hc = M/VH, where M is the moment, V the base shear and H the height of the building. Figure 6.17 plots Hc for the fixed base configuration of each of the building models.

167

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.5

5 T=0.2

3 T=0.5

No Devices Triangular 3 T=0.2

HEIGHT OF INTERIA LOAD / H

Although there were some variations between buildings, these results show that the assumption of a triangular distribution is a reasonable approximation and produces a conservative overturning moment for most of the structures considered in this study.

Figure 6.16: Height of Inertia Loads

An isolation system produces fundamental modes comprising almost entirely of deformations in the isolators with the structure above moving effectively as a rigid body with small deformations. With this type of mode shape it would be expected that the distribution of inertia load with height would be essentially linear with an effective height of application of one-half the total height, as was shown above for the response spectrum analysis results. Figure 6.18 plots the effective heights of inertia loads, Hc, for the 8 isolation system variations considered in this study. Each plot contains the effective period variations for a particular device. Each plot has three horizontal lines 1. Hc = 0.50, a uniform distribution 2. Hc = 0.67, a triangular distribution 3. Hc = 1.00, a distribution with all inertia load concentrated at roof level.

168

1.00 0.80 0.60 0.40 FPS 1 T=1.5 FPS 1 T=3.0 Top

0.20

FPS 1 T=2.0 Uniform

FPS 1 T=2.5 Triangular

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.2

3 T=0.5

5 T=0.5

8 T = 1.0

5 T=1.0

5 T=0.5

8 T=0.5

PTFE T=3.7 Triangular

1.20 1.00 0.80 0.60 0.40

FPS 2 T=1.5 FPS 2 T=3.0 Top

0.20

FPS 2 T=2.0 Uniform

FPS 2 T=2.5 Triangular

0.00

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.5

5 T=0.2

3 T=0.5

0.00 3 T=0.2

1.40

PTFE T=2.8 Uniform

0.00

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.5

5 T=0.2

3 T=0.5

3 T=0.2

0.00

PTFE T=2.2 PTFE T=5.6 Top

0.50

8 T = 1.0

HDR T=2.5 Triangular

Figure 6.17: Effective Height of Inertia Loads for Isolation Systems

169

8 T = 1.0

HDR T=2.0 Uniform

1.00

8 T=0.5

HDR T=1.5 HDR T=3.0 Top

1.50

8 T=0.5

0.40

2.00

5 T=1.0

0.60

LRB 3 T=2.5 Triangular

0.00

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.5

5 T=0.2

3 T=0.5

0.80

LRB 3 T=2.0 Uniform

5 T=1.0

1.20

1.00

0.20

2.50

LRB 3 T=1.5 LRB 3 T=3.0 Top

0.20

5 T=0.5

HEIGHT OF INERTIA LOAD / H

1.20

HEIGHT OF INERTIA LOAD / H

3 T=0.2

0.00

0.40

5 T=0.5

LRB 2 T=2.5 Triangular

5 T=0.2

0.20

LRB 2 T=2.0 Uniform

0.60

3 T=0.2

LRB 2 T=1.5 LRB 2 T=3.0 Top

0.80

5 T=0.2

0.40

LRB 1 T=2.5 Triangular

1.00

5 T=0.2

0.60

LRB 1 T=2.0 Uniform

0.00

3 T=0.5

0.80

LRB 1 T=1.5 LRB 1 T=3.0 Top

0.20

3 T=0.5

1.00

1.20

0.40

3 T=0.5

8 T = 1.0

8 T=0.5

5 T=1.0

5 T=0.5

5 T=0.2

3 T=0.5

3 T=0.2

0.00

0.60

3 T=0.2

ELAST T=2.0 ELAST T=3.0 Triangular

0.80

3 T=0.2

ELAST T=1.5 ELAST T=2.5 Uniform

0.20

1.00

3 T=0.2

0.40

HEIGHT OF INERTIA LOAD / H

0.60

HEIGHT OF INERTIA LOAD / H

0.80

1.20

HEIGHT OF INERTIA LOAD / H

HEIGHT OF INERTIA LOAD / H

1.20

1.00

HEIGHT OF INERTIA LOAD / H

HEIGHT OF INERTIA LOAD / H

1.20

Unexpectedly, few of the isolation systems provided a uniform distribution and in some, particularly the sliding (PTFE) systems, the effective height of application of the inertia forces exceeded the height of the structure by a large margin. Trends from these plots are: 

The elastic isolation systems provide inertia loads close to a uniform distribution except for the 1 second period buildings.



The LRB systems provide a uniform distribution for the short period (0.2 seconds) buildings but a triangular distribution for the longer period buildings. As the isolation system yield level increases (going from LRB 1 to LRB 2 to LRB 3) the height of the centroid tends toward the top of the building.



The HDR isolators exhibit similar characteristics to LRB 1, the lowest yield level.



The PTFE (sliding) systems provide an effective height much higher than the building height for all variations and provide the most consistent results for all buildings. As the coefficient of friction decreases (increased T) the effective height increases.



The FPS system with the lower coefficient of friction (FPS 1) provides a similar pattern to the PTFE systems but less extreme. The FPS system with the higher coefficient of friction (FPS 2) produces results closer to the LRB and HDR systems although the trends between buildings are different.

To investigate these results, the force distributions in Figures 6.19 to 6.21 have been generated. These are for the 3 storey 0.2 second building with 2 second period isolators, the 5 storey 0.5 second building with 2.5 second period isolators and the 8 storey 1 second building with 3 second period isolators. These have been selected as typical configurations for the three building heights. For the fixed base case and each isolator case for these buildings two force distributions are plotted: 1. The force at each level when the maximum base shear force is recorded. 2. The force at each level when the maximum base overturning moment is recorded. The distributions producing these two maximums are almost invariably at different times and in many cases are vastly different: 3 Storey Building (Figure 6.19) For the stiff building without isolators the distributions for both maximum shear and maximum moment are a similar shape with forces increasing approximately uniformly with height. The elastic isolators produce a very uniform distribution for both shear and moment as does the LRB with a low yield level (LRB 1). The LRB with the higher yield level (LRB 2) and the HDR isolators produce a uniform distribution for shear but the moment distribution shows a slight increase with height. The PTFE (sliding) isolator distribution for shear is approximately linear with height, forming a triangular distribution. However, the distribution for maximum moment has very high shears at the top level with a sign change for forces at lower levels. This distribution provides a high moment relative to the base shear. This indicates that the building is “kicking back” at the base.

170

The FPS 2 isolators (higher coefficient of friction) produce a shear distribution that has the shape of an inverted triangle, with maximum inertia forces at the base and then reducing with height. The distribution producing the maximum moment has a similar form to the PTFE plots, exhibiting reversed signs on the inertia loads near the base. The FSP 1 isolators (lower coefficient of friction) also show this reversed sign for the moment distribution. 5 Storey Building (Figure 6.20) The distributions for the 5 storey building follow the trends in the 3 storey building but tend to be more exaggerated. The elastic isolators still produce uniform distributions but all others have distributions for moment which are weighted toward the top of the building, extremely so for the sliding bearings. 8 Storey Building (Figure 6.21) The 8 storey buildings also follow the same trends but in this case even the elastic isolator moment distribution is tending toward a triangular distribution. These results emphasize the limited application of a static force procedure for the analysis and design of base isolated buildings as the distributions vary widely from the assumed distributions. A static procedure based on a triangular distribution of inertia loads would be non-conservative for all systems in Figure 6.18 in which the height ratio exceeded 0.67. This applies to about 25% of the systems considered, including all the flat sliding systems (PTFE).

171

NO DEVICES 1 T=0.0

Elastic 1 T=2.0

L3

L3

L2

L2

L1

Max Shear Max Moment

L0 0

500

1000 1500

2000 2500

L1

Max Shear Max Moment

L0

3000 3500

0

500

1000 1500

Inertia Force (KN)

LRB 1 T=2.0

LRB 2 T=2.0 L3

L2

L2 L1

Max Shear Max Moment

L0 0

500

1000 1500

2000 2500

3000 3500

Max Shear Max Moment

L0 0

500

1000 1500

Inertia Force (KN)

L3

L2

L2 L1

Max Shear Max Moment 0

500

1000 1500

2000 2500

3000 3500

Inertia Force (KN)

-100 -500 0

L3

L2

L2

-500

Max Shear Max Moment 0

0

500 1000 1500 2000 2500 3000 3500 Inertia Force (KN) FPS 2 T=2.0

L3

L0

Max Shear Max Moment

L0

FPS 1 T=2.0

L1

3000 3500

PTFE 1 T=2.8

L3

L0

2000 2500

Inertia Force (KN)

HDR 1 T=2.0

L1

3000 3500

Inertia Force (KN)

L3

L1

2000 2500

500 1000 1500 2000 2500 3000 3500 Inertia Force (KN)

L1

Max Shear Max Moment

L0 -500

0

500 1000 1500 2000 2500 3000 3500 Inertia Force (KN)

Figure 6.17: Time History Inertia Forces: 3 storey Building T = 0.2 Seconds

172

NO DEVICES 1 T=0.0

Elastic 1 T=2.5

L4

L4

L2

L2 Max Shear Max Moment

L0 0

500

1000

1500

2000

Max Shear Max Moment

L0

2500

0

500

Inertia Force (KN)

1000

1500

2000

2500

Inertia Force (KN)

LRB 1 T=2.5

LRB 2 T=2.5

L4

L4

L2

L2 Max Shear

Max Shear

Max Moment

L0 0

500

1000

1500

2000

Max Moment

L0

2500

-500

0

Inertia Force (KN)

500

1000

1500

2000

2500

Inertia Force (KN)

HDR 1 T=2.5

PTFE 1 T=3.7

L4

L4

L2

L2 Max Shear Max Moment

L0 0

500

1000

1500

2000

Max Shear Max Moment

L0

2500

-500

0

Inertia Force (KN)

500

FPS 1 T=2.5

1500

2000

2500

FPS 2 T=2.5

L4

L4

L2

L2 Max Shear Max Moment

L0 -500

1000

Inertia Force (KN)

0

500

1000

1500

2000

Max Shear Max Moment

L0 2500

-500

Inertia Force (KN)

0

500

1000

1500

2000

Inertia Force (KN)

Figure 6.18: Time History Inertia Forces 5 Storey Building T = 0.5 Seconds

173

2500

NO DEVICES 1 T=0.0

Elastic 1 T=3.0

L8

L8

L6

L6

L4

L4 Max Shear

L2 L0 -200

0

200

400

600

800

Max Shear

L2

Max Moment

Max Moment

L0 1000

0

200

400

Inertia Force (KN) LRB 1 T=3.0 L8

L6

L6

L4

L4

L2

L2

Max Shear Max Moment

L0 200

400

600

800

L0

1000

-200

0

200

HDR 1 T=3.0

L6

L6

L4

L4 L2

Max Shear Max Moment

L0 200

400

600

800

1000

-400

-200

0

200

FPS 1 T=3.0

L6

L6

L4

L4

L2

600

L2

Max Shear Max Moment

L0 400

400

800

1000

FPS 2 T=3.0 L8

200

1000

Inertia Force (KN)

L8

0

800

Max Shear Max Moment

L0

Inertia Force (KN)

-200

600

PTFE 1 T=5.6 L8

L2

400

Inertia Force (KN)

L8

0

1000

Max Shear Max Moment

Inertia Force (KN)

-200

800

LRB 2 T=3.0

L8

0

600

Inertia Force (KN)

600

800

Max Shear Max Moment

L0 1000

-200

Inertia Force (KN)

0

200

400

600

800

Inertia Force (KN)

Figure 6.19: Time History Inertia Forces 8 storey Building T = 1.0 Seconds

174

1000

6.1.7

Floor Accelerations

The objective of seismic isolation is to reduce earthquake damage, which includes not only the structural system but also non-structural items such as building parts, components and contents. Of prime importance in attenuating non-structural damage is the reduction of floor accelerations. Response Spectrum Analysis The floor accelerations from the response spectrum analysis are proportional to the floor inertia forces, as shown in Figure 6.22. The accelerations for the building without devices increase approximately linear with height, from a base level equal to the maximum ground acceleration (0.4g) to values from 2.5 to 3 times this value at the roof (1.0g to 1.2g). The isolated displacements in all cases are lower than the 0.4g ground acceleration and exhibit almost no increase with height. 5 Story Building T = 0.5 Seconds Ti = 2.5 Seconds

3 Story Building T = 0.2 Seconds Ti = 2.0 Seconds F5

F3 F4

FPS 2 F2

F1

F0 0.000

0.200

0.400

0.600

0.800

1.000

F2

LRB 2 LRB 1

F1

Elastic No Devices

F0

1.200

FPS 2 FPS 1 PTFE HDR LRB 2 LRB 1 Elastic No Devices

F3

FPS 1 PTFE HDR

1.400

0.000

0.500

8 Story Building T = 1.0 Seconds Ti = 3.0 Seconds F8 F7 F6 F5 FPS 2 FPS 1 PTFE HDR LRB 2 LRB 1 Elastic No Devices

F4 F3 F2 F1 F0 0.000

0.200

1.000

ACCELERATION (g)

ACCELERATION (g)

0.400

0.600

0.800

1.000

1.200

ACCELERATION (g)

Figure 6.20: Response Spectrum Floor Accelerations

175

1.500

Time History Analysis Plots of maximum floor accelerations for three building configurations, one of each height, are provided in Figures 6.23, 6.24 and 6.25. These are the same building and isolation system configurations for which the inertia forces are plotted in Figures 6.19 to 6.21. All plots are the maximum values from any of the three earthquakes. They include the accelerations in the building with no isolation as a benchmark. The acceleration at Elevation 0.0, ground level, is the peak ground acceleration from the three earthquakes, which is constant at 0.56g. The most obvious feature of the plots is that most isolation systems do not provide the essentially constant floor accelerations developed from the response spectrum analysis in Figure 6.22. There are differences between isolation systems but the trends for each system tend to be similar for each building. 

The elastic (E) isolation bearings provide the most uniform distribution of acceleration. As the period of the isolators increases, the accelerations decrease. The longest period, 3.0 seconds, produces accelerations in the structure equal to about one-half the ground acceleration and as the period reduces to 1.5 seconds, the accelerations in the structure are about equal to the ground acceleration. As the building period increases the short period isolators show some amplification with height but this is slight.



The lead rubber bearings (L) produce distributions which are generally similar to those for the elastic bearings but tend to produce higher amplifications at upper levels. The amplification increases as the yield level of the isolation system increases (L1 to L2 to L3 have yield levels increasing from 5% to 7.5% to 10% of W). Again as for the elastic bearings, the accelerations are highest for the shortest isolated periods.



The PTFE sliding bearings (T) tend to increase the ground accelerations from base level with some amplification with height. Accelerations increase as the coefficient of friction increases, that is, as the effective isolated period reduces.



The friction pendulum bearings (F) produce an acceleration profile which, unlike the other types, is relatively independent of the isolated period. This type of isolator is more effective in reducing accelerations for the coefficient of friction of 0.06 (F 1) compared to the 0.12 coefficient (F 2). The accelerations are generally higher than for the elastic or lead rubber systems.

Although some systems produce amplification with height and may increase acceleration over the ground value, all isolation systems drastically reduce accelerations compared to the building without isolators by a large margin although, as the plots show, the system type and parameters must be selected to be appropriate for the building type.

176

12.0 ELEVATION (m)

ELEVATION (m)

12.0 10.0 8.0 6.0

No Isolators E 1 T=1.5 E 1 T=2.0 E 1 T=2.5 E 1 T=3.0

4.0 2.0 0.0 0.00

0.50

1.00

1.50

2.00

2.50

10.0 8.0 6.0

No Isolators L 1 T=1.5 L 1 T=2.0 L 1 T=2.5 L 1 T=3.0

4.0 2.0 0.0 0.00

3.00

0.50

ELEVATION (m)

10.0 8.0 6.0

No Isolators L 2 T=1.5 L 2 T=2.0 L 2 T=2.5 L 2 T=3.0

4.0 2.0 0.0 0.00

2.50

3.00

0.50

1.00

1.50

2.00

2.50

10.0 8.0 6.0

No Isolators L 3 T=1.5 L 3 T=2.0 L 3 T=2.5 L 3 T=3.0

4.0 2.0 0.0 0.00

3.00

0.50

1.00

1.50

2.00

2.50

3.00

ACCELERATION (g)

ACCELERATION (g) 12.0 ELEVATION (m)

12.0 10.0 8.0 6.0

No Isolators H 1 T=1.5 H 1 T=2.0 H 1 T=2.5 H 1 T=3.0

4.0 2.0 0.0 0.00

0.50

1.00

1.50

2.00

2.50

10.0 8.0 6.0

No Isolators T 1 T=2.2 T 1 T=2.8 T 1 T=3.7 T 1 T=5.6

4.0 2.0 0.0 0.00

3.00

0.50

12.0

1.50

2.00

2.50

3.00

12.0 ELEVATION (m)

10.0 8.0 6.0

No Isolators F 1 T=1.5 F 1 T=2.0 F 1 T=2.5 F 1 T=3.0

4.0 2.0 0.0 0.00

1.00

ACCELERATION (g)

ACCELERATION (g)

ELEVATION (m)

2.00

12.0

12.0 ELEVATION (m)

1.50

ACCELERATION (g)

ACCELERATION (g)

ELEVATION (m)

1.00

0.50

1.00

1.50

2.00

2.50

3.00

ACCELERATION (g)

10.0 8.0 6.0

No Isolators F 2 T=1.5 F 2 T=2.0 F 2 T=2.5 F 2 T=3.0

4.0 2.0 0.0 0.00

0.50

1.00

1.50

2.00

ACCELERATION (g)

Figure 6.21: Floor Accelerations 3 Storey Building T = 0.2 Seconds

177

2.50

3.00

20.0

15.0 10.0

ELEVATION (m)

ELEVATION (m)

20.0

No Isolators E 1 T=1.5 E 1 T=2.0 E 1 T=2.5 E 1 T=3.0

5.0 0.0 0.00

0.50

1.00

1.50

2.00

2.50

15.0 10.0

No Isolators L 1 T=1.5 L 1 T=2.0 L 1 T=2.5 L 1 T=3.0

5.0 0.0

3.00

0.00

0.50

ACCELERATION (g)

ELEVATION (m)

ELEVATION (m)

2.00

2.50

3.00

20.0

15.0 10.0

No Isolators L 2 T=1.5 L 2 T=2.0 L 2 T=2.5 L 2 T=3.0

5.0 0.0 0.00

0.50

1.00

1.50

2.00

2.50

15.0 10.0

No Isolators L 3 T=1.5 L 3 T=2.0 L 3 T=2.5 L 3 T=3.0

5.0 0.0

3.00

0.00

0.50

ACCELERATION (g)

1.00

1.50

2.00

2.50

3.00

ACCELERATION (g)

20.0

20.0

10.0

ELEVATION (m)

15.0 No Isolators H 1 T=1.5 H 1 T=2.0 H 1 T=2.5 H 1 T=3.0

5.0 0.0 0.00

0.50

1.00

1.50

2.00

2.50

15.0 10.0

No Isolators T 1 T=2.2 T 1 T=2.8 T 1 T=3.7 T 1 T=5.6

5.0 0.0

3.00

0.00

0.50

ACCELERATION (g)

20.0

1.50

2.00

2.50

3.00

20.0

15.0 10.0

No Isolators F 1 T=1.5 F 1 T=2.0 F 1 T=2.5 F 1 T=3.0

5.0 0.0 0.00

1.00

ACCELERATION (g)

0.50

1.00

1.50

2.00

2.50

3.00

ELEVATION (m)

ELEVATION (m)

1.50

ACCELERATION (g)

20.0

ELEVATION (m)

1.00

15.0 10.0

No Isolators F 2 T=1.5 F 2 T=2.0 F 2 T=2.5 F 2 T=3.0

5.0 0.0 0.00

ACCELERATION (g)

0.50

1.00

1.50

2.00

ACCELERATION (g)

Figure 6.23: Floor Accelerations 5 Storey Building T = 0.5 Seconds

178

2.50

3.00

25.0

25.0

ELEVATION (m)

30.0

20.0 15.0

No Isolators E 1 T=1.5 E 1 T=2.0 E 1 T=2.5 E 1 T=3.0

10.0 5.0 0.0 0.00

0.50

1.00

1.50

20.0 15.0

No Isolators L 1 T=1.5 L 1 T=2.0 L 1 T=2.5 L 1 T=3.0

10.0 5.0 0.0

2.00

0.00

0.50

ACCELERATION (g)

25.0

25.0

ELEVATION (m)

30.0

20.0 15.0

No Isolators L 2 T=1.5 L 2 T=2.0 L 2 T=2.5 L 2 T=3.0

10.0 5.0 0.0 0.00

0.50

1.00

1.50

15.0

5.0 0.0 0.00

2.00

0.50

1.00

1.50

2.00

ACCELERATION (g)

30.0

25.0

25.0

20.0 15.0

No Isolators H 1 T=1.5 H 1 T=2.0 H 1 T=2.5 H 1 T=3.0

10.0 5.0 0.0 1.00

1.50

ELEVATION (m)

ELEVATION (m)

2.00

No Isolators L 3 T=1.5 L 3 T=2.0 L 3 T=2.5 L 3 T=3.0

10.0

30.0

0.50

1.50

20.0

ACCELERATION (g)

0.00

1.00 ACCELERATION (g)

30.0

20.0 15.0

No Isolators T 1 T=2.2 T 1 T=2.8 T 1 T=3.7 T 1 T=5.6

10.0 5.0 0.0

2.00

0.00

ACCELERATION (g)

0.50

1.00

1.50

2.00

ACCELERATION (g)

25.0 20.0 15.0

No Isolators F 1 T=1.5 F 1 T=2.0 F 1 T=2.5 F 1 T=3.0

10.0 5.0 0.0 0.00

0.50

1.00

1.50

ELEVATION (m)

30.0 30.0 ELEVATION (m)

ELEVATION (m)

ELEVATION (m)

30.0

25.0 20.0 15.0

No Isolators F 2 T=1.5 F 2 T=2.0 F 2 T=2.5 F 2 T=3.0

10.0 5.0 0.0 0.00

0.50

1.00 ACCELERATION (g)

2.00

ACCELERATION (g)

Figure 6.24: Floor Accelerations 8 Storey Building T = 1.0 Seconds

179

1.50

2.00

6.1.8

Optimum Isolation Systems

The results presented in the previous sections illustrate the wide differences in performance between systems and between different properties of the same system. Different systems have different effects on isolation system displacement, shear coefficient and floor accelerations and no one device is optimum in terms of all possible objectives. Table 6.4 lists the top 15 systems (of the 32 considered) arranged in ascending order of efficiency for each of three potential performance objectives: 1. Minimum Base Shear Coefficient. The PTFE sliding systems provide the smallest base shear coefficients, equal to the coefficient of friction. These are followed by the LRB with a high yield level (Qd = 0.10) and 3 second period. However, none of these 4 systems provide a restoring force and so the design displacement is three times the calculated value (UBC provisions). After these four systems, the optimum systems in terms of minimum base shear coefficient are variations of the LRB and FPS systems. 2. Minimum Isolation System Displacement. The FPS systems with a coefficient of friction of 0.12 and relatively short isolated periods are the most efficient at controlling isolation system displacements and the lowest five displacements are all produced by FPS variations. After these are 3 LRB variations and then HDR and FPS. Most of the systems that have minimum displacements have relatively high base shear coefficients and accelerations. 3. Minimum Floor Accelerations. Accelerations are listed for three different building periods and are ordered in Table 6.4 according to the maximum from the three buildings. Some systems will have a higher rank for a particular building period. The elastic isolation systems produce the smallest floor accelerations, followed by variations of LRB and HDR systems. The FPS and PTFE systems do not appear in the optimum 15 systems for floor accelerations. No system appears within the top 15 of all three categories but some appear in two of three: 1. The FPS systems with a coefficient of friction of 0.12 and a period of 2.5 or 3.0 provide minimum base shear coefficients and displacements. However, floor accelerations are quite high. 2. The LRB with a period of 2 seconds and Qd = 0.05, 0.075 or 0.10 appear on the list for both minimum displacements and minimum accelerations. The base shear coefficients for these systems are not within the top 15 but are moderate, with a minimum value of 0.203 (compared to 0.06 to 0.198 for the top 15). 3. Five LRB variations and two HDR variations appear in the top 15 for both base shear coefficients and floor accelerations. Of these, the minimum isolated displacement is 258 mm, compared to the range of 103 mm to 213 mm for the top 15 displacements. These results show that isolation system selection needs to take account of the objectives of isolating and the characteristics of the structure in which the system is to be installed. For most projects a series of parameter studies will need to be performed to select the optimum system.

180

System

Variation

Period

 (mm) Minimum Base Shear Coefficient, C PTFE =0.06 5.6 1291 PTFE =0.09 3.7 926 PTFE =0.12 2.8 669 LRB Qd=0.1 3.0 1152 LRB Qd=0.075 3.0 332 PTFE =0.15 2.2 613 LRB Qd=0.05 3.0 344 FPS =0.06 3.0 228 LRB Qd=0.1 2.5 269 LRB Qd=0.075 2.5 258 FPS =0.12 3.0 130 HDR 3.0 320 LRB Qd=0.05 2.5 269 FPS =0.06 2.5 199 FPS =0.12 2.5 122

C

Maximum Floor Acceleration (g) T = 0.2 s T = 0.5 s T = 1.0 s

0.060 0.090 0.120 0.137 0.141 0.150 0.153 0.162 0.163 0.167 0.178 0.179 0.180 0.188 0.198

0.58 0.65 0.75 0.15 0.15 0.83 0.16 0.50 0.18 0.19 0.77 0.19 0.20 0.46 0.77

0.89 0.99 1.02 0.25 0.27 1.07 0.31 0.83 0.33 0.33 1.03 0.25 0.34 0.80 1.05

1.09 1.45 1.48 0.42 0.43 1.32 0.39 1.08 0.58 0.55 1.38 0.41 0.62 1.13 1.33

Minimum Isolation System Displacement,  FPS =0.12 1.5 103 0.301 FPS =0.12 2.0 111 0.231 FPS =0.12 2.5 122 0.198 FPS =0.06 1.5 124 0.280 FPS =0.12 3.0 130 0.178 LRB Qd=0.075 1.5 140 0.272 LRB Qd=0.1 1.5 140 0.267 LRB Qd=0.05 1.5 144 0.280 HDR 1.5 148 0.277 FPS =0.06 2.0 160 0.221 HDR 2.0 177 0.225 LRB Qd=0.075 2.0 195 0.204 LRB Qd=0.1 2.0 197 0.203 FPS =0.06 2.5 199 0.188 LRB Qd=0.05 2.0 213 0.225

0.75 0.75 0.77 0.53 0.77 0.35 0.33 0.35 0.33 0.49 0.26 0.27 0.28 0.46 0.24

1.01 1.07 1.05 0.86 1.03 0.70 0.74 0.53 0.50 0.83 0.38 0.41 0.51 0.80 0.36

1.11 1.23 1.33 0.94 1.38 0.85 1.01 0.77 0.79 1.14 0.70 0.68 0.76 1.13 0.56

Minimum Floor Accelerations, A ELASTIC 3.0 528 ELASTIC 2.5 434 LRB Qd=0.05 3.0 344 HDR 3.0 320 LRB Qd=0.1 3.0 1152 LRB Qd=0.075 3.0 332 ELASTIC 2.0 369 HDR 2.5 269 LRB Qd=0.075 2.5 258 LRB Qd=0.05 2.0 213 LRB Qd=0.1 2.5 269 LRB Qd=0.05 2.5 269 LRB Qd=0.075 2.0 195 HDR 2.0 177 LRB Qd=0.1 2.0 197

0.25 0.29 0.16 0.19 0.15 0.15 0.40 0.20 0.19 0.24 0.18 0.20 0.27 0.26 0.28

0.26 0.30 0.31 0.25 0.25 0.27 0.42 0.27 0.33 0.36 0.33 0.34 0.41 0.38 0.51

0.29 0.34 0.39 0.41 0.42 0.43 0.49 0.51 0.55 0.56 0.58 0.62 0.68 0.70 0.76

0.247 0.279 0.153 0.179 0.137 0.141 0.371 0.202 0.167 0.225 0.163 0.180 0.204 0.225 0.203

Table 6.4: Optimum Isolation Systems

181

6.2 EXAMPLE ASSESSMENT OF ISOLATOR PROPERTIES The limited studies discussed above have shown that there is no one isolation system type, or set of system parameters, which provides optimum performance in all aspects. For projects, it is recommended that a series of studies by performed to tune the system to the structure. Following is an example of how this has been applied to a building project. For this project a lead rubber system was selected as the isolation type based on a need for relatively high amounts of damping. The LRB properties were selected by assessing performance for a wide range of properties. For this type of bearing the plan size is set by the vertical loads. The stiffness, and so effective period, is varied by changing the height of the bearing, which is accomplished by changing the number of rubber layers. The yield level of the system is varied by modifying the size of the lead cores in the bearing. For this project the performance was assessed by varying the number of layers from 40 to 60 (changing stiffness by 50%) and by varying the lead core diameter from 115 mm (4.5”) to 165 mm (6.5”), changing the yield level by 100%. A program was set up to cycle through a series of 3D-BASIS analyses. For each variation, the program adjusted the input file properties for stiffness and yield level, performed the analysis and extracted the output response quantities from the output file. From these results the plots in Figures 6.25 and 6.26 were generated. The isolator naming convention is, for example, L40-6, which indicates 40 layers with a 6” lead core. These plots are used to determine trends in isolator displacements, shear forces and maximum floor accelerations. For this particular structure and seismic input, both the isolator displacement and the base shear coefficient decrease as either the stiffness is decreased or the yield level is increased. However, the maximum floor accelerations increase as the displacements and coefficients decrease and there is a point, in this case when the lead core is increased beyond 6”, where the accelerations increase dramatically. From the result of this type of analysis, isolators can be selected to minimize respective floor accelerations, drifts, and base shears of isolator coefficients. As listed in Table 6.5, in this case the minimum accelerations and drifts occur for a tall bearing (60 layers) with a small lead core (4.5”). The isolator displacement can be reduced from 420 mm (16.5”) to 350 mm (13.8”) and the base shear coefficient from 0.121 to 0.113 by increasing the lead core from 4.5” to 5” (a 23% increase in yield level). This only increases the floor accelerations and drifts by 10% so is probably a worthwhile trade-off. Minimum isolator displacements are provided by a stiff bearing (44 layers) with a large core (6.5”) but there is a small penalty in base shear coefficient and a very large penalty in floor accelerations associated with his. For this project, design should accept isolator displacements of 350 mm to ensure the best performance of the isolated structure.

182

20.0

0.20 DECREASING STIFFNESS

0.16

14.0

0.14

12.0

0.12

10.0

0.10

8.0

0.08

Isolator Displacement Base shear Coefficient

6.0 4.0

0.06 0.04

INCREASING YIELD LEVEL

L60-C6.5

L54-C6.5

L48-C6.5

L42-C6.5

L58-C6

L52-C6

L46-C6

L40-C6

L56-C5.5

L50-C5.5

L44-C5.5

L60-C5

L48-C5

L42-C5

0.00 L58-C4.5

0.0 L52-C4.5

0.02 L46-C4.5

2.0 L40-C4.5

BASE SHEAR COEFFICIENT

0.18

16.0

L54-C5

DISPLACEMENT (inches)

18.0

ISOLATOR TYPE

2.0

18.0

1.8

16.0

1.6

14.0

1.4

12.0

1.2

Isolator Displacement Maximum Floor Acceleration

10.0

DECREASING STIFFNESS

1.0

8.0

0.8

6.0

0.6

4.0

0.4 INCREASING YIELD LEVEL

2.0

0.2

ISOLATOR TYPE

Figure 6.26: Displacement versus Floor Acceleration

183

L60-C6.5

L54-C6.5

L48-C6.5

L42-C6.5

L58-C6

L52-C6

L46-C6

L40-C6

L56-C5.5

L50-C5.5

L44-C5.5

L60-C5

L54-C5

L48-C5

L42-C5

L58-C4.5

L52-C4.5

0.0 L46-C4.5

0.0

FLOOR ACCELERATION (g)

20.0

L40-C4.5

DISPLACEMENT (inches)

Figure 6.25: Displacement versus Base Shear

Isolator Base Maximum Maximum Displacement Shear Floor Drift mm Coefficient Acceleration (Inches) (g) (g) Minimum Floor Acceleration L60-C4.5 Minimum Drift L60-C4.5 Minimum Base Shear Coefficient L60-C5 Minimum Isolator Displacement L44-C6.5

420 (16.5)

0.121

0.420

0.0032

420 (16.5)

0.121

0.420

0.0032

350 (13.8)

0.113

0.460

0.0035

260 (10.2)

0.132

1.590

0.0071

Table 6.5: Optimum Isolator Configuration

These analyses also illustrate the discussion earlier about the non-uniform nature of the acceleration distribution when determined from the time history method of analysis. Figure 6.27 plots the acceleration profiles for the systems which provide the minimum floor accelerations and minimum isolator displacements, respectively. Even though these systems provide a similar base shear coefficient, the stiff system with high damping provides floor accelerations over three times as high. The shape of the acceleration profile for the latter system exhibits the characteristics of very strong higher mode participation. An analysis which used only effective stiffness would not reflect this effect. 6

FLOOR LEVEL

5

4

3

2

L60-C4.5 L44-C6.5 Base Shear Coefficient 0.121 Base Shear Coefficient 0.132

1

0 0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

MAXIMUM ACCELERATION (g)

Figure 6.27: Floor Acceleration Profiles

184

1.60

1.80

CHAPTER 7:

SEISMIC ISOLATION OF BUILDINGS AND BRIDGES

7.1 INTRODUCTION TO ISOLATION OF BUILDINGS As discussed in previous chapters, the ideal of base isolation is to install flexible devices to increase the period beyond 2.0 seconds. The preferred site conditions are a stiff subsoil profile and the building preference is for a relatively heavy building so as to achieve the target isolated period within the range of stiffness provided by the usual type of device. The reality is often different and this example is intended to illustrate how benefits can be achieved even when these ideal conditions are not met. The example structure is relatively light and it is located on a soft soil site close to a major fault. Favoring isolation was the building type, an essential medical facility which was required to remain operational during and after an earthquake. This required essentially elastic response of the structure. Following the design of the isolated building, a description of a spreadsheet based procedure which can be used to implement base isolation for buildings is described.

7.2 SCOPE OF BUILDING EXAMPLE This example design is based on the submittal for a small health care facility located in New Zealand. The contract documents for supply of isolation bearings specified that design calculations were to be provided for the isolators and the results of dynamic analysis of the structure modeled using the assumed isolator properties. The Structural Engineer had set performance criteria for the isolation system based on considerations of seismic loads, building weights and performance requirements and the isolation system had to meet the following requirements: 1. Total design displacement not to exceed 350 mm for DBE. 2. Total maximum displacement not to exceed 400 mm for MCE 3. Elastic base shear for DBE not to exceed 0.65. 4. Inter-storey drift ratio of the structure above the isolation system not to exceed 0.0100. The building was a low-rise structure located in a high seismic zone with relatively light column loads. As will be seen in the design of the isolation system, this limits the extent of the period shift and so the degree of isolation which can be achieved.

185

7.3 SEISMIC INPUT A site-specific seismic assessment of the site developed a suite of time histories to define each of the DBE and MCE levels of load. Five time histories defined the lower level earthquake and four the upper level. For each level, one modified (frequency scaled) and four or three as-recorded time histories were used. The records are listed in Table 7.1. Figure 7.1 plots the envelopes of the 5% damped response spectra of the records used to define the DBE and MCE levels of load respectively. Also plotted on Figure 7.1 is the code response spectrum for a hospital building on this site without a site specific study. The seismic definition has an unusual characteristic in that the MCE level of load is approximately the same as the DBE level of load whereas usually it would be expected to be from 25% to 50% higher. This is because the earthquake probability at this location is dominated by the Wellington Fault which has a relatively short return period and is expected to generate an earthquake of high magnitude. The elastic base shear coefficient on this site for a non-isolated building with a period of 0.42 seconds is approximately 2.5, based on the envelope of the scaled time histories. The specification requires a maximum base shear of 0.65, which is a reduction by a factor of almost 4.

Level EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7 EQ8 EQ9

DBE

MCE

Filename EL40N00E EL40N90W HOLSE000 GZ76N00E HMEL40NE GZ76N00E SYL360 EL79723 MEL79723

Record El Centro 1940 NS El Centro 1940 EW Hollister and Pine0 deg, 1989 Loma Prieta Gazli, 1976 NS Modified El Centro 1940 NS Gazli 1976 NS Sylmar Hospital 360 deg, 1994 Northridge El Centro Array No. 7 230 deg, 1979 Modified El Centro Array No. 7, 1979

Table 7.1: Input Time Histories

186

Scale Factor 3.25 3.90 1.69 1.17 1.30 1.20 1.00 1.70 1.00

3.5

ACCELERATION (g)

3.0 2.5 DBE Envelope MCE Envelope NZS4203 Soft Z 1.2 Sp 1 R 1.3

2.0 1.5 1.0 0.5 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

PERIOD (Seconds) Figure 7.1: 5% Damped Envelope Spectra

7.4 DESIGN OF ISOLATION SYSTEM The isolation system was designed using a spreadsheet developed following the procedures described in Chapter 4. A series of design studies was performed using the spreadsheet to optimize the isolator dimensions, shear modulus and lead core diameter for the level of seismic load as determined from envelope spectra of the time histories. These studies resulted in an isolator size of 675 mm diameter x 380 mm high (total rubber thickness 210 mm) a 130 mm diameter lead core. Design was based on a moderately soft rubber (G = 0.60 MPa). Figure 7.2 summarizes the performance of the isolation system as designed. This isolation system configuration provided an effective period of approximately 1.5 seconds. The lead cores provided displacement-dependent hysteretic damping. The equivalent viscous damping ranged from 32% at 50 mm displacement to 13% at 400 mm displacement. Figure 7.3 shows the theoretical hysteresis of this isolator. The factors of safety listed for each limit case are close to the acceptable limit for lead rubber bearings under MCE, where the strain factor of safety is less than 2. An acceptable lower limit for the ratio of reduced area to gross area is 25% and an acceptable upper limit on strain is 200%. This design is very close to these limits for this type of device.

187

PERFORMANCE SUMMARY DBE

MCE

1.455

1.479

Displacement D D D M

313

358

Total Displacements DTD D TM

360

412

0.596

0.659

Force Coefficient Vs / W 1.5 x Yield Force / W Wind Force / W Fixed Base V at TD Governing Design Coefficient Base Shear Force Damping eff

0.298 0.229 0.000 0.348 0.348 8730 15.66%

14.22%

Damping Coefficients BD BM

1.35

1.32

Gravity Strain F.S. Buckling F.S DBE Strain F.S Buckling F.S MCE Strain F.S Buckling F.S Reduced Area / Gross Area Maximum Shear Strain Effective Period TD TM

Type 1 16.34 12.25 2.14 3.71 1.76 2.81 25.6% 196%

Pad B

Force Coefficient Vb / W

Figure 7.2: Summary of Isolation Design

188

600

400

SHEAR FORCE (KN)

Type 1 LRB 200

0 -400

-300

-200

-100

0

100

200

300

400

-200

-400

-600 SHEAR DISPLACEMENT (mm) Figure 7.3: Hysteresis to Maximum Displacement

7.5 ANALYSIS MODELS The performance was quantified using time history analysis of a matrix of 18 ETABS models (Figure 7.4). The models included the 9 earthquake records, one mass eccentricity location (+5% X and Y) and earthquakes applied along the X and Y axes of the structure respectively. As the structure is doubly symmetric only the positive eccentricity case was evaluated. Spring properties for the isolators were as listed in Figure 7.5. These were calculated using the equations given in the design procedure in Chapter 5.

189

Figure 7.4: ETABS Model

Type 1 LRB First Data Line: ID ITYPE KE2 KE3 DE2 DE3 Second Data Line: K1 K2 K3 FY2/K11/CFF2 FY3/K22/CFF3 RK2/K33/CFS2 RK3/CFS3 A2 A3 R2 R3

1 ISOLATOR1 1.28 1.28 0.092 0.092

Identification Number Biaxial Hysteretic/Linear/Friction Spring Effective Stiffness along Axis 2 Spring Effective Stiffness along Axis 3 Spring Effective Damping Ratio along Axis 2 Spring Effective Damping Ratio along Axis 3

895.7 9.55 9.55 118.39 118.39 0.103 0.103

Spring Stiffness along Axis 1 (Axial) Initial Spring Stiffness along Axis 2 Initial Spring Stiffness along Axis 3 Yield Force Along Axis 2 Yield Force Along Axis 3 Post-Yield stiffness ratio along Axis 2 Post-Yield stiffness ratio along Axis 3 Coefficient controlling friction Axis 2 Coefficient controlling friction Axis 3 Radius of Contact 2 direction Radius of Contact 3 direction

Figure 7.5: ETABS Properties

190

7.6 ANALYSIS RESULTS Figures 7.6 to 7.8 show histograms of maximum response quantities for each of the scaled earthquakes used to evaluate performance (refer to Table 7.1 for earthquake names and scale factors). 1. The maximum response to DBE motions is dominated by EQ3, which is the Hollister Sth and Pine Drive 0 degree record from the 1989 Loma Prieta earthquake, scaled by 1.69. This record produced maximum displacements about 20% higher than the next highest records, the 1940 El Centro NW record scaled by 3.90 and the 1976 Gazli record scaled by 1.17. 2. A similar dominant record appears for MCE response, the El Centro Array No. 7 230 degree component from the 1979 Imperial Valley earthquake, which produced results higher than the other two records for all response quantities. Figure 7.9 shows the input acceleration record for the dominant DBE earthquake, EQ3. This record has peak ground accelerations of approximately 0.6g. The trace is distinguished by a large amplitude cycle at approximately 8 seconds, a characteristic of records measured close to the fault. The maximum bearing displacement trace, Figure 7.10, shows a one and one-half cycle high amplitude displacement pulse between 8 and 10 seconds, with amplitudes exceeding 300 mm. The remainder of the record produces displacements not exceeding 150 mm. This is typical of the response of isolation systems to near fault records. Figure 7.11 plots the time history of storey shear forces. The bi-linear model used to represent the isolators has calculated periods of 0.54 seconds (elastic) and 1.69 seconds (yielded). The fixed base building has a period of 0.42 seconds. The periodicity of response would be expected to reflect these dynamic characteristics and Figure 7.11 does show shorter period response imposed on the longer period of the isolation system.

191

EQ7

EQ8

EQ9

EQ7

EQ8

EQ9

EQ6

EQ5

EQ4

EQ3

EQ2

X Direction Y Direction

EQ1

Displacement (mm)

450 400 350 300 250 200 150 100 50 0

Figure 7.6: Total Design Displacement

X Direction Y Direction

0.60 0.50 0.40 0.30 0.20 0.10

EQ6

EQ5

EQ4

EQ3

EQ2

0.00 EQ1

Base Shear Coefficient

0.70

Figure 7.7: Base Shear Coefficient

192

0.8% 0.7%

X Direction Y Direction

Drift (%)

0.6% 0.5% 0.4% 0.3% 0.2% 0.1%

EQ9

EQ8

EQ7

EQ6

EQ5

EQ4

EQ3

EQ2

EQ1

0.0%

Figure 7.8: Maximum Drift Ratios

0.80

INPUT ACCELERATION (g)

0.60 0.40 0.20 0.00 0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

-0.20 -0.40 -0.60 -0.80 TIME (Seconds) Figure 7.9: DBE Earthquake 3 Input

193

16.00

18.00

20.00

400

BEARING DISPLACEMENT (mm)

300 200 100 0 0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

14.00

15.00

-100 -200 -300 -400 TIME (Seconds) Figure 7.10: DBE Earthquake 3 : Bearing Displacement

15000 Roof First Floor Ground Floor

STOREY SHEAR FORCE (kN)

10000

5000

0

-5000

-10000

-15000 5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

TIME (Seconds) Figure 7.11: DBE Earthquake 3: Storey Shear Forces

194

13.00

7.6.1

Summary of Results

Table 7.2 lists the maximum values of the critical response parameters identified in the specifications: 

Maximum bearing displacements of 323 mm (DBE) and 397 mm (MCE) were within the specification limits of 350 mm and 400 mm respectively.



A maximum bearing force of 423 kN at DBE levels, less than the maximum specified value of 450 kN.



A maximum drift ratio of 0.0067 (MCE), within the specification limits of 0.0100.

Base Shear Coefficient Center of Mass Displacement Maximum Bearing Displacement Maximum Bearing Force Maximum Drift

DBE 0.549 290 323 423 0.0061

LIMIT

350 450

MCE 0.650 364 397 497 0.0067

LIMIT

400 0.0100

Table 7.2: Summary of Results

7.7 TEST CONDITIONS The results of the ETABS analysis were used to derive the prototype and production test conditions, as listed in Table 7.3. The displacements and vertical loads define the test conditions. The shear force and the hysteresis loop area define the performance required of the prototype and production tests. Test Parameter Total Design Displacement (mm) Total Maximum Displacement (mm) Average DL (kN) Average 1.2D + 0.5LL + E (kN) Average 0.8D - E (kN) Maximum 1.2D + LL + E (kN) Shear Force (kN) Hysteresis Loop Area (kN-mm)

Prototype Test 323 397 950 795 369 1224 424 131,925

Production Test 260

1100 375.4 117,520

Table 7.3: Prototype Test Conditions

The acceptance criteria for prototype and production tests are set out in codes such as the UBC and AASHTO. Some obvious criteria relate to the requirements that the bearings remain stable and that there be no signs of damage in the test. Other UBC requirements relate to the change in properties over multiple cycles. However, the UBC does not provide guidance as to the comparison between test properties and design properties. AASHTO provides some guidance in this respect, requiring that the effective stiffness be within 10% of the design value and that the hysteresis loop area be at least 70% of the design value for the lowest cycle.

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For building projects, specifications generally require that the average effective stiffness (or shear force, which is proportional) be within 10% of the design value and that the average loop area be at least 80% of the design value (no upper limit). These were the limits for this project.

7.8 PRODUCTION TEST RESULTS A total of 38 isolation bearings were tested under combined compression and shear to the center of mass DBE displacement of 260 mm. The isolators were tested in pairs and so 19 individual results were obtained. Table 7.4 provides a summary of the production tests results. The measured shear forces ranged from –2.5% to +3.2% of the design value, with a mean value –0.8% lower than the design value. The measured hysteresis loop areas exceeded the design value by at least 17.8%, with a mean value 22% higher than the design value. Measured

Maximum Mean Minimum Maximum Mean Minimum

Deviation Deviation From From Specification Mean Shear Force (kN) 387.4 3.2% 4.0% 372.5 -0.8% 0.0% 365.9 -2.5% -1.8% Loop Area (kN-mm) 148,757 26.5% 3.7% 143,425 22.0% 0.0% 138,456 17.8% -3.5%

Table 7.4: Summary of 3 Cycle Production Test Results

Figure 7.12 provides an example of one production test of a pair of isolation bearings. As is typical of LRBs, the first loading cycles produces a much higher shear force than subsequent unloading and loading cycles. Although the reasons for this are not fully understood, the increase is believed to be a function of both lead core characteristics and the effect of the initial loading pulse from zero displacement and velocity. For most LRB tests it is common to test for one cycle additional to the test requirements and exclude the first cycle from the evaluation of results. This is shown in Figure 7.12. The production tests specify 3 cycles at a 260 mm displacement and the test is performed for 4 cycles with the results processed from Cycles 2 to 4. Max Load kN 480.5 416.0 400.4 392.6

Min Disp mm -264.7 -264.7 -264.7 -264.7

Max Disp mm 266.2 265.7 265.7 265.7

Loop Area kN.mm 173081 149232 140849 136797

Strain %

Keff kN

Qd kN

Damping %

1 2 3 4

Min Load kN -390.6 -359.4 -349.6 -345.7

126% 126% 126% 126%

1.641 1.462 1.414 1.392

154.3 132.8 125.0 121.1

23.8% 23.1% 22.5% 22.2%

Avg

-351.6

403.0

-264.7

265.7

142293

126%

1.423

126.3

22.6%

Loop

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Figure 7.12: Example Production Test

7.9 SUMMARY In terms of suitability for isolation this building would be termed marginal in terms of site suitability (soft soils) and building suitability (a light building with relatively low total seismic mass). However, in terms of need for isolation it scored highly as the site-specific earthquake records indicated a maximum elastic coefficient of over 2.5g at the fixed base period. The low mass necessitated a short isolated period (approximately 1.5 seconds) and a high yield level to provide damping to control displacements due to the soft soil (yield level equal to 15% of the weight). This resulted in a high base shear coefficient at the MCE level of 0.65g. However, in spite of these restrictions on isolation system performance the force levels in the structure were still reduced by a factor of almost 4 (from 2.5g to 0.65g) and floor motions would be reduced proportionately. Standard design office software (ETABS) was used to evaluate the performance of the structure and isolation system using the non-linear time history method of analysis. The results from this analysis provided the displacements, vertical loads and required performance characteristics to define the prototype and production test requirements. The prototype and production test results demonstrated that the design performance could be achieved. In this example, the production test results produced a mean shear force within 1% of the design values and hysteresis loop areas exceeding the design values by at least 15%.

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7.10 IMPLEMENTATION IN SPREADSHEET Included with this book is a spreadsheet which can be used to evaluate system performance and factors of safety based on user selected isolator details. The spreadsheet is not intended for final design or to substitute for the calculations by the structural engineer of record. It is a tool provided to assist users in developing their own isolation design procedures. The example provided in this section is based on design to 1997 UBC requirements. Designs based on other codes follow the same general principles. In the spreadsheet, cells colored red indicate user-specified input. The workbook contains a number of sheets with the design performed within the sheet Design. The spreadsheet is set up for up to three types of isolator mixed in a project. This can be extended by inserting additional columns and copying formulas across the sheet.

7.10.1 Material Definition The material definitions are contained on the sheet Design Data, as shown in Figure 7.13. This is the basic information used for the design process. The range of properties available for rubber is restricted and some properties are related to others, for example, the ultimate elongation, material constant and elastic modulus are all a function of the shear modulus. Information on available rubbers is provided elsewhere in this book. Users should also check with manufacturers, especially for high damping rubber formulations. As for the rubber, the PTFE properties used for sliding bearings are supplier-specific. The values listed in Figure 7.13 are typical of the material but other properties are available. High damping rubber is the most variable of the isolator materials as each manufacturer has specific properties for both stiffness and damping. The design procedure is based on tabulated values of the shear modulus and equivalent damping, as listed in Figure 7.13. The damping values tabulated may include viscous damping effects if appropriate. Default HDR properties listed are for a relatively low damping rubber formulation and so any design based on these properties should be easily achievable from a number of manufacturers. As such, they should be conservative for preliminary design.

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DESIGN PROPERTIES Units Elastomer Properties Shear Modulus Ultimate Elongation Material Constant, k Elastic Modulus, E Bulk Modulus Damping Lead Yield Strength Teflon Coeff of Friction Gravity TFE Properties Vertical Stiffness Lateral Stiffness Coeff of Friction - Lo Vel Coeff of Friction - Hi Vel Coefficient a

1

0.001

KN,mm 0.0004 6.5 0.87 0.00135 1.5 0.05 0.008 0.1 9810

MPa 0.4 6.5 0.87 1.35 1500 0.05 8.00 0.10 9810

KN/cm^2 0.040 6.5 0.87 0.14 150 0.05 0.8 0.1 981

ksi 0.057 6.5 0.87 0.19 215 0.05 1.15 0.1 386.4

5000

5000000

500000

28222

2000 0.04 0.1 0.9

2000000 0.04 0.1 0.9

200000 0.04 0.1 0.9

11289 0.04 0.1 0.9

TEST DATA HDR Bearings

Shear Strain % 10 25 50 75 100 125 150 175 200

Shear Modulus MPa

Equivalent Damping %

1.21 0.79 0.57 0.48 0.43 0.40 0.38

12.72 11.28 10.00 8.96 8.48 8.56 8.88

0.37 0.35

9.36 9.36

Figure 7.13: Material Properties Used For Design

7.10.2 Project Definition The project definition section of the spreadsheet is as shown in Figure 7.14. The information provided defines the seismic loads and the structural data required in terms of the UBC requirements for evaluating performance: 1. The design units, metric (KN, mm) or U.S units (kip, in). The example used here is in metric units. 2. The seismic information is extracted from UBC tables for the particular site. This requires the zone, soil type and fault information and the isolated lateral force coefficient, RI. 3. The response modification coefficient, R, and importance factor, I, for an equivalent fixed base building are required as they form a limitation on base shear. Note that, for base isolated structures, the importance factor is assumed to be unity for all structures for UBC designs. 4. Building dimensions are required to estimate the torsional contribution to the total isolation system displacement. The project definition information is specific to a project and, once set, does not need to be changed as different isolation systems are assessed and design progresses.

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UBC Design Example

PROJECT: Units:

KN,mm

Seismic Zone Factor, Z Soil Profile Type Seismic Coefficient, CA

0.4 SC 0.400

Table 16-I Table 16-J Table 16-Q

Seismic Coefficient, CV

0.672

Table 16-R

Near-Source Factor Na

1.000

Table 16-S

Near-Source Factor Nv

1.200

Table 16-T

MCE Shaking Intensity MMZNa

0.484

MCE Shaking Intensity MMZNv Seismic Source Type Distance to Known Source (km) MCE Response Coefficient, MM

0.581 A 10.0 1.21

Lateral Force Coefficient, RI Fixed Base Lateral Force Coefficient, R Importance Factor, I Seismic Coefficient, CAM

2.0 5.5 1.0 0.484

Table A-16-E Table 16-N Table 16-K Table A-16-F

Seismic Coefficient, CVM

0.813

Table A-16-G

Eccentricity, e Shortest Building Dimension, b Longest Building Dimension, d Dimension to Extreme Isolator, y DTD/DD = DTM/DM

0.31 5.03 6.23 3.1 1.182

Table 16-U Table A-16-D

Figure 7.14: Project Definition

7.10.3 Isolator Types and Load Data The isolator types and load data are defined as shown in Figure 7.14. This stage assumes that the user has decided on the type of isolator at each location. See elsewhere in this book for assistance on selecting the device types and the number of variations in type. For most projects, there will be some iteration as the performance of different types and layouts is assessed. 1. The types of isolators which can be included in this spreadsheet are lead rubber bearings (LRB), high damping rubber bearings (HDR), elastomeric bearings (ELAST, equivalent to an LRB with no lead core), flat sliding bearings (TFE) and curved sliding bearings (FPS). 2. For each isolator type, vertical load conditions are defined. The average DL + SLL is used to assess seismic performance. The maximum and minimum load combinations are used to assess the isolator capacity. 3. The total wind load on the isolators may be provided if it applied a lower limit to the design shear forces.

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4. Most building projects will not have a non-seismic displacement or rotation; these are more common on bridge projects. If they do apply, they are entered on this sheet. High rotations will severely limit the capacity of the elastomeric types of isolator (LRB, HDR and ELAST). Other types of bearing may be more suited for high rotations, for example, pot type sliding bearings. For most projects, the data in this section will be changed as variations of isolation systems are assessed. Often, the isolator type will be varied and sometimes variation of the number of each type of isolator will be considered.

BEARING TYPES AND LOAD DATA Location Type (LRB, HDR, ELAST,TFE,FPS) Number of Bearings Number of Prototypes Average DL + SLL Maximum DL + LL Maximum DL + SLL + EQ Minimum DL - EQ Seismic Weight Total Wind Load Non-Seismic Displacement Non-Seismic Rotation (rad) Seismic Rotation (rad)

LRB-A

LRB-B

TFE-C

LRB 12 2 800 1100 1600 0 9600

LRB 12 2 1200 1600 2400 0 14400

TFE 6 2 500 250 500 0 3000

Total

30

27000 620

Figure 7.15: Isolator Types & Load Data

7.10.4 Isolator Dimensions The spreadsheet provides specific design for the elastomeric types of isolator (LRB, HDR and ELAST). For other types (TFE and FPS) the design procedure uses the properties specified on this sheet and the Design Data sheet but does not provide design details. For these types of bearings the load and design conditions will need to be supplied to manufacturers for detailed design. The isolators are defined by the plan size and rubber layer configuration (elastomeric based isolators) plus lead core size (lead rubber bearings) or radius of curvature (curved slider bearings). For curved slider bearings the radius defines the post-yielded slope of the isolation system and the period of response. Appropriate starting values are selected from the project performance specifications and fine tuned by trial and error. 1. The minimum plan dimensions for the elastomeric isolators are those required for the maximum gravity loads. The gravity factor of safety (F.S.), at zero displacement, should be at least 3 for both the strain and buckling limit states. A starting point for the design procedure is to set a plan dimension such that this factor of safety is achieved. 2. The design process is iterative because the plan dimension is also a function of the maximum displacement. For moderate to high seismic zones the plan size based on a F.S. of 3 will likely need to be increased as the design progresses.

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3. The rubber layer thickness is generally a constant at 10 mm. This thickness provides good confinement for the lead core and is sufficiently thin to provide a high load capacity. If vertical loads are critical the load thickness may be reduced to 8 mm or even 6 mm although manufacturers should be consulted for these thin layers. Thinner layers add to the isolator height, and also cost, as more internal shims are required. The layer thickness should not usually exceed 10 mm for LRBs but thicker layers may be used for elastomeric or HDR bearings. The load capacity drops off rapidly as the layer thickness increases. 4. The number of layers defines the flexibility of the system. This needs to be set so that the isolated period is in the range required and so that the maximum shear strain is not excessive. This is set by trial and error. 5. The size of the lead core for LRBs defines the amount of damping in the system. The ratio of QD/W is displayed for guidance. This ratio usually ranges from 3% in low seismic zones to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level for a given seismic zone. As for the number of rubber layers, the core is sized by trial and error. 6. Available plan shapes are circular and square (plus rectangular for bridges). Most building projects use circular bearings as it is considered that these are more suitable for loading from all horizontal directions. Square and rectangular bearings are more often used for bridges as these shapes may be more space efficient.

BEARING DIMENSIONS

Plan Dimension (Radius for FPS) Depth (R only) Layer Thickness Number of Layers Lead Core Size Shape (S = Square, C = Circ) Side Cover Internal Shim Thickness Load Plate Thickness Load Plate Dimension Load Plate Shape (S or C) Total Height

LRB-A 670

LRB-B 770

10 20 90 C 10 2.7 25.4 670 S 301

10 20 110 C 10 2.7 25.4 770 S 301

TFE-C

Qd/W 6.75%

Figure 7.16: Isolator Dimensions

The procedure for fine tuning dimensions is to set initial values, activate the macro to solve for the isolation performance and change the configuration to achieve the target performance. At each step, the effect of the change is evaluated by assessing the isolation system performance, as described below.

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7.10.5 Isolator Performance The workbook contains a macro which solves for isolation performance once all dimensions and properties have been set. This is not automatic, and must be activated once changes are made. If changes affect the performance of the isolation system a message DBE (or MCE) NOT CONVERGED will be displayed. Running the macro will update the performance summary. As changes are made, two parameters are checked, (1) the status of the isolation bearings to safely support the loads and (2) the performance of the isolation system. The isolation bearing status for all elastomeric based isolators is summarized by the factors of safety, as shown in Figure 7.17. Although generally factors of safety exceeding 1.0 indicate satisfactory performance, experience has shown that some more severe restrictions should be imposed during the design process. This conservatism in design is recommended as it will increase the probability of successful prototype tests.

PERFORMANCE SUMMARY Gravity Strain F.S. Buckling F.S DBE Strain F.S Buckling F.S MCE Strain F.S Buckling F.S Reduced Area / Gross Area Maximum Shear Strain Effective Period TD TM

LRB-A 12.26 7.88 2.10 2.50 1.38 1.52 28.2% 196%

LRB-B 12.91 9.54 2.28 3.37 1.62 2.33 36.6% 196%

TFE-C

DBE

MCE

2.08

2.17

Displacement DD DM

240.8

331.8

Total Displacements DTD DTM

284.5

392.1

Force Coefficient Vb / W

0.225

0.284

0.112 0.101 0.023 0.070 0.112 18.39%

14.70%

1.44

1.32

Force Coefficient Vs / W 1.5 x Yield Force / W Wind Force / W Fixed Base V at TD Design Base ShearCoefficient Damping eff Damping Coefficients BD BM

Figure 7.17: Performance Summary

1.

The gravity factor of safety should exceed 3.0 for both strain and buckling. For high seismic zones it will generally be at least 6.0 as performance is governed by seismic limit states.

2.

The DBE factor of safety should be at least 1.5 and preferably 2.0 for both strain and buckling.

203

3.

The MBE factor of safety should be at least 1.25 and preferably 1.5 for both strain and buckling.

4.

The ratio of reduced area to gross area should not go below 25% and should preferably be at least 30%.

5.

The maximum shear strain should not exceed 250% and preferably be less than 200%.

The limit states are governed by both the plan size and the number of rubber layers. Both these parameters may need to be adjusted to achieve a design within the limitations above. At each change, a check is also required to assess whether the seismic performance is achieved. The performance of the isolated structure is summarized for the DBE and MCE in the final two columns in Figure 7.17. Performance indicators to assess are: 1.

The isolated period. Most isolation systems have an effective period in the range of 1.50 to 2.50 seconds for DBE, with the longer periods tending to be used for high seismic zones. It may not be possible to achieve a period near the upper limit if isolators have light loads.

2.

The displacements and total displacements. The displacements are estimated values at the center of mass and also total displacements, which include an allowance for torsion. The latter values, at MCE loads, define the separation required around the building.

3.

The force coefficient Vb/W is the maximum base shear force that will be transmitted through the isolation system to the structure above. This is the base shear for elastic performance but is not necessarily the design base shear.

4.

The design base shear coefficient is defined by UBC as the maximum of four cases: a) The elastic base shear reduced by the isolated response modification factor VS = VB/RI. b) The yield force of the isolation system factored by 1.5. c) The base shear corresponding to the wind load. d) The coefficient required for a fixed base structure with a period equal to the isolated period.

For this example, the first condition governs. The designer should generally aim for this situation as the isolation system will be used most efficiently if this limit applies. The performance summary also lists the equivalent viscous damping of the total isolation system and the associated damping reduction factor, B. Design should always aim for at least 10% damping at both levels of earthquake and preferably 15%.

204

The design worksheet also provides details of the calculations used to obtain this performance summary. Figure 7.18 shows the calculations for the MCE level. In this example, the TFE slider bearing provides much higher damping than the LRBs on an individual bearing basis. However, as only about 10% of the total seismic weight is supported on sliders the contribution to total system damping of the sliders is not large. Seismic Performance : Maximum Capable Earthquake Number of Isolators Elastic Stiffness, Ku Yielded Stiffness, Kr* Yield Displacement, Dy Characteristic Strength, Qd Seismic Displacement, Dm Bearing Force = Qd+DmKr* Effective Stiffness = F/Dm Seismic Weight Seismic Mass = W/9810 Effective Period = 2(M/K) Ah = 4QD(m-y)  = (1/2)(Ah/Ke ) B Factor SA = Cvd/BT 2 SD = (g/4 )*CvdTd/Bd Check Convergence = Sd/m 2

LRB-A 12 5.56 0.63 10.46 50.89

LRB-B 12 7.49 0.84 11.55 76.03

TFE-C 6 0.00 0.00 0.00 50.00

259.4 0.782

354.9 1.070

50.000 0.151

MCE 30

331.80 23.124 27000 2.752 2.17

65415

97388

66359

2351797

12.10%

13.16%

63.66%

14.70% 1.32 0.28 331.81 1.00

Figure 7.18: Performance at MCE Level

There is quite an art to the selection of final isolation design parameters. For example, in this case damping could be increased by increasing lead core sizes in the LRBs. The core sizes cannot be increased much, however, as the yield force will increase. As shown in Figure 7.17, the design base shear force will be governed by the 1.5FY condition if core sizes are increased. Therefore, the extra damping may actually result in an increase in structural design forces.

7.10.6 Properties for Analysis The workbook provides a plot of the hysteresis curves for each of the isolator types as designed for displacements up to the MCE total displacement level. These plots (Figure 7.19) show the bi-linear properties to be used for system evaluation. The properties used to develop the hysteresis loop are also listed in a format suitable for the ETABS program, as shown in Figure 7.20. The use of these properties is discussed elsewhere in this book.

205

SHEAR FORCE (KN)

400

-400

LRB-A LRB LRB-B LRB TFE-C TFE

300 200 100 0

-300

-200

-100

-100

0

100

200

300

400

-200 -300 -400 SHEAR DISPLACEMENT (mm) Figure 7.19: Hysteresis of Isolators

ETABS Spring Properties LRB-A LRB First Data Line: ID ITYPE KE2 KE3 DE2 DE3 Second Data Line: K1 K2 K3 FY2/K11/CFF2 FY3/K22/CFF3 RK2/K33/CFS2 RK3/CFS3 A2 A3 R2 R3

LRB-B LRB

TFE-C TFE

1 2 3 Identification Number ISOLATOR1 ISOLATOR1 ISOLATOR2 Biaxial Hysteretic/Linear/Friction 0.78 1.07 0.15 Spring Effective Stiffness along Axis 2 0.78 1.07 0.15 Spring Effective Stiffness along Axis 3 0.071 0.081 0.587 Spring Effective Damping Ratio along Axis 2 0.071 0.081 0.587 Spring Effective Damping Ratio along Axis 3 709.4 5.49 5.49 57.47 57.47 0.11 0.11

1145.0 7.41 7.41 85.59 85.59 0.11 0.11

5000.0 2000.00 2000.00 0.10 0.10 0.04 0.04 0.90 0.90 0.000 0.000

Spring Stiffness along Axis 1 (Axial) Initial Spring Stiffness along Axis 2 Initial Spring Stiffness along Axis 3 Yield Force Along Axis 2 Yield Force Along Axis 3 Post-Yield stiffness ratio along Axis 2 Post-Yield stiffness ratio along Axis 3 Coefficient controlling friction Axis 2 Coefficient controlling friction Axis 3 Radius of Contact 2 direction Radius of Contact 3 direction

Figure 7.20: Analysis Properties for ETABS

206

7.11 INTRODUCTION TO ISOLATION FOR BRIDGES The concept of isolation for bridges is fundamentally different than for building structures. There are a number of features of bridges which differ from buildings and which influence the isolation concept: 1. Most of the weight is concentrated in the superstructure, in a single horizontal plane. 2. The superstructure is robust in terms of resistance to seismic loads but the substructures (piers and abutments) are vulnerable. 3. The seismic resistance is often different in the two orthogonal horizontal directions, longitudinal and transverse. 4. The bridge must resist significant service lateral loads and displacements from wind and traffic loads and from creep, shrinkage and thermal movements. The objective of isolation a bridge structure also differs. In a building, isolation is installed to reduce the inertia forces transmitted into the structure above in order to reduce the demand on the structural elements. A bridge is typically isolated immediately below the superstructure and the purpose of the isolation is to protect the elements below the isolators by reducing the inertia loads transmitted from the superstructure. Although the type of installation shown in Figure 7.21 is typical of most isolated bridges, there are a number of variations. For example, the isolators may be placed at the bottom of bents; partial isolation may be used if piers are flexible (bearings at abutments only); a rocking mechanism for isolation may be used.

Seismic Isolation Bearings

Separation Gap

Figure 7.21: Typical Isolation Concept for Bridges

207

Bridge isolation does not have the objective of reducing floor accelerations which is common for most building structures. For this reason, there is no imposed upper limit on damping provided by the isolation system. Many isolation systems for bridge are designed to maximize energy dissipation rather than providing a significant period shift.

7.12 SEISMIC SEPARATION OF BRIDGES It is often difficult to provide separation for bridges, especially in the longitudinal direction. However, the consequences of lack of separation may not be severe. For any isolated structure, if there is insufficient clearance for the displacement to occur then impact will occur. For buildings, impact almost always has very undesirable consequences. The impact will send a high frequency shock wave up the building, damaging the contents that the isolation system is intended to protect. For bridges, the most common impact will be the superstructure hitting the abutment back wall. Generally, the high accelerations will not in themselves be damaging and so the consequences of impact may not be high. The consequences may be minimized by building in a failure sequence at the location of impact. For example, a slab and “knock off” detail as shown in Figure 7.22.

Thermal Separation Friction Slab on Grade

Friction Joint

Seismic Separation

Figure 7.22: Example "Knock-Off" Detail

An example of the seismic separation reality is the Sierra Point Bridge, on US Highway 101 between San Francisco and the airport. This bridge was retrofitted with lead rubber bearings on top of existing columns that had insufficient strength and ductility. The bearings were sized such that the force transmitted into the columns at maximum displacement would not exceed the moment capacity of the columns. The existing superstructure is on a skew and has a separation of only about 50 mm (2”) at the abutments. In an earthquake, it is likely that the deck will impact the abutment. However, regardless of whether this occurs, or the superstructure moves transversely along the direction of skew, the columns will be protected as the bearings cannot transmit a level of shear sufficient to damage them.

208

There may well be local damage at the abutments but the functionality of the bridge is unlikely to be impaired. This type of solution may not achieve “pure” isolation, and may be incomplete from a structural engineer’s perspective, but nevertheless it achieves the project objectives.

7.13 DESIGN SPECIFICATIONS FOR BRIDGES Design of seismic isolations systems for bridges often follow the AASHTO Guide Specifications, published by the American Association of State Highway and Transportation Officials. The initial specifications were published in 1991, with a major revision in 1999. These bridge design specifications have in some ways followed the evolution of the UBC code revisions. The original 1991 edition was relatively straightforward and simple to apply but the 1999 revision added layers of complexity. Additionally, the 1999 revision changed the calculations of the seismic limit state to severely restrict the use of elastomeric type isolators under high seismic demands.

7.13.1 The 1991 AASHTO Guide Specifications The 1991 AASHTO seismic isolation provisions permitted isolated structures to be designed for the same ductility factors (as implemented through the R factor) as for non-isolated bridges. This differed from buildings where the UBC at this time recommended an R value for isolated structures of one-half the value for non-isolated structures. However, AASHTO recommended a value of R = 1.5 for essentially elastic response as a damage avoidance design strategy. AASHTO defined two response spectrum analysis procedures, the single-mode and multimode methods. The former was similar to a static procedure and the latter to a conventional response spectrum analysis. Time history analysis was permitted for all isolated bridges and required for systems without a self-centering capability (sliding systems). Prototype tests were required for all isolation systems, following generally similar requirements to the UBC both for test procedures and system adequacy criteria. In addition to the seismic design provisions, the 1991 AASHTO specifications provided additions to the existing AASHTO design provisions for Elastomeric Bearings when these types of bearings were used in implementing seismic isolation design. This section provided procedures for designing elastomeric bearings using a limiting strain criterion. As this code was the only source providing elastomeric design conditions for seismic isolation the formulations provided here were also used in design of this type of isolator for buildings (see Chapter 9 of these Guidelines).

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7.13.2 The 1999 AASHTO Guide Specifications The 1999 revision to the AASHTO Guide Specifications implemented major changes. The main differences between the 1991 and 1999 Guide Specifications were: 1.

Limitations on R factors. The R factor was limited to one-half the value specified for nonisolated bridges but not less than 1.5. For bridges, this provided a narrow range of R from 1.5 to 2.5, implying very limited ductility.

2.

An additional analysis procedure, the Uniform Load Method. This is essentially a static load procedure that takes account of sub-structure flexibility.

3.

Guidelines are provided for analyzing bridges with added viscous damping devices.

4.

Design must account for lower and upper bounds on displacements, using multipliers to account for temperature, aging, wear contamination and scragging. These factors are device-specific and values are provided for sliding systems, low-damping rubber systems and high-damping rubber systems. In general the multipliers tend to have the greatest effect in increasing displacements in sliding systems. This is similar to UBC that requires a displacement multiplier of 3.0 for sliders.

5.

More extensive testing requirements, including system characterization tests. There are requirements for vertical load stability design and testing using multipliers that are a function of seismic zone.

6.

Additional design requirements for specific types of device such as elastomeric bearings and sliding bearings.

Although the 1999 AASHTO specifications introduced a number of new factors and equations, a commentary is provided and the procedures are straight-forward to apply. Design procedures for isolated bridges may be based on the AASHTO provisions for either (1) the uniform load method or (2) the time history analysis method.

7.14 USE OF BRIDGE SPECIFICATIONS FOR BUILDING ISOLATOR DESIGN Codes for building isolation system design, such as UBC and FEMA-356, provide detailed requirements for isolation system design, analysis and testing but do not provide detailed design requirements for the design of the devices themselves. Most projects have adopted provisions of bridge codes for the device design as bridges have always been supported on bearings and so contain specific requirements for sliding bearings and elastomeric bearings. As AASHTO incorporates design requirements for using these bearings as seismic isolators this has been the code of choice for this aspect on most projects. In the 1999 revision, the formulas for elastomeric bearing design are based on a total shear strain formulation, as in the 1991 edition, but with modifications. One of the major changes is the inclusion of bulk modulus effects on load capacity.

210

Prior to this edition, the bulk modulus was used to calculate vertical stiffness but not to calculate the shear strain due to compression. Its inclusion in AASHTO for calculating vertical load capacity is controversial as other codes (for example, AustRoads) explicitly state that the bulk modulus effect does not reduce the load capacity. Figure 7.23 shows the difference in load capacity at earthquake displacements for elastomeric bearings designed using the 1991 and 1999 AASHTO load specifications. The plot is for typical isolators (10 mm layer thickness, area reduction factor of 0.5 and seismic shear strain of 150%). The load capacity is similar for smaller isolators (600 mm plan size or less) but the 1999 requirements reduce the load capacity for larger isolators such that for 1000 mm isolators the load capacity is only one-half that permitted by the earlier revision. Isolators of 1.0 m diameter or more are now common for high seismic zones as near fault displacements cause high deformations.

LOAD CAPACITY (KN)

25000 1991 AASHTO

20000

1999 AASHTO

15000 10000 5000 0 200

400

600

800

1000

ISOLATOR PLAN SIZE (mm) Figure 7.23: Elastomeric Bearing Load Capacity

This change in load capacities has little effect on most projects but has a major impact on design for conditions of high vertical loads and high seismic displacements. For example, on a California building project bearings were 970 mm diameter, designed to the 1991 AASHTO requirements. If design had been based on the 1999 provisions the diameter would have needed to be increased to 1175 mm. This 48% increase in plan area would require a corresponding increase in height to achieve the same flexibility. This would have made base isolation using LRBs impossible for this retrofit project as there were space restrictions. These bearings were successfully tested beyond the design displacement to a point close to the design limit of the 1991 code. This implies a factor of safety of at least 2 for vertical loads relative to the 1999 AASHTO. This factor of safety is beyond what would normally be required for displacements based on an extreme MCE event.

211

If project specifications require compliance with 1999 AASHTO then if will be required to use the formulation for total shear strain that includes the bulk modulus. However, there does not seem enough evidence that designs excluding the bulk modulus are non-conservative, to change procedures for other projects for which compliance with this code is not mandatory.

7.15 DESIGN OF ISOLATION SYSTEMS Isolation systems for bridges are designed using the same principles as outlined in Chapter 5. For design according to AASHTO, the seismic input is defined by the acceleration coefficient, A, and the coefficient for site-soil profile, Si, which ranges from 1.0 to 2.7. These coefficients, together with the isolation period and damping coefficient (Teff and B respectively) define the maximum spectral acceleration as: SA 

ASi g Teff B

(in units of acceleration)

(7.1)

and the spectral displacement as SD 

SA



2 S ATeff



2

( 2 )

2



ASiTeff

(7.2)

4 2 B





The damping coefficient is derived from the hysteresis loop area A h  4Q d  m   y , the effective stiffness, Keff, and the displacement, , which gives the equivalent viscous damping as:



1 2

 Ah  2  K eff 

  

(7.3)

The B factor is then interpolated from the values in Table 7.5 for the calculated value of .

B

2 0.8

Percentage of Critical Damping,  5 10 20 30 40 50 1.0 1.2 1.5 1.7 1.9 2.0 Table 7.5: Damping Coefficient, B

These equations provide the maximum force coefficient, SA, and the maximum However, practical displacement, SD, for a rigid mass on a specified isolation system. isolation systems for bridges also need to provide resistance to non-seismic loads and for most bridges the seismic response will be modified by flexibility of the structure below the isolation plane. The following sections discuss the influence of these factors on design of the isolation system.

7.15.1 Non-Seismic Loads Bridges are required to resist a number of load types in service. Table 7.6 lists the three categories of non-seismic loads which may apply for a particular bridges: 1.

Vertical loads, which arise from the self-weight of the bridge plus surfacing and the live loads from traffic. The bearings are sized to resist the maximum combinations of these loads with a minimum factor of safety of 3.

212

2.

Service horizontal loads, which may arise from wind load, wind on live load, longitudinal breaking forces and centrifugal forces for bridges on a curved alignment. The lead cores are sized to resist the maximum combinations of these loads.

3.

Service horizontal displacements are applied from creep and shrinkage and from thermal movements. These are typically slowly applied loads. These displacements will deform the bearings and transmit a force into the substructure. For slowly applied loads the lead will creep and the maximum force transmitted will be less than for rapidly applied loads.

Vertical Loads D Dead load Select plan size and layer configuration to resist L Live load maximum vertical load combinations. Short Term Service Horizontal Loads W Wind load Size lead cores to resist each combination of short WL Wind on live load term service loads using short term force in lead core FST  Qd LF Longitudinal force CF Centrifugal Force Long Term Service Horizontal Displacements R Rib Shortening Calculate maximum force in bearing using long term S Shrinkage force in lead core (equal to 0.25 x short term yield T Temperature force) FLT 

Qd  K r  LT 4

Table 7.6: Bearing Non-Seismic Design Actions

7.15.2 Effect of Bent Flexibility The most common location of the isolation plane for bridges is immediately below the superstructure, on top of the bents (piers or abutments). The seismic mass is concentrated in the superstructure and so maximum inertia loads are transmitted from the deck through the bearings. The bearing forces will deform the bents below, modifying the dynamics of the response. Figure 7.24 shows schematically the usual configuration of an isolated bridge. The total deck displacement is a combination of bearing displacement plus bent displacement. The relative proportions of each are a function of the relative stiffness of each, taking into account the nonlinearity of the bearings. AASHTO 1999 provides guidance in incorporating the effect of substructure flexibility on response and the equations in this section are extracted from this source.

213

Superstructure Keff

Bearing(s)

kd

Substructure

Qd

Ksub keff

i

y  sub

i 

Figure 7.24: Effect of Substructure Flexibility

For calculating the effective stiffness of an isolator, the effects of substructure flexibility must be included where appropriate. The isolator and the substructure act as a pair of springs in series and the total stiffness, Keff, is a function of the effective stiffness of the individual bearings, keff, and the stiffness of the substructure, ksub K eff 

 k sub keff    sub  keff 

  k j

K

(7.4)

eff , j

j

Similarly, the effective damping must also account for substructure flexibility  

EnergyDissipated



2K eff 

2

TotalDissipatedEnergy 2

 (K

2 eff , j  )

(7.5)

j

For lead rubber bearings, the hysteresis loop area of each bearing is 4Qd(i – y) and so the effective damping can be calculated as:  

2Qd (i   y )

 ( i   sub ) 2 K eff

 Q (      K (   2

d

i

y)

eff , j

i

sub )

j

2



(7.6)

j

Once the effective stiffness is defined the effective period can be calculated. The effective period and damping can then be used to calculate the force coefficient and spectral displacement as described earlier. However, both the period and damping are each a function of the spectral displacement and so an iterative solution is required.

214

7.16 ANALYSIS OF ISOLATED BRIDGES AASHTO specifies four analysis procedures, in increasing order of complexity (1) uniform load, (2) single mode spectral method, (3) multimode spectral method or (4) time history methods of analysis. For isolated bridges, the uniform load and single mode spectral method are essentially the same as the method described in this chapter and implemented in the sample workbook. This method includes the effect of bent flexibility but does not account for flexure of the bridge deck or the self-weight of the bents. The multimode spectral method is often difficult to implement for isolated bridges. This is because of the displacement dependent nature of both the effective stiffness and the damping. Some form of iteration needs to be incorporated to solve for a compatible displacement, stiffness and damping at each bearing location. This will require a large number of changes to the computer input and will generally not be practical unless an automated procedure is developed. The time history method can be based on either the maximum response from three time histories or the mean results of 7 time histories. Two dimension analyses are permitted for normal bridges without skews or curves and this simplifies the procedure, allowing programs such as DRAIN-2D to be used with separate longitudinal and transverse models. Figure 7.25 shows the form of the longitudinal model for an isolated bridge. Each bent is modeled with two truss elements in series, one representing the bent and the second representing the sum of the bearings at the top of the bent. Usually, one-half the bent weight is lumped as a seismic mass at the top of the bent. For substructures which are heavy relative to the substructure, multiple mass points may be used within the height of the bent, each with tributary mass derived from the bent weight.

Earthquake Loads Applied Along X

Mass Point of Superstructure Mass Point of Bent Fixed Nodes A

B

Truss Elements in series A: Substructure EA/L = Ksub B: Bi-linear Bearing EA1/L = Ku EA2 / K = Kr Beam Element EA = EAdeck

Figure 7.25: DRAIN-2D Longitudinal Model

215

The transverse model uses similar elements to those of the longitudinal model but is oriented as shown in Figure 7.26. This orientation allows for the effects of deck flexural deformations and rotations to be incorporated into the results.

Earthquake Loads Applied Along X

Mass Point of Superstructure Mass Point of Bent Fixed Nodes A

B

Truss Elements in series A: Substructure EA/L = Ksub B: Bi-linear Bearing EA1/L = Ku EA2 / K = Kr Beam Element EA = EAdeck

Figure 7.26: DRAIN-2D Transverse Model

7.17 DESIGN PROCEDURE FOR BRIDGE ISOLATION This section develops a procedure for design of isolation systems for bridges, using an example bridge to develop the methodology. The procedure requires an iterative solution for damping and displacement. This has been incorporated into an automated spreadsheet procedure, an example of which is provided on the CD supplied with this book.

7.17.1 Example Bridge This example is the design of lead-rubber isolators for a 4 span continuous bridge. The bridge configuration is a superstructure of 4 steel plate girders with a concrete deck. The substructure is hollow concrete pier walls (see Figures 7.27 and 7.28).

216

Figure 7.27: Longitudinal Section of Bridge

Figure 7.28: Transverse Section of Bridge

217

Two isolation options, both using lead rubber bearings, are examined: 1. Full base isolation (period approximately 2 seconds). (This option is contained on the example spreadsheet provided on the CD with this book). 2. Energy dissipation (period approximately 1 second). For the base isolation design the aim is to minimize forces and distribute them approximately uniformly over all abutments and piers. The objective of the energy dissipation design is to minimize displacements and attempt to resist more of the earthquake forces at the abutments than at the piers. These represent different design strategies which may be adopted for bridge design. The response predicted by the design procedure was checked using nonlinear analysis. The designs were based on an AASHTO design spectrum with an acceleration level, A, of 0.32 and a soil factor, S, of 1.5. All calculation are performed using metric units (kN, mm).

7.17.2 Design of Isolators The bearing design was based on a natural rubber formulation with a shear modulus G of 0.71 MPa, a medium hardness rubber which has been used widely for bridge isolation systems. Table 7.7 lists the material properties for this rubber. The lead yield strength was 9 MPa, which represents the mid-point of measured effective yield strengths for LRBs. Rubber Shear Modulus Lead Yield Strength Elongation at Break Material Constant, k Elastic Modulus, E Bulk Modulus

0.00071 0.00900 6.00 0.65 0.00284 287

KPa KPa

KPa KPa

Table 7.7: Material Properties

Base Isolation Design Designed was performed using a trial and error method. Original sizes were selected based on the maximum vertical loads, with a starting point of setting the strain under vertical loads approximately one-half the strain limit. The lead cores were sized so as to provide a total Qd/W of about 5%, a typical value for moderate seismic zones. The number of rubber layers was successively increased to produce the target period of 2.0 seconds. The base isolation design used 500 mm square lead rubber bearings with 100 mm diameter lead cores at each abutment. At the piers, the size was increased to 600 mm and the lead core to 110 mm diameter. All bearings had 19 rubber layers each 10 mm thick, providing a total bearing height of 324 mm, slightly above one-half the plan dimension. These isolators met all AASHTO requirements for lead rubber bearings.

218

Table 7.8 summarizes the configuration and properties of these bearings, based on the formulas provided in Chapter 5. Note that the total isolator yield strength is 283 kN at the abutments and 342 kN at the piers. The designer must ensure that this value exceeds the maximum combination of non-seismic loads at each of these locations. These non-seismic loads may define the minimum lead core size. (Units mm) Number of Bearings Type Plan Dimension Number of Layers, N Rubber Thickness, Tr Lead Core Size, dpl Kr Ku

Qd y

Abut 1 4 LR 500 19 190 100 3.3 30.4

Pier 2 4 LR 600 19 190 110 4.7 41.4

Pier 3 4 LR 600 19 190 110 4.6 40.5

Pier 4 4 LR 600 19 190 110 4.6 40.2

283 10.44

342 9.34

342 9.53

342 9.60

Abut 5 4 LR All lead rubber 500 19 190 100 3.1 G(Ag-Apl)/Tr  12 A pl  29.0  K u  6.5K r 1  A r  

283 10.92

yApl Fy Ku



Qd K u (1 

Kr ) Ku

Table 7.8: Isolator Properties – Base Isolation

Energy Dissipation Design For the energy dissipation option the abutment bearings were increased in size to 750 mm square lead rubber bearings and the lead cores increased to 250 mm diameter. At the piers, the plan size of 600 mm square was retained but the lead cores were reduced from 110m to 100mm diameter. The abutment bearings had 8 rubber layers 10 mm thick, providing a total bearing height of 181 mm, about one-quarter the plan dimension. The pier bearings had 12 layers and a total height of 233 mm. Table 7.9 provides the properties for this option. (Units mm) Number of Bearings Type Plan Dimension Number of Layers, N Rubber Thickness, Tr Lead Core Size, dpl Kr Ku

Qd y

Abut 1 4 LR 750 8 80 250.0 18.1 260.6

Pier 2 4 LR 600 12 120 100.0 7.8 65.4

Pier 3 4 LR 600 12 120 100.0 7.7 64.6

Pier 4 4 LR 600 12 120 100.0 7.7 64.3

1767 7.29

283 4.91

283 4.97

283 5.00

Abut 5 4 LR All lead rubber 750 8 80 250.0 18.0 G(Ag-Apl)/Tr  12A pl  259.8  K u  6.5K r 1  A r  

1767 7.31

yApl Fy Ku

Table 7.9: Isolator Properties – Base Isolation

219



Qd K u (1 

Kr ) Ku

7.17.3 Accounting for Bent Flexibility in Design The bearing properties listed in Tables 7.8 and 7.9 can be used directly to solve for the isolation performance if they are mounted on rigid substructures. Most bridges have flexible substructures, at least at the pier locations, and the stiffness of these elements must be included. For cantilever bents, the stiffness under lateral loads can be calculated as: K sub 

E

col I col

3

(7.7a)

H3

If the columns are in double curvature, such as under transverse loads on a multi-column bent with a stiff cross beam: K sub 

12

E

col I col

H

(7.7b)

3

For more complex bent configurations, a model of the bent may be required to define the stiffness. For example, this can be obtained by using a computer model of the bridge; apply a load at deck level, obtain the displacement, sub at the top of each substructure and record the total force in the substructure, Fsub. The stiffness is then K sub 

Fsub .  sub

This method

also permits the effect of sub-soil flexibility to be included. For the example bridge, the bent data required for the design are listed in Table 7.10. The stiffness is based on gross dimensions of the concrete section. For final design, more refined calculations would be warranted.

Span Weight, Wi Longitudinal Stiffness Transverse Stiffness

Bent 1 35 2880 8.9E+08 5.7E+10

Bent 2 45 6560 1.5E+05 9.8E+06

Bent 3 50 7800 1.1E+05 7.1E+06

Bent 4 50 8200 2.6E+05 1.7E+07

Bent 5 4120 8.9E+08 5.7E+10

Total 180 29560 1.8E+09 1.1E+11

Table 7.10: Data for Bent Calculations

Calculation of the seismic performance is based on the bearing properties and bent properties listed in Tables 7.9 and 7.10. The procedure is iterative to obtain isolation deformations and damping which is consistent with the spectral displacement and hysteresis area. The steps, tabulated in Table 7.11, are: 1.

Assume a deck displacement.

2.

Assume a damping factor.

3.

Calculate the bearing displacement at each bent for this deck displacement.

4.

Calculate the hysteresis loop area and effective stiffness at each bent for this bearing displacement.

5.

Calculate the bent effective stiffness.

220

6.

Calculate the effective period for this effective stiffness.

7.

Obtain the spectral acceleration and spectral displacement corresponding to this period. From this, calculate the total seismic shear force.

8.

Calculate the shear force in each bent due to this spectral acceleration.

9.

Calculate the bent displacement under this shear force.

10.

Calculate the total elastic energy at each bent and sum over all bents.

11.

Calculate the equivalent viscous damping and interpolate the damping coefficient.

12.

If the calculated damping coefficient is not within a specified tolerance of the assumed coefficient, modify the assumed damping factor and return to Step 2. above.

13.

If the spectral displacement is not within a specified tolerance of the assumed deck displacement, modify the assumed deck displacement and return to Step 1. above.

The formula for the calculation of equivalent viscous damping is modified to account for bent flexibility by using the relationship Keff = Vb/i. This is substituted into the denominator Keff2 which becomes Vb = elastic strain energy Ei. The procedure requires convergence on both the displacement and the damping factor. The spreadsheet supplied with this book uses Newton-Raphson iterations for each parameter. Although there is no guarantee of convergence, it appears to work well in practice.

221

For Each Bent Deck Displacement,  Damping Factor, B Bearing Displacement, i

i   



A h  4Q d  m   y

Isolator Loop Area, Ah Bearing Effective Stiffness, Keff Bent Stiffness, ksub Bent Effective Stiffness Period ( M  g

W ) , T i

Qd  K r  k sub  kr

kr 

Total Bridge Solved by iteration Solved by iteration



k sub keff k sub  keff

eff

K

eff

M K eff

Teff  2

bents

Spectral Acceleration, SA

SA 

Spectral Displacement, SD Total Shear Force ( W 

h

Qd i

calculated from properties K eff 

A

Convergence when SD = deck displacement, 

W )

SD

ASi g Teff B 2 S ATeff

(2 ) 2

Vtotal  S AW

i

bents

Added here calculations for transverse response – see Table 5-8 keff Bent Shear Force, Vb Vb  Vtotal

k

Bent Displacement

V i  b K eff

Elastic Energy

Ei  Vb  i

eff

Equivalent Damping

E  1  A   2  E   i

h

i

B Factor

Convergence when B = assumed B factor

    

Interpolate

Table 7.11: Calculation of Seismic Performance

For longitudinal earthquake loading the deck displacement is equal at each bent location, assuming a rigid deck. However, under lateral loads there will be a rotation of the deck if the substructure flexibility is not symmetric about the centerline of the bridge. Table 7.12 describes the additional steps required to account for this rotation. The transverse evaluation procedure is the same for the longitudinal procedure through Step 7, calculation of total seismic shear force. Additional steps are then required:

222

a. b. c. d. e.

The location of the center of mass is calculated by taking moments about the left hand abutment. The location of the center of rotation is calculated by taking the first moment of the bent stiffness. The torsional stiffness of the bridge is calculated as keffx2. The applied torque is the total seismic force times the eccentricity between the center of mass and the center of rotation. Total shear at each bent is then calculated as the sum of the direct shear plus the shear due to torsion.

The procedure then continues as for the longitudinal direction from Step 9 above. The additional variables complicate the iterations on displacement and damping and it may be more difficult to obtain convergence in this direction. Often, a higher tolerance is used. For Each Bent Total Shear Force Distance from Left Hand Bent, L Weight x Lever Arm,

Total Bridge Vtotal  S AW

from geometry WiL

W L i

bents

W L

Center of Mass, LCM

i

bents

W

Stiffness x Distance to Centroid

k

k sub L

sub L

bents

k L K

Distance to Center of Rotation, LCR

sub

bents

eff

bents

Distance to Center of Rotation, lcr Torsional Inertia, IT

L - LCR keff ( L  LCR ) 2

k

eff

( L  LCR ) 2

bents

Eccentricity, e Torque, T Direct Bent Shear, Vd

LCM – LCR eVtotal Vtotal

Torsional Bent Shear, Vt

keff

k

eff

keff TlCR IT

Total Bent Shear, Vb Total Bent Displacement

Vd + Vt Vb keff

Table 7.12: Additional Calculations for Deck Rotation

223

7.17.4 Evaluation of Performance The iterative procedure described above was used to solve for longitudinal and transverse seismic performance for each isolation option for the example bridge, base isolation and energy dissipation. Implementation used an Excel spreadsheet, supplied with this book. Base Isolation Design Tables 7.13 and 7.14 list the seismic performance calculations for the longitudinal and transverse directions respectively For longitudinal loads, the isolation system provided an effective period of 2.00 seconds and equivalent viscous damping of 19%. The design spectrum gives a displacement of 162 mm and a force coefficient of 0.162 for this period and damping. The 162 mm displacement was the total displacement at deck level. Displacements in the bearings ranged from a maximum of 162 mm at the abutments to a minimum of 152 mm at the central pier, the most flexible bent. In the transverse direction the piers are stiffer and so the effective period is slightly less, 1.94 seconds, and damping the same at 19%. Corresponding displacements and force coefficient were 159 mm and 0.164. In the transverse direction the deck rotated as the spans are not symmetrical about the center of the bridge. Bearing displacements increased from 126 mm at Abutment 1 to 200 mm at the opposite end of the bridge.

Deck Displacement Damping Factor, B Bearing Displacement Isolator Loop Area Bearing Effective Stiffness Bent Stiffness Bent Effective Stiffness Period Acceleration Displacement Total Shear Force Bent Shear Force Bent Displacement Elastic Energy Equivalent Damping B Factor

Bent 1 161.6 1.48 162 170995 5.0 892721 5.0

Bent 2

Bent 3

Bent 4

Bent 5

155 198835 6.9 153 6.6

152 195322 6.9 112 6.5

158 202543 6.8 265 6.6

162 170448 4.9 892721 4.9

813 162 131457

1072 162 173242

1046 162 169013

1065 162 172194

790 162 127661

Table 7.13: Seismic Performance Calculations – Longitudinal

224

Total Solved by Iteration 938143

29.6 2.004 0.162 161.62 4786 4786 773567 0.193 1.479

Deck Displacement Damping Factor, B Bearing Displacement Isolator Loop Area Bearing Effective Stiffness Bent Stiffness Bent Effective Stiffness Period Acceleration Displacement Total Shear Force Distance to Center of Mass Mass x Distance to Centroid Center of Mass Stiffness x Distance to Centroid Center of Rotation Distance to Center of Rotation Stiffness x Distance ^2 Eccentricity Torque Direct Bent Shear Torsional Bent Shear Total Bent Shear Total Bent Displacement Elastic Energy = F x D Equivalent Damping B Factor

Bent 1 Bent 2 159.3 1.48 125.9 140.4 130552 179216 5.5 7.2 57134128 9797 5.5 7.2

0 0

35 229600

Bent 3

Bent 4

159.1 204435 6.8 7142 6.8

179.8 200.6 232854 214493 6.5 4.5 16929 57134128 6.5 4.5

80 130 624000 1066000

Bent 5

Total Solved by Iteration 961550

30.5 1.976 0.164 159.3 4855

180 741600

2661200 90.03 2453

0

250

541

844

818

-80

-45

0

50

100

35817

14800

2

15904

45017

881 -185 696 126 87592

1139 -135 1004 140 140975

1078 -1 1076 159 171222

1034 133 1167 180 209841

724 188 912 201 182914

80.49

111540 9.54 46294 4855 0 4855 792544 0.193 1.479

Table 7.14: Seismic Performance Calculations - Transverse

Energy Dissipation Design The evaluation was repeated with bearing plan sizes and lead core sizes adjusted as described earlier. For seismic loads, the energy dissipation system provided an effective period of 1.00 seconds and equivalent viscous damping of 29%. Table 7.15 compares the seismic response of the base isolation and energy dissipation options. The energy dissipation design produces displacements less than one-half that of the base isolation design but the force coefficient is almost twice as high. This is a result of lesser benefits from the period shift effect but higher levels of damping for the energy dissipation option.

225

Effective Period (seconds) Deck Displacement (mm) Equivalent Viscous Damping Base Shear Coefficient Bearing Displacement (mm) Maximum Minimum Bent Shear (kN) Maximum Minimum

Longitudinal Direction Base Energy Isolation Dissipation 2.00 1.00 162 70 19% 29% 0.162 0.286

Transverse Direction Base Energy Isolation Dissipation 1.98 0.99 159 70 19% 29% 0.164 0.288

162 152

70 64

201 126

76 64

1072 790

3040 772

1167 695

3135 800

Table 7.15: Summary of Results

Comparison with Time History Analysis A time history analysis was performed of the base isolation option using the mean results from 7 time histories, each frequency scaled to be compatible for the AASHTO design spectrum. To be equivalent with the design procedure, bent weights were excluded from the time history analysis. The effect of this is discussed later. Figures 7.29 and 7.30 compare the results from the single mode method (termed Design Procedure) with the minimum, maximum and mean results from the 7 time histories for the base isolation and the energy dissipation option respectively. In the longitudinal direction, the bent displacements are equal at each location as the deck does not deform axially. Figures 7.29 and 7.30 show that the design procedure estimate of longitudinal displacements lies approximately midway between the mean and the maximum time history values for the base isolation option and close to maximum time history values for the energy dissipation option. The transverse response of the bridge includes a rotational component because of the unequal height of the piers and non-symmetrical span lengths, as shown in Figure 7.29 for the base isolation option. The energy dissipation option is designed to distribute a higher proportion of superstructure inertia loads to the abutments which requires the deck to function as a deep beam. Figure 7.30 shows the influence of deck flexural deformations on transverse displacements for this option. As for longitudinal displacements, the transverse displacements estimated from the design procedure are between the mean and maximum values from the time history analysis. The design procedure shows similar levels of rotation to the time history results but does not include the deck flexural deformations which are important for the energy dissipation option.

226

Transverse 250

200

200

Deck Displacement (mm)

Deck Displacement (mm)

Longitudinal 250

150 100 Time History Minimum Time History Average Time History Maximum Design Procedure

50 0 BENT 1

BENT 2

BENT 3

BENT 4

150 100 Time History Minimum Time History Average Time History Maximum Design Procedure

50 0

BENT 5

BENT 1

BENT 2

BENT 3

BENT 4

BENT 5

Figure 7.29: Base Isolation Displacements

Transverse

120

100

100

Deck Displacement (mm)

Deck Displacement (mm)

Longitudinal

120

80 60 40

Time History Minimum Time History Average Time History Maximum Design Procedure

20 0 BENT 1

BENT 2

BENT 3

BENT 4

80 60 40

Time History Minimum Time History Average Time History Maximum Design Procedure

20 0

BENT 5

BENT 1

BENT 2

BENT 3

BENT 4

BENT 5

Figure 7.30: Energy Dissipation Displacements

These results show that the simplified design procedure, including bent flexibility, provides a good approximation to the more accurate response calculated from the time history. The design procedure results are higher than the mean from the 7 time history results but lower than the maximum results. However, the results also show that when a system incorporates significant force distribution between bents, as for the energy dissipation option, more detailed analysis of deck deformations may be required. These results imply that, depending on whether the mean of 7 or maximum of 3 time history method were chosen, the design procedure would be either slightly conservative or slightly non-conservative. Given the uncertainties implicit in the selection of the time histories, this suggests that an isolation system based on the simplified design procedure would provide a system with satisfactory performance.

227

7.17.5 Effect of Isolation System on Displacements The design of an isolation system for the example bridge has considered two options, a base isolation system (large period shift, moderate damping) and an energy dissipation system (moderate period shift, high damping). A range of systems between these two could also be designed. The type of system selected depends on the objectives as there are significant differences in displacements and force distributions. Figures 7.31 and 7.32 compare respectively the longitudinal and transverse deck displacements for the base isolation system and the energy dissipation system.

Deck Displacement (mm)

In the longitudinal direction the displacements at deck level are enforced to be equal by the axial stiffness of the deck. The base isolation displacements of 162 mm are 2.3 times as high as the maximum energy dissipation displacements of 70 mm. In the transverse direction the large lead cores at the abutments restrain rotation and there is some deformation due to flexure of the deck. The maximum isolated displacement of 201 mm at Abutment B is 2.6 times the displacement with with the energy dissipation bearings, 76 mm. Therefore, the energy dissipation option requires much smaller expansion joints at the abutments.

180 160 140 120 100 80 60 40 20 0

Base Isolated Energy Dissipation

Bent 1

Bent 2

Bent 3

Bent 4

Figure 7.31: Longitudinal Displacements

228

Bent 5

Deck Displacement (mm)

250 200

Base Isolated Energy Dissipation

150 100 50 0 Bent 1

Bent 2

Bent 3

Bent 4

Bent 5

Figure 7.32: Transverse Displacements

7.17.6 Effect of Isolation on Forces Figures 7.33 and 7.34 compare the longitudinal and transverse bearing forces respectively for the fixed bearings, the base isolation bearings and the energy dissipation bearings. 1.

The total seismic force with fixed bearings is equal to the maximum acceleration coefficient (2.5A) times the seismic weight, V = 0.8 x 29,560 = 23,648 kN.

2.

With seismic isolation the total seismic force at a 2.0 second period, with 19% damping, is 4,786 kN, a reduction by a factor of almost 5.

3.

With energy dissipation the total seismic force at a 1.0 second period, with 29% damping, is 8,440 kN, a reduction by a factor of 2.8.

The distribution of forces is changed by the isolation systems and so the ratio between fixed base and isolated forces at each bent varies from the overall reduction factor. Longitudinal In the longitudinal direction, when the bearings are fixed the total seismic force is resisted equally at the two abutments with a maximum force of 11,800 kN at each location. When isolation bearings are used the loads are distributed approximately equally over the abutments and piers with maximum forces ranging from 790 kN to 1046 kN, a reduction by a factor of over 10 compared with the fixed bearing configuration. The energy dissipation bearings produce a force distribution where most force is resisted at the abutments (maximum 3040 kN) and a much lower force at the piers (maximum 800 kN). The forces are higher than for the isolated bridge but still reduce the fixed bearing abutment forces by a factor of almost 4.

229

12000 10000 Base Isolated Energy Dissipation Fixed

8000 6000 4000 2000 0 Bent 1

Bent 2

Bent 3

Bent 4

Bent 5

Force (kN) Figure 7.33: Longitudinal Forces

Transverse In the transverse direction, the fixed bearings distribute seismic forces to the piers in approximate proportion to their stiffness as shown in Figure 7.34. The maximum abutment force is 5244kN and the maximum pier force is 5,447kN at Pier 3, the shortest pier. With isolation bearings, the forces are distributed relatively uniformly between all abutments and piers. The maximum abutment force is 912kN, the maximum pier force is 1167kN. As for the longitudinal direction, peak forces are reduced by a factor of over 5. The energy dissipation bearings produce a force distribution which differs from both the fixed bearings and isolation bearings. Most force is resisted at the abutments, which have a maximum force of 3134kN and a small proportion at the piers, where the maximum force is 840kN.

6000

Base Isolated Energy Dissipation Fixed

5000 4000 3000 2000 1000 0 Bent 1

Bent 2

Bent 3

Bent 4

Force (kN) Figure 7.34: Transverse Forces

230

Bent 5

7.17.7 Summary This bridge example has illustrated how bearings can be used in bridge structures both to reduce overall seismic forces on the bridge and to alter the distribution of these forces to the different substructure elements. In this example, a typical seismic isolation design is based on a 2 second isolated period and similar isolators at all abutments and piers. This reduces total seismic forces by a factor of almost 5 in both the longitudinal and transverse directions. Because the forces are approximately equally distributed, the isolation bearings reduce local forces by a greater factor. The longitudinal abutment forces are reduced by a factor of 10, the transverse pier forces are reduced by a factor of almost 5. However, the force reductions were associated with maximum deck displacements of over 160 mm and so a substantial expansion joint will be required to permit this amount of free movement. The energy dissipation design used stiffer bearings with large lead cores at the abutments to reduce the isolated period to 1 second and concentrate forces in the abutments. This reduced the displacements compared to the isolated design, with longitudinal displacements of 70 mm, 40% of the isolated displacements. This provides savings in the provision of expansion joints at the abutments. As the period shift was less, the seismic force reductions compared to the fixed bearing design were smaller. This example provides two examples of achieving different objectives using lead rubber bearings and there are numerous other possible permutations. The aim of a design procedure is to enable rapid evaluation of alternative isolator configurations, as implemented in the spreadsheet provided with this book.

7.18 IMPLEMENTATION IN SPREADSHEET Included with this book is a spreadsheet which can be used to evaluate system performance and factors of safety based on user selected isolator details. The spreadsheet is not intended for final design or to substitute for the calculations by the engineer of record. It is a tool provided to assist users in developing their own isolation design procedures. The example provided in this section is based on design to 1991 AASHTO requirements. Designs based on other codes follow the same general principles. In the spreadsheet, cells colored red indicate user-specified input. The workbook contains a number of sheets with the design performed within the sheet CONTROL. The spreadsheet is set up for up to 8 substructures. This can be extended by inserting additional columns and copying formulas across the sheet.

231

7.18.1 Material Properties The material definitions are contained on the sheet ISOLATORS, as shown in Figure 7.35. This is the basic information used for the design process. The range of properties available for rubber is restricted and some properties are related to others, for example, the ultimate elongation, material constant and elastic modulus are all a function of the shear modulus. Information on available rubbers is provided elsewhere in this book. MATERIAL PROPERTIES Rubber Shear Modulus Lead Yield Strength Elongation at Break Material Constant, k Elastic Modulus, E Bulk Modulus

0.00071 0.009 6.00 0.65 0.00284 287

KPa KPa

KPa KPa

Figure 7.35: Material Properties

7.18.2 Dimensional Properties Dimensional properties are also set on the ISOLATORS sheet (Figure 7.36). These are properties which are constant for the type of bearing and which do not change as plan size changes: 1.

Rubber layer, usually 10 mm (or 3/8”) but may be changed depending on load conditions.

2.

Isolator shape, usually square for bridge bearings.

3.

Internal shim thickness, typically 3 mm (1/8”).

4.

Load plate thickness, usually at least 25 mm (1”).

Other dimensional parameters (plan size, number of layers) are not set on this sheet as they are altered from the CONTROL sheet as design progresses.

232

BEARING DIMENSIONS Plan Dimension Layer Thickness Number of Layers Lead Core Size Shape (S = Square, C = Circ) Total Height BEARING PROPERTIES Gross Area Side Cover Bonded Dimension Bonded Area Plug Area Net Bonded Area Total Rubber Thickness Bonded Perimeter Shape Factor Internal Shim Thickness Load Plate Thickness Lead Yield Strength (KPa) Characteristic Strength, Qd Shear Modulus (50%) Yielded Stiffness Kr (50%) Elastic Stiffness Ku (50%) Yield Force Yield Displacement

500 10 19 100.00 S 294.00

600 10 19 110.00 S 294.00

600 10 19 110.00 S 294.00

600 10 19 110.00 S 294.00

500 10 19 100.00 S 294.00

250000 10 480 230400 7854 222546 190.00 1920 11.6 3.00 25.00 0.01 70.7 0.0006 0.82 7.59 79.3 10.44

360000 10 580 336400 9503 326897 190.00 2320 14.1 3.00 25.00 0.01 85.5 0.0006 1.18 10.34 96.5 9.34

360000 10 580 336400 9503 326897 190.00 2320 14.1 3.00 25.00 0.01 85.5 0.0006 1.15 10.13 96.5 9.53

360000 10 580 336400 9503 326897 190.00 2320 14.1 3.00 25.00 0.01 85.5 0.0006 1.15 10.06 96.5 9.60

250000 10 480 230400 7854 222546 190.00 1920 11.6 3.00 25.00 0.01 70.7 0.0006 0.78 7.26 79.3 10.92

Figure 7.36: Dimensions and Properties

7.18.3 Load and Design Data The required load and design conditions are entered on the DESIGN sheet, as shown in Figure 7.37. Required data from this sheet is: 1.

Superstructure seismic weight at each bent, usually dead load alone. This is divided by the number of bearings to get the seismic vertical load per bearing.

2.

Total dead plus live load at each bent. This is divided by the number of bearings to get the maximum gravity load per bearing.

3.

Calculated stiffness of each bent in the longitudinal and transverse directions. Note that the spreadsheet contains formulas for cantilever piers. These can be replaced by other formulas, or stiffness values can be entered directly. For stiffness properties, only the rows for Longitudinal K and Transverse K are used for the design.

233

DESIGN DATA (KN, m) Span Superstructure Weight (Longl) Superstructure Weight (Trans) Total D + L at Bent Pier Dimensions Dimension Longitudinal Dimension Transverse Pier Height (Longl) Pier Height (Trans) Elastic Modulus Calculated Stiffnesses Longitudinal I Longitudinal K Transverse I Transverse K Transverse Breakaway Force Thermal Span o Temperature Change, F Thermal Movement

Abut 1

Pier 2

Pier 3

Pier 4

Abut 5

35 2880 2880 6080

45 6560 6560 12960

50 7800 7800 14200

50 8200 8200 14600

4120 4120 7320

2.0 16.0 1.0 1.0 2.8E+07

2.0 2.0 2.0 2.0 16.0 16.0 16.0 16.0 18.0 20.0 15.0 1.0 18.0 20.0 15.0 1.0 2.8E+07 2.8E+07 2.8E+07 2.8E+07

10.7 8.9E+08 683 5.7E+10

10.7 10.7 10.7 10.7 1.5E+05 1.1E+05 2.6E+05 8.9E+08 683 683 683 683 9.8E+06 7.1E+06 1.7E+07 5.7E+10

90 54 31.6

55

10

-40

-90

19.3

3.5

14.0

31.6

Figure 7.37: Load and Design Data

7.18.4 Isolation Solution Once material, dimensional and design data have been entered the isolation system is designed by entering values on the CONTROL worksheet. This is an iterative process, controlled by the portion of the spreadsheet shown in Figure 7.38. The procedure is to enter dimensional values in the cells and then active the macro to Solve Displacement for this configuration. As part of the design process, changes are made to the following parameters: 1. Plan dimensions. These must be set so that the isolator status (at the bottom of Figure 519) is “OK” for each AASHTO condition. 2. The number of layers defines the flexibility of the system. This needs to be set so that the isolated period is in the range required and so that the maximum shear strain is not excessive. This is set by trial and error. 3. The size of the lead core for LRBs defines the amount of damping in the system. The ratio of QD/W is displayed for guidance. This ratio usually ranges from 3% in low seismic zones to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level for a given seismic zone. As for the number of rubber layers, the core is sized by trial and error. The user must ensure that the total yield strength of the lead cores at each substructure is sufficient to resist all combinations of short term non-seismic lateral loads, as discussed earlier.

234

Solve Displacement

ISOLATORS (Units mm) Number of Bearings Type (LR or F (fixed)) Isolator Plan Dimension Number of Layers Isolator Rubber Thickness Isolator Lead Core Size Kr Ku Qd Dy

PERFORMANCE Longitudinal Displacement Longitudinal Force Transverse Displacement Transverse Force ISOLATOR STATUS Maximum Displacement AASHTO Condition 1 AASHTO Condition 2 AASHTO Condition 3 Buckling Reduced Area

Job title Bridge Number: Units Gravity AASHTO G 0.32 S 1.50

Test Bridge 1 M (US (kip,ft) or Metr 9.81 9810 1000

Abut 1 4 LR 500 19 190 100.0 3.3 30.4 283 10.44

Pier 2 4 LR 600 19 190 110.0 4.7 41.4 342 9.34

Pier 3 4 LR 600 19 190 110.0 4.6 40.5 342 9.53

Pier 4 4 LR 600 19 190 110.0 4.6 40.2 342 9.60

Abut 5 4 LR 500 19 190 100.0 3.1 29.0 283 10.92

Abut 1

Pier 2

Pier 3

Pier 4

Abut 5

161.6 813.3 125.9 695.9

161.6 1071.8 140.4 1004.1

161.6 1045.6 159.1 1076.3

161.6 1065.3 179.8 1166.9

161.6 789.8 200.6 911.9

Abut 1 161.6 OK OK OK OK

Pier 2 161.6 OK OK OK OK

Pier 3 161.6 OK OK OK OK

Pier 4 179.8 OK OK OK OK

Abut 5 200.6 OK OK OK OK

Figure 7.38: Control of Design Process

235

CHAPTER 8

8.1

APPLICATIONS OF SEISMIC ISOLATION

INTRODUCTION

This chapter presents details of seismically isolated buildings, bridges and other structures all over the world, up to the time it was written, in 1992. The information, photographs and tables were compiled with input from the authors’ colleagues worldwide and this enabled compilation of a wide-ranging and objective overview of applications of seismic isolation to that date. In order to retain the information as a complete unit, it is reproduced here as it was written in 1992. Chapter 10 will present results that have been achieved in the twelve years since then, up to the time of writing this new book, in 2004. The authors began by noting that, since beginning their studies of seismic isolation, some 25 years before, (1967), they had been in more or less continuous contact with colleagues in Japan, the United States of America, and more recently Italy. They were thus well aware of the situation in New Zealand and in those countries and the emphasis of this chapter is placed on applications of seismic isolation there. However, as discussed by Buckle & Mayes (1990), seismic isolation has also been applied in many other countries, as summarised in Table 8.1. This table, together with Tables 8.2 to 8.8, gives an indication of the criteria for choosing the seismic isolation option, namely the likelihood of a seismic event occurring, multiplied by the intensity of the anticipated event, multiplied by the value or the hazard of the structure and/or contents. In the text we have discussed seismic applications under three broad headings, namely, buildings, bridges and 'delicate' or 'hazardous' structures. An issue of prime importance is the performance of seismically isolated structures in severe earthquakes, but none of the structures discussed below have been subjected to such a test. Of the buildings and bridges seismically isolated in New Zealand to date, only one, the Te Teko Bridge over the Rangitaiki River, has undergone the effects of a large earthquake. This was the Edgecumbe earthquake in March 1987, Richter magnitude 6.3, MM9, epicentre 9 km north of the bridge. A strong-motion accelerograph located 11 km south of the bridge recorded a peak horizontal ground acceleration of 0.33 g. This bridge "provides an example of good performance of modern earthquake resistance technology, i.e., base isolation using lead rubber bearings" (Dowrick, 1987). However, one of the standard elastomeric bearings elsewhere on the bridge was not properly restrained against sliding, and was thrown out of position, so that it ceased supporting the deck (Skinner & Chapman, 1987). The behaviour of the bridge was, therefore, not perfect. In order that seismic isolation be effective, it must be stressed that it is the responsibility of all the people concerned in the design, manufacture and use of a seismically isolated structure, to ensure that the system is maintained operative, and particularly that the seismic gap is protected. As mentioned in Chapter 1, this space must be uncluttered by waste material, and it must be respected during subsequent building alterations. The seismic gap must remain free at all times, so that the structure can move by the required amount during the 5 or so seconds of a major earthquake, which can occur at any unpredictable time in the life of the structure. This is obviously an educational problem, which is currently severe because seismic isolation is a relatively new technology. New owners/operators are likely, through ignorance, to abuse the seismic gap and thereby render the seismic isolation system inoperative.

237

It is suggested that permanent notices or plaques be situated at or near the gap, that the state and relevance of the seismic isolation be stressed in the 'ownership papers', and that engineers and building inspectors take particular notice of the need for security of the gap.

Country

Constructed Facilities

Canada

Coal ship loader, Prince Rupert, BC

Chile

Ore ship loader, Guacolda

China

2 houses (1975); weigh station (1980); 4-storey dormitory, Beijing (1981)

England

Nuclear fuel processing plant

France

4 houses (1977-82) 3-storey school, Lambesc (1978) Nuclear waste storage facility (1982) 2 nuclear power plants, Cruas and Le Pelliren

Greece

2 office buildings, Athens

Iceland

5 bridges

Iran/Iraq

Nuclear power plant, Karun River 12-storey building (1968)

Italy

See text and Table 8.8

Japan

See text and Tables 8.4 and 8.5

Mexico

4-storey school (Mexico City)

New Zealand

See text and Tables 8.2 and 8.3

Rumania

Apartment

USSR

3 buildings, Sevastopol 3-storey building

South Africa

Nuclear power plant

USA

See text and Tables 8.6 and 8.7

Yugoslavia

3-storey school, Skopje (1969)

Table 8.1: Applications of Seismic Isolation World-wide (after Buckle & Mayes, 1990)

238

8.2

STRUCTURES ISOLATED IN NEW ZEALAND

8.2.1

Introduction

In New Zealand, seismic isolation has been achieved by a variety of means: transverse rocking action with controlled base uplift, horizontally flexible elastomeric bearings, and flexible sleevedpile foundations. Damping has been provided through hysteretic energy dissipation arising from the plastic deformation of steel or lead in a variety of devices such as steel bending-beam and torsional-beam dampers, elastomeric bearings with and without lead plugs, and lead-extrusion dampers (See Chapter 3). The New Zealand approach to seismic isolation incorporates energy dissipation in the isolation system, in order to reduce the displacements required across the isolating supports, to further reduce seismic loads, and to safeguard against unexpectedly strong low-frequency content in the earthquake motion. Combined yield-level forces of the hysteretic energy dissipators range from about 3% to 15% of the structure's weight, with a typical value of about 5%. Displacement demands across the isolators range from about 100-150 mm for motions of El Centro type and severity, to about 400 mm for the Pacoima Dam record. Structural response can often be limited to the elastic range in the design-level earthquake, with limited ductility requirements during extreme earthquake conditions. Substantial cost savings of up to 10% of the structure's cost, together with an expected improvement in the seismic performance of the structure, have resulted from the adoption of the isolation approach. Some New Zealand applications are discussed by McKay et al (1990). Bridges and structures which have been built in New Zealand are discussed in this section. Table 8.2 shows the variety of techniques used in the seismic isolation of buildings, of which the William Clayton Building in Wellington, started in 1978 and completed in 1981, was the first in the world to incorporate lead rubber bearings. This and other buildings are discussed in the text. Current work is the design of a retrofitted seismic isolation system for New Zealand Parliament Buildings (Poole & Clendon, 1991). Table 8.3 shows that lead rubber bearing isolation is the technique favoured in bridges. The particular applicability of lead rubber bearings for bridge isolation arises from the fact that elastomeric bearings, made of laminated steel and rubber as described in Chapter 3, are already an accepted technology for the accommodation of thermal expansion in bridges. Isolation can then be added at a small additional cost by the removal of further constraints, by provision for larger displacements, and by the incorporation of suitable lead plugs to provide high levels of hysteretic damping.

239

Height/ Storeys

Total Floor Area (m2)

Isolation System

Date Completed

William Clayton Building, Wellington

4 storeys 17 m

17000

Lead Rubber bearings

1981

Union House, Auckland

12 storeys 49 m

7400

Flexible piles and steel dampers

1983

Wellington Central Police Station

10 storeys

11000

Flexible piles and lead extrusion dampers

1990

Press Hall, Press House, Petone

4 levels 14 m

950

Lead rubber bearings

1991

Parliament House, Wellington

5 storeys 19.5 m

26500

Retrofit of elastomeric bearings and lead rubber

Original building 1921; retrofit proposed

Parliament Library, Wellington

5 storeys 16 m

6500

Retrofit of elastomeric bearings and lead rubber

Original 1883/1899; retrofit proposed

Building

Table 8.2: Seismically Isolated Buildings in New Zealand

240

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21-24 25 26 27 28 29 30 31 32 33 34,35 36,37 38 39 40 41 42 43 44 45 46 47 48 49

Bridge Name

Superstructure Type

Length (m)

Isolation System

Date Built

Motu South Rangitikei viaduct Bolton Street Aurora Terrace Toetoe King Edward Street Cromwell Clyde Waiotukupuna Ohaaki Maungatapu Scamperdown Gulliver Donne Whangaparoa Karakatuwhero Devils Creek Upper Aorere Rangitaiki (Te Teko) Ngaparika Hikuwai No. 1-4 (retrofit) Oreti Rapids Tamaki Deep Gorge Twin Tunnels Tarawera Moonshine Makarika No. 2 (retrofit) Makatote (retrofit) Kopuaroa No. 1 & 4 (retrofit) Glen Motorway & Railway Grafton No. 4 Grafton No. 5 Northern Wairoa Ruamahanga at Te Ore Ore Maitai (Nelson) Bannockburn

Steel Truss PSC Box Steel I Beam Steel I Beam Steel Truss PSC Box Steel Truss PSC U-Beam Steel Truss PSC U-Beam PSC Slab Steel Box Steel Truss Steel Truss PSC I-Beam PSC I-Beam PSC U-Beam Steel Truss PSC U-Beam Steel Truss Steel Plate Girder PSC I-Beam PSC I & U-Beam PSC I-Beam Steel Truss PSC I-Beam PSC I-Beam PSC U-Beam Steel Plate Girder Steel Plate Girder Steel Plate Girder PSC T-Beam PSC T-Beam PSC I-Beam PSC I-Beam PSC U-Beam PSC I-Beam Steel Truss

170 315 71 61 72 52 272 57 44 83 46 85 36 36 125 105 26 64 103 76 74-92 220 68 40 72 90 63 168 47 87 25 & 55 60 50 80 492 116 93 147

1973 1974 1974 1974 1978 1979 1979 1981 1981 1981 1981 1982 1983 1983 1983 1983 1983 1983 1983 1983 1983-4 1984 1984 1985 1984 1985 1985 1985 1985 1986 1986-7 1987 1987 1987 1987 1987 1987 1988

PSC Slab Steel Truss PSC U-Beam Steel Truss PSC T-Beam PSC U-Beam

62 72 135 52 38 84

Steel UBs in flexture Steel torsion bar/rocking piers Lead extrusion Lead extrusion Lead/rubber Steel Cantilever Steel flexural beam Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Steel Cantilever Lead/rubber Steel Cantilever Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber & Lead extrusion Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber Lead/rubber

Hairini Limeworks Waingawa Mangaone Porirua State Highway Porirua Stream Key:

PSC UB

= =

prestressed concrete U-beam Table 8.3: Seismically Isolated Bridges in New Zealand

241

1989 1990 1990 1992 1992

8.2.2

Road Bridges

Since 1973 forty-eight road bridges and one rail bridge in New Zealand have been seismically isolated, see Table 8.3. Four examples of seismic upgrading by the retrofitting of isolation systems are included in this list. By far the most common form of isolation system for bridges uses lead rubber bearings, usually installed between the bridge superstructure and the supporting piers and abutments. The lead rubber bearing combines the functions of isolation and energy dissipation in a single compact unit, while also supporting the weight of the superstructure and providing an elastic restoring force. The lead plug in the centre of the elastomeric bearing is subjected to a shear deformation under horizontal loading, providing considerable energy dissipation when it yields under severe earthquake loading. The lead rubber bearing provides an extremely economic solution for seismically isolating bridges. Many unisolated New Zealand bridges use elastomeric bearings between superstructures and their supports, to accommodate thermal movements. Little modification to standard structural forms has been necessary in order to incorporate the lead plug to produce seismic isolation bearings, apart from the removal of some constraints and provision of a seismic gap to accommodate the increased superstructure displacements which may occur under seismic loading. As well as providing energy dissipation during large movements, the lead plug also stiffens the bearing under slow lateral forces up to its yield point, reducing the displacements under wind and traffic loading (Robinson, 1982). Further information on the seismic isolation of road bridges in New Zealand, including case studies and design procedures, is given by Blakeley (1979), Billings & Kirkcaldie (1985), & Turkington (1987). The first bridge to be seismically isolated in New Zealand was the Motu Bridge, built in 1973. The light-weight replacement superstructure was a 170 m steel truss supported by the existing reinforced-concrete slab-wall piers. The superstructure was isolated using sliding bearings with the damping provided by vertical-cantilever structural-type steel columns. An example of the use of lead rubber bearings in bridges is illustrated in Figures 8.1 and 8.2, which show the Moonshine Bridge, a 168 m prestressed, concrete, curving bridge on a motorway in the Hutt area, New Zealand.

Figure 8.1: Moonshine Bridge, Upper Hutt, New Zealand

242

Figure 8.2: Moonshine Bridge, Upper Hutt, showing lead rubber bearing under the beams, and restraining stops.

Figure 8.3: Aurora Terrace over bridge, Wellington City.

Figure 8.3 shows a bridge over the Wellington Motorway which is fitted with lead extrusion dampers at the lower abutment. It is one of a pair of sloping bridges which were seismically isolated by being mounted on glide bearings, the restoring force being provided by steel columns. The advantage of the extrusion dampers is that they lock the bridges in place during the braking of vehicles travelling downhill, yet at earthquake loads allow the bridges to move. Thermal expansion forces can be released by the creep of the extrusion dampers. After a large earthquake it is expected that the bridges will no longer have the seismic gaps ideally positioned. If necessary the bridges can then be jacked to the ideal position or allowed to creep back with the flexible columns providing the restoring force.

243

8.2.3

South Rangitikei Viaduct with Stepping Isolation

The South Rangitikei Viaduct, which was opened in 1981, is an example of isolation through controlled base-uplift in a transverse rocking action. The bridge is 70 metres tall, with six spans of prestressed concrete hollow-box girder, and an overall length of 315 metres (Cormack, 1988). Figure 8.4 shows the stepping isolation schematically, and Figures 8.5 and 8.6 are photographs of the bridge under construction, and of the first train to use it.

Figure 8.4: Schematic of base of stepping pier, South Rangitikei Viaduct.

Figure 8.5: South Rangitikei Viaduct during construction.

Figure 8.6: Inaugural train on South Rangitikei Viaduct.

244

The stresses which can be transmitted into the slender reinforced concrete H-shaped piers under earthquake loading are limited by allowing them to rock sideways, with uplift at the base alternating between the two legs of each pier. The extent of stepping, and the associated lateral movement of the bridge deck, is limited by energy dissipation provided by the hysteretic working of torsionally-yielding steel-beam devices connected between the bottom of the stepping pier legs and the caps of the high-stiffness supporting piles. (The E-type steel damper used is shown in Figure 3.3.) The stepping action reduces the maximum tension calculated in the tallest piers, for the 1940 El Centro NS record, to about one-quarter that experienced when the legs are fixed at the base; unlike the fixed-base case there is little increase in base-level loads for stronger seismic excitations. The dampers reduce the displacements to about one-half those in the undamped case, and reduce the number of large displacements to less than one-quarter. The maximum displacement at the deck level for the damped stepping bridge is about 50% greater than for the fixed-leg bridge, Beck & Skinner (1974). The twenty-four energy dissipators operate at a nominal force of 450 kN with a design stroke of 80 mm. The maximum uplift of the legs is limited to 125 mm by stops. The weight of the bridge at rest is not carried by the dampers, but is transmitted to the foundations through thin laminatedrubber bearings whose primary functions are to allow rotation of each unlifted pier foot, and to distribute loads at the pier/pile-cap interfaces. The stepping action is very effective in reducing seismic loads on this bridge because its centre of gravity is high, so that the non-isolated design was strongly dominated by overturning moments at the pier feet. The hysteretic damping during stepping is quite effective because the estimated self-damping of the stepping mechanism is quite low, owing to the relatively rigid pile caps. A chimney structure at the Christchurch Airport was also provided with a stepping base. The resultant cost saving was about 7% (Sharpe & Skinner, 1983). 8.2.4

William Clayton Building

The William Clayton Building in Wellington, started in 1978 by the New Zealand Ministry of Works and Development and completed in 1981, was the first building in the world to be seismically isolated on lead rubber bearings. (See Chapter 3 and Figure 3.16.)

Figure 8.7: Diagram showing detail of lead rubber bearing, William Clayton Building, Wellington.

245

Details of a lead rubber bearing for this building are shown in Figure 8.7. The 80 bearings are located under each of the columns of the 4-storey reinforced concrete frame building, which is 13 bays long by 5 bays wide with plan dimensions of 97 m x 40 m. Each bearing carries a vertical load of 1 to 2 MN and is capable of taking a horizontal displacement of + 200 mm. Detailed descriptions of the building have been given by Meggett (1978) and Skinner (1982). It is shown, during construction and after completion, in Figures 8.8 and 8.9.

Figure 8.8: Wellington Clayton Building during construction; note lead rubber bearing.

Figure 8.9: William Clayton Building completed and occupied.

The pioneering nature of the building and its proximity to the active Wellington fault dictated that a conservative design approach be taken. The design earthquake was taken as 1.5 El Centro NS 1940, for which the calculated maximum dynamic base shear was 0.20 times the total building weight W, and this was selected as the design static base shear force. The artificial A1 record, which is intended to represent near-fault motion in a magnitude 8 earthquake, was considered as the 'maximum credible' motion, producing a calculated maximum base shear of 0.26 W. Even though the calculated response of the seismically isolated structure was essentially elastic for the design earthquake motions, a capacity design procedure was used, as required for design with high ductility.

246

The bearing size and lead diameter were chosen after careful dynamic analysis. Meggett (1978) discussed this design in detail and found that accelerations, inter-storey drifts and maximum base shear forces were approximately halved by the introduction of the seismically isolated system. He concluded that reasonable values for the shear stiffness of the elastomeric bearing and lead yield stiffness were -1 (6.1) K b (r) /W = 1 to 2 m giving and

T b 2 = 2.0 to 1.4 s

(6.2)

Qy /W  0.04 to 0.09 ,

(6.3)

while in fact the bearings were measured with Kb(r)/W = 1.1 m-1 and Qy = 0.07W for 1.5 El Centro. Horizontal clearances of 150 mm were provided before the base slab impacts on retaining walls. This corresponds to the maximum bearing displacement calculated for the A1 record, with 105 mm calculated for 1.5 El Centro. Water, gas and sewerage pipes, external stairways and sliding gratings over the seismic gap were detailed to accommodate the 150 mm isolator displacement. Thus the lead rubber bearings lengthened the period of the structure from 0.3 seconds for the frame structure alone, to 0.8 seconds for the isolated structure with the lead plugs unyielded, and 2.0 seconds in the fully yielded state (i.e. calculated from the structural mass and post-yield stiffness of the bearings). The combined yield force of all the bearings and lead plugs was calculated to be approximately 7% of the structure's 'dead plus seismic live' load. The maximum base shear for the isolated structure calculated for 1.5 El Centro was 0.20 W, which is half the value of 0.38 W for the unisolated structure. Only the roof beam yielded for the isolated structure with a rotational ductility of less than 2 and no hinge reversal. For both 1.5 El Centro and the A1 record, the maximum inter-storey drifts for the isolated structure were about 10 mm, about 0.002 times the storey height, and were uniform over the structure's height. For the unisolated structure, the inter-storey drifts increased up the height of the building, reaching a maximum of 52 mm. The markedly reduced inter-storey drifts should minimise the secondary damage in the isolated structure, and greatly simplified the detailing for partitions and glazing. As a first attempt at seismic isolation of a building with lead rubber bearings, the design of the William Clayton Building was very much a learning experience. The design was conservative, and if it was repeated now, it is probable that more advantage would be taken of potential economies offered by the isolation approach to seismic design. Nevertheless, the design analysis demonstrated the improved seismic performance which can be achieved through isolation of appropriate structures. Moreover, in the light of subsequent tests on lead rubber bearings, the extreme-earthquake capacity could in principle be extended substantially simply by increasing the base-slab clearance to 200 or 250 mm. 8.2.5 Union House The 12-storey Union House (Boardman et al. 1983), completed in 1983, achieves isolator flexibility by using flexible piles within clearance sleeves. It is situated in Auckland alongside Waitemata Harbour. Poor near-surface soil conditions, consisting of natural marine silts and land reclaimed by pumping in hydraulic fill, led to the adoption of long end-bearing piles, sunk about 2.5 metres into the underlying sandstone at a depth of about 10-13 metres below street level, to carry the weight of the structure.

247

Although Auckland is in a region of only moderate seismic activity, there is concern that it could be affected by large earthquakes, up to magnitude 8.5, centred 200 km or more away in the Bay of Plenty and East Cape regions near the subduction zone boundary between the Pacific and Indo-Australian plates. Such earthquakes could cause strong shaking in the flexible soils at the site. Isolation was achieved by making the piles laterally flexible with moment-resisting pins at each end. The piles were surrounded by clearance steel jackets allowing ±150 mm relative movement, thus separating the building from the potentially troublesome earthquake motions of the upper soil layers and making provision for the large base displacements necessary for isolation. An effective isolation system was completed by installing steel tapered-cantilever dampers at the top of the piles at ground level to provide energy dissipation and deflection control. The structure was stiffened and strengthened using external steel cross-bracing, (see Figure 8.10).

Figure 8.10: Union House, Auckland City; note the external diagonal bracing. The increased stiffness improved the seismic responses, giving reduced inter-storey displacements, a reduced shear force bulge at mid-height and reduced floor spectra. Moreover, the cross-bracing provided the required lateral strength at low cost. The reduced structure ductility was adequate with the well-damped isolator. The dampers are connected between the top of the piles supporting the superstructure and the otherwise structurally separated basement and ground-floor structure, which is supported directly by the upper soil layers. As Auckland is a region where earthquakes of only moderate magnitude are expected, the seismic design specifications for Union House are less severe than for many other seismically isolated structures. The maximum dissipator deflections in the 'maximum credible' El Centro motion were 150 mm, with 60 mm in the design earthquake. The effective period of the isolated structure was about 2 seconds. Maximum inter-storey deflections were typically 10 mm for the maximum credible earthquake and 5 mm for the design earthquake.

248

Union House is an example of the economical use of seismic isolation in an area of moderate seismicity. An appropriate structural form was chosen to take advantage of the reductions of seismic force, ductility demands and structural deformations offered by the seismic isolation option. The inherently stiff cross-braced frame is well-suited to the needs for a stiff superstructure in the seismically isolated approach. Isolation in turn makes the cross-bracing feasible, because low ductility demands are placed on the main structure. However, if very low floor spectra are required, it may be necessary to use more linear velocity dampers. An important factor in the design of such isolation systems is the need for an appropriate allowance for the displacement of the pile-sleeve tops with respect to the fixed ends of the piles. Other structural forms were investigated during the preliminary design stages, including two-way concrete frames, peripheral concrete frames, and a cantilever shear core. The cross-braced isolated structure allowed an open and light structural facade, and a maximum use of precast elements. The seismically isolated option produced an estimated cost saving of nearly 7 percent in the total construction cost of NZ$6.6 million (in 1983), including a construction-time saving of three months. 8.2.6

Wellington Central Police Station

The new Wellington Central Police Station (Charleson et al., 1987), completed in 1991, is similar in concept to Union House. The ten-storey tower block is supported on long piles founded 15 m below ground in weathered greywacke rock. The near-surface soil layer consists of marine sediments and fill of dubious quality.

Figure 8.11: Lead extrusion damper in basement of Wellington Central Police Station.

249

Figure 8.12: Wellington Central Police Station; note the external diagonal bracing.

Again the piles are enclosed in oversize casings, with clearances which allow considerable displacements relative to the ground. Energy dissipation is provided by lead-extrusion dampers, (Robinson & Greenbank, 1976), connected between the top of the piles and a structurally separate embedded basement (see Figure 8.11). A cross-braced reinforced concrete frame provides a stiff superstructure (see Figure 8.12). The flexible piles and lead-extrusion dampers provide an almost elastic-plastic force-displacement characteristic for the isolation system, which controls the forces imposed on the main structure. The seismic design specifications for the Wellington Central Police Station are considerably more severe than those for Union House in Auckland. The Police Station has an essential Civil Defence role and is therefore required to be in operation after a major earthquake. The New Zealand Loadings Code requires a risk factor R=1.6 for essential facilities. The site is a few hundred metres from the major active Wellington fault, and less than 20 km from several other major fault systems. Functional requirements dictated that the lateral load-resisting structure should be on the perimeter of the building. Three structural options were considered: a cross-braced frame, a moment-resisting frame or a seismically isolated cross-braced frame. This last option looked attractive from the outset because the foundation conditions required piling, but the perimeter moment-resisting frame was also considered at length. The structure is required to respond elastically for seismic motions with a 450-year return period, corresponding to a 1.4 times scaling of the 1940 El Centro accelerogram. The building must remain fully functional and suffer only minor non-structural damage for these motions. This is assured by the low inter-storey deflections of approximately 10 mm. With an isolation system with a nearly elastic-plastic force-deflection characteristic, and a low yield level of 0.035 of the building seismic weight, it was found that there was only a modest increase in maximum frame forces for the 1000-year return period motions, corresponding to 1.7 El Centro NS 1940 or the 1971 Pacoima Dam record. The increase in force was almost accommodated by the increase from dependable to probable strengths appropriate to the design and ultimate load conditions respectively. It is possible that some yielding will occur under the 1000-year return period motions, but the ductility demand will be low and specific ductile detailing was considered unnecessary. The Pacoima Dam record poses a severe test for a seismic isolation system because it contains a strong long-period pulse, thought to be a 'fault-fling' component, as well as high maximum accelerations. The Pacoima record imposes severe ductility demands on many conventional structures. 250

The degree of isolation required to obtain elastic structural response with these very severe earthquake motions requires provision for a large relative displacement between the top of the piles and the ground. A clearance of 375 mm was provided between the 800 mm diameter piles and their casings, to give a reasonable margin above the maximum calculated displacements; 355 mm was calculated for one of the 450-year return period accelerograms. Consideration was also given to even larger motions, when moderately-deformable column stops will contact the basement structure, which has been designed to absorb excess seismic energy in a controlled manner in this situation. The large displacement demands on the isolation system and the almost elastic-plastic response required from the energy dissipators led to the choice of lead-extrusion dampers rather than steel devices as used in Union House. In total, 24 lead-extrusion dampers each with a yield force of 250 kN and stroke of ± 400 mm were required. This was a considerable scaling-up of previous versions of this type of damper used in several New Zealand bridges: the bridge dampers had a yield level of 150 kN and a stroke of ± 200 mm. The new model damper was tested extensively to ensure the required performance. The seismically isolated option was estimated to produce a saving of 10% in structural cost over the moment-resisting frame option. In addition, the seismically isolated structure will have a considerably enhanced earthquake resistance. Moreover, the repair costs after a major earthquake should be low. Importantly, the seismically isolated structure should be fully operational after a major earthquake.

8.3

STRUCTURES ISOLATED IN JAPAN

8.3.1

Introduction

The first seismically isolated structure to be completed in Japan was the Yachiyodai Residential Dwelling, a 2-storey building, completed in 1982. This building is mounted on six laminated rubber bearings and relies on the friction of a precast concrete panel for the damping. Since 1985, more than 50 buildings have been authorised, of 1 to 14 storeys in height. They range from dwellings to tower blocks, with floor areas from 114 m2 to 38 000 m2. Details of buildings seismically isolated in Japan are given in Table 6.4 (Shimoda 1989-1992; Saruta, 1991, 1992; Seki, 1991, 1992). Various seismic isolation and damping systems have been used, often in hybrid combinations, as indicated in Table 6.4 and its footnote. The most popular isolation systems for buildings are laminated rubber for the isolation, with either steel or lead providing the damping. The first seismically isolated bridge in Japan was completed in 1990 and is mounted on lead rubber bearings. Details of some bridges seismically isolated in Japan are given in Table 8.5 (Shimoda 1989-1992; Seki, 1991, 1992; Saruta, 1991, 1992). Except for one mounted on a highdamping rubber bearing, all of these use lead rubber bearings.

251

Type

Dwelling Institute Institute Laboratory Dormitory Institute Museum Test Mdl Apartment Office Institute Institute Office Institute Apartment Office Apartment Dormitory Institute Rest house Apartment Office Store Dwelling Computer Office Clinic Dwelling Apartment Institute Office Laboratory Office Institute Office

Building Name

Yachiyodai Research Lab High-Tech. Research Lab Oiles Tech. Centre Tikuyu-Ryo Acoustic Lab Elizabeth Sanders (re-design) Tohoku University Apt. Hukumiya Sibuya Simizu Building Research Lab No. 6 Tsukuba Muki-Zaiken Tsuchiura branch Lab. J building Kousinzuka Toranomon Building Itoh Mansion Itinoe Dormitory Clean Room Lab Atagawa Hoyojo Ogawa Mansion Asano Building Kusuda Building Ichikawa residence Computer Centre Sagamihara Centre Gerontology Res. Lab. M-300 Hoyosyo Harvest Hills Acoustic Lab Toshin Building Dwell. Test Lab MSB-21 Ootuka Wind Laboratory CP Fukuzumi

252

Storey

Total Floor area (m2)

Isolation System

Licence Date

2 4 5 5 3 2 2

114 1330 1623 4765 1530 656 293

EB+F EB+S EB+S LRB+E EB+V EB+S EB+S

3 4 5+B1 3 1 4 4 3 8 10 3 2 1 4 7 4+B1 2 6 3 2+B1 2 6 2 9+B1 3 12+B2 3 5

208 681 3385 306 616 636 1173 476 3373 3583 770 405 140 1186 3255 1047 297 10032 255 1615 309 2065 656 7573 680 5962 555 4406

EB EB+S EB+S LRB EB+S LRB SL+R EB+S EB+S LRB EB+S EB+V SL+S HDR LRB HDR EB HDR HDR EB+S LRB EB+S EB+S EB+S EB+S LRB HDR EB+F

1982 1985 1986 1986 1986 1986 1986 1986 1986 1987 1987 1987 1987 1987 1987 1987 1988 1988 1988 1988 1988 1988 1988 1988 1988 1988 1988 1989 1989 1989 1989 1989 1989 1989 1989

Type

Building Name

Apartment Office Dormitory Dwelling Apartment Computer Factory Office Computer Office Office Office Institute Dormitory Dormitory Computer Laboratory Dormitory Office Dormitory

Employees Buildings Toho-Gas Centre Tudanuma Dormitory M-300 Yamada's Koganei-Apartment Operation Centre Urawa-Kogyo Kanritou Noukyou Centre C-1 Building Keisan Kenkyusyo Kasiwa Kojyo Acoustic Laboratory Yamato-ryo Kawaguchi-ryo Dounen Computer Centre Andou Tech. Centre Toyo Rubber Shibamata-ryo Aoki Tech. Centre Dai Nippon Daboku Ichigayaryo Domani-Musashino

Apartment EB LRB HDR SL S V F RS LD B1,B2

= = = = = = = = = =

Storey

Total Floor area (m2)

Isolation System

Licence Date

4 3 2 2 3 2 5 3 3 7+B1 3 4 2 8 4 4 3 7 4+B1 4

652 1799 202 214 714 10463 1525 955 5423 37846 627 2186 908 1921 659 3310 545 3520 4400 1186

LRB+HDR SL+RS EB+S LRB LRB+EB LRB HDR EB+V LRB LRB EB+V HDR EB+F EB+S LRB EB+LD LRB EB+S+oil LRB EB+LD

1989 1989 1989 1989 1989 1989 1989 1990 1990 1990 1990 1990 1990 1990 1990 1991 1991 1991 1991 1991

3

742

EB+S

1991

elastomeric bearing lead rubber bearing high damping rubber bearing sliding system (PTFE) steel damper viscous damper friction damper rubber spring lead damper basements Table 8.4: Seismically Isolated Buildings in Japan

253

Bridge name

Site

Superstructure Type

Bridge Length (m)

Isolation System

Completion (Scheduled)

On-netoh Oh-hashi Bridge

Hokkaido

4-span continuous steel girder

102

RB(12 Pcs) LRB(18 Pcs)

1991

Nagaki-gawa Bridge

Akita

3-span Continuous steel girder

99

LRB(20 Pcs)

1991

Maruki Bridge

Iwate

3-span Continuous PC Girder

122

LRB(8 Pcs)

1991

Shizuoka

3-span Continuous steel girder

104

LRB(10 Pcs)

1991

Metropolitan Highway Bridge No. 12

Tokyo

6-span Continuous PC slab

138

LRB(10 Pcs)

1991

Hokuso Viaduct (Railway)

Chiba

2-span Continuous steel girder

80

LRB(8 Pcs)

1990

Kanko Bridge

Tochigi

6-span Continuous PC girder

296

LRB(10 Pcs)

1991

Matsuno-hama Bridge

Osaka

4-span Continuous steel girder

211

LRB(12 Pcs)

1991

Uehara Bridge

Aichi

2-span Continuous steel girder

65

LRB(18 pcs)

1991

Shirasuji Viaduct (Railway)

Chiba

2-span Continuous steel girder

76

RB(4 pcs) LRB(4 pcs)

1993 (scheduled)

Trans-Tokyo Bay Highway Bridge

Tokyo Bay

10-span Continuous steel girder

800

LRB(18 Pcs)

1994 (scheduled)

Tochigi

6-span Continuous PC girder

245

High Damping Rubber (14 Pcs)

1992 (scheduled)

Miyagawa Bridge

Line

Karasu-yama No. 1 Bridge

EB HDR S F LD

= = = = =

elastomeric bearing high damping rubber bearing steel damper friction damper lead damper

LRB SL V RS B1,B2

= = = = =

Table 8.5: Seismically Isolated Bridges in Japan

254

lead rubber bearing sliding system (PTFE) viscous damper rubber spring basements

8.3.2

The C-1 Building, Fuchu City, Tokyo

This large building is expected to be completed in 1992, with a total area of more than 45000 m2, of which the isolated parts (higher building) have an area of 37846 m2, a height of 41 m and a weight of 62800 tonne. It will be used as a computer centre; seismic isolation was chosen to protect the equipment. The building will consist of a 7-floor superstructure, a penthouse and a 1-floor basement, with the composite structure being formed of steel and steel-reinforced concrete. It is mounted on 68 lead rubber bearings for seismic isolation. The bearings are between 1.1 and 1.5 m in diameter, with lead plugs from 180 to 200 mm in diameter (Nakagawa & Kawamura, 1991). Each bearing is surrounded by a thickness of 10 mm of rubber to protect it from attack by ozone and damage due to fire. At small displacements the natural period for the isolated building is expected to be about 1.4 s, while at large displacements, about 300 mm, the period is about 3 s. This should give an adequate frequency shift for an earthquake of the kind expected at the site. The maximum base shear force at the isolators due to wind is not expected to exceed 45% of the yield shear force of the bearings, so the building should not move appreciably during strong winds.

8.3.3

The High-Tech R&D Centre, Obayashi Corporation

This reinforced concrete structure, 5 storeys high, was completed in August 1986 (Teramura et al, 1988). It is equipped with a seismic isolation system consisting of 14 laminated rubber bearings, with an axial dead load of 200 tonnes, as well as 96 steel bar dampers, of a diameter of 32 mm. It also has friction dampers as sub-dampers for experimental purposes. The laminated rubber bearings give the seismically isolated structure a horizontal natural period of 3 s. (See Figures 8.13 and 8.14.)

Figure 8.13: Isolation system used in the Obayashi High-tech R & D Centre, Tokyo (Photograph courtesy Obayashi Corporation)

255

Figure 8.14: Obayashi High-tech R & D Centre (photograph courtesy Obayashi Corporation)

Seismic isolation has allowed a reduction of design strength and permits a large span structure with smaller columns and beams, which in turn provides open space. Key equipment, including a supercomputer, is installed on the top floor. During the 1989 Ibaraki earthquake, accelerograms recorded on the roof of the isolated building, and on the roof of the unisolated main building of the institute, clearly demonstrated the effectiveness of the seismic isolation, with a ten-fold reduction in roof acceleration in the isolated building.

8.3.4

Comparison of Three Buildings with Different Seismic Isolation Systems

A comparative study has been carried out (Kaneko et al, 1990) on the effectiveness and dynamic characteristics of four types of base isolation system, namely: laminated rubber bearing with oil damper system, high-damping rubber bearing system, lead rubber bearings, and laminated rubber bearings with a steel damper system. The study was carried out by earthquake response observations of full-sized structures, as well as by numerical analyses. The three buildings studied were the test building at Tohoku University in Sendai, northern Japan, Tsuchiura Office building northeast of Tokyo, and the Toranomon building in Tokyo. The test building at Tohoku University was seismically isolated in order to be used in experiment; for comparison, an identical building on the same campus was conventional, i.e. had not been isolated. Both buildings are 3-storey reinforced concrete structures 6 m x 10 m in plan. In the first stage of the investigation, the isolated building was fitted with 6 laminated rubber bearings and 12 viscous dampers (oil), (see Figures 8.15 and 8.16) and earthquake observation was conducted for a year. After that, the devices were changed to high-damping rubber bearings, and observations continued.

256

Figure 8.15: Oil dampers and laminated rubber bearings in Test Building at Tohoku University, Sendai (photograph courtesy Shimizu Corporation)

Figure 8.16: Test Buildings at Tohoku University. On the left is the conventional building, and on the right is the seismically isolated building (photograph courtesy Shimizu Corporation)

The natural frequencies and damping ratios of each building were obtained by forced vibration tests. The damping ratios of the isolated building with viscous dampers were about 15% and those with high-damping rubber about 12%, which are about 10 times and 8 times larger than those of the unisolated building respectively. The Tsuchiura office building of Shimizu Corporation is a four-storey reinforced concrete structure 12.5m x 12.5 m in plan. It is isolated by lead rubber bearings and the damping ratios were found to be anisotropic, being 9.9% and 12.7% along two orthogonal directions. The Toranomon building is 8.storey steel-framed reinforced concrete with an irregular shape and large eccentricity. The isolation devices have been arranged to reduce the eccentricity for earthquake loading. The building is supported by bearing piles on the Tokyo gravel layer, about 22 m below the surface. The isolation devices consist of 12 laminated rubber bearings and 25 steel dampers, each consisting of 24 steel bars (see Figure 8.17). Eight oil dampers (four for each direction) are also installed for small vibration amplitudes.

257

Figure 8.17: High damping rubber bearing, steel dampers and oil damper in basement of Bridgestone Toranomon Building, Tokyo (photograph courtesy Shimizu Corporation)

Accelerograms of the largest earthquake motions in the records of each building can be summarised as follows. In the two systems studied on the test building at Tohoku University, the maximum accelerations at the roof of the isolated building were about one-third of those on the unisolated building. For the lead rubber bearing system at Tsuchiura, the maximum acceleration at the roof was about 0.6 times that at the base. The response of the Toranomon building could not be clearly evaluated because only small amplitude earthquakes occurred and the steel damper system was still in the elastic region. Torsional responses were small in all four isolated structures.

8.3.5

Oiles Technical Centre Building

The Technical Centre Building of the Oiles Corporation (Shimoda et al, 1991) received special authorisation from the Ministry of Construction, based on the provisions under Article 38 of the Building Standards Law of Japan, since it was the first building in Japan to be equipped with lead rubber bearings for seismic isolation, and it was completed in February 1987. It is a 5-storey structure of reinforced concrete, with a total floor area of approximately 4800 m2 and a total weight of 7500 tons (see Figures 8.18 and 8.19).

Figure 8.18: Diagram of Oiles Technical Centre showing seismic accelerations as measured on 18/03/88 (courtesy Oiles Corporation)

258

Figure 8.19: Oiles Technical Centre, Tokyo (photograph courtesy Oiles Corporation)

Tests were carried out to verify the reliability of the base-isolated building under an earthquake. The tests consisted of free vibration tests, forced vibration tests and micro tremor observations. The appropriateness and accuracy of the method were also verified. The results of dynamic analysis showed that the response acceleration of each floor of the building was reduced to about 0.2g even during strong earthquakes (0.3-0.5g) at an input of 50 cm/sec. The maximum response acceleration was reduced to between 0.2 and 0.3g even under a velocity of 0.75 m/s. The building remained elastic since the shearing force for each storey was shown to be less than the yielding force, while the maximum response displacement was 370 mm.

8.3.6

Miyagawa Bridge

The Miyagawa Bridge, across the Keta River in Shizuoka prefecture, is the first seismically isolated bridge constructed in Japan (Matsuo & Hara, 1991). The three-span continuous bridge with steel plate girders of length 110 m, is in an area where the ground is stiff, and is mounted on lead rubber bearings (see Figures 8.20-8.22). In the traverse direction the bridge superstructure is restrained, allowing movements in the longitudinal direction of +150 mm before restraints at the abutments stop further displacement. The lead rubber bearings were chosen and distributed so that 38% and 12% of the total inertia force was allocated to each pier and each abutment, respectively. The fundamental period of the unisolated bridge was computed as 0.3 seconds, while the isolated design has a natural period of 0.8 seconds for small amplitude vibrations, and 1.2 seconds for larger. The system used for the design for seismic isolation is known in Japan as the "Menshin design method" (Matsuo & Hara, 1991).

259

Figure 8.20: Miyagawa Bridge, Shizuoka Prefecture, showing bridge deck, isolation system and piers.

Figure 8.21: Lead Rubber Bearing in Miyagawa Bridge showing transverse restraints (Photograph courtesy Oiles Corporation).

Figure 8.22: Miyagawa Bridge, Shizuoka Prefecture, Japan (photograph courtesy Oiles Corporation)

260

8.4

STRUCTURES ISOLATED IN THE USA

8.4.1

Introduction

The first use of seismic isolation in the USA occurred during 1979, when circuit breakers were mounted on 7% damped elastomeric bearings. Since that time a number of bridges and buildings have been built or retrofitted with seismic isolation. The Foothill Communities Law and Justice Centre, on elastomeric bearings, was the first new building in the USA to be mounted on seismic isolation. Tables 8.6 and 8.7 show buildings and bridges which have been seismically isolated in the USA.(Mayes, 1990, 1992). Building

Height/ Storeys

Floor Area m2

Isolation System

Date

Foothill Communities Law and Justice Centre

4

17,000

10% damped elastomeric bearings

1985/6

Salt Lake City and County Building (Retrofit)

5

16,000

Rubber and Lead rubber bearings

1987/8

Salt Lake City Manufacturing Facility (Evans and Sutherland Building)

4

9,300

Lead rubber bearings

1987/88

USC University Hospital

8

33,000

Rubber and Lead rubber bearings

1989

Fire Command and Control Facility

2

3,000

10% damped elastomeric bearings

1989

Rockwell Building (Retrofit)

8

28,000

Lead rubber bearings

1989

Kaiser Computer Center

2

10,900

Lead rubber bearings

1991

Mackay School of Mines (Retrofit)

3

4,700

10% damped elastomeric bearings plus PTFE

1991

Hawley Apartments (Retrofit)

4

1,900

Frictionpendulum/slider

1991

Channing House Retirement Home (Retrofit)

11

19,600

Lead rubber bearings

1991

Long Beach VA Hospital (Retrofit)

12

33,000

Lead rubber bearings

1991

Table 8.6: Seismically Isolated Buildings in the United States

261

Bridge

Superstructure type

Bridge length (m)

Isolation System

Completion Date

Longitudinal steel plate girders

190

LRB

1984/5

Santa Ana River Bridge, California (Retrofit)

Steel trusses

310

LRB

1986/7

Main Yard Vehicle Access Bridge, California (Retrofit)

Steel plate girders

80

LRB

1987

Eel River Bridge, California (US101) (Retrofit)

Steel through truss simple spans

185

LRB

1987

All American Canal Bridge, California (Retrofit)

Continuous steel plate girders

125

LRB

1988

Sexton Creek Bridge, Illinois

Continuous steel plate girders

120

LRB

1990

Toll Plaza Road Bridge, Pennsylvania

Simple span steel plate girder

55

LRB

1990

Lacey V. Murrow Bridge West Approach, Washington (Retrofit)

Continuous concrete box girders

340

LRB

1991

Cache River Bridge, Illinois (Retrofit)

Continuous steel plate girders

85

LRB

1991

Steel plate girder

110

LRB

1991

Steel beam

50

LRB

1991

US 40 Wabash River Bridge, Indiana

Continuous steel plate girders

270

LRB

1991

Metrolink Light Rail, St Louis, (7 dual bridges)

Concrete box girder

65 to 280

LRB

1991

Pequannock River Bridge, New Jersey

Steel plate girders

260

LRB

1991

Blackstone River Bridge, Rhode Island

Steel plate girders

305

LRB

1992

Bridges, B764 E & W, Nevada (Retrofit)

Steel plate girders

135

LRB

1992

Squamscott River Bridge, New Hampshire

Steel plate girders

270

LRB

1992

Olympic Blvd Separation, California

Steel plate girders

210

LRB

1992

Carlson Blvd Bridge, California

Concrete box girder

45

LRB

1992

Clackamas Connector, Oregon

Concrete box girder

305

LRB

1992

Cedar River Bridge, Washington

Steel plate girders

160

LRB

1992

Sierra Point Bridge, California (US101) (Retrofit)

Route 161 Over Dutch Hollow Road, Illinois West Street Overpass, New York (Retrofit)

Table 8.7: Seismically Isolated Bridges in the United States

262

8.4.2

Foothill Communities Law and Justice Centre, San Bernardino, California

This building, the first in the USA to be seismically isolated, in 1986, is mainly of steel frame construction with the basement level consisting of concrete shear walls. It is a 4-storey building with a total floor area of about 17 000 m2 mounted on 96 'high damping' rubber bearings (see Figures 8.23 and 8.24) (Way, 1992). The 'high damping' of 10 to 15% is obtained by increasing the amount of carbon black in the rubber. Before the plans were finalised, estimates were made of the accelerations and displacements of the structure when isolated and unisolated. For an unisolated building with a structural damping of 5%, it was estimated that the resonant period would be 1.1 sec, the base shear 0.8 g and the rooftop would undergo accelerations and displacements of 1.6 g and 300 mm respectively. For the isolated case with a conservative value of 8% for the damping, the acceleration above the bearings was estimated to be 0.35 g, while at the rooftop the acceleration was estimated at 0.4 g with a displacement of 380 mm. The resonant period had a value of 2 sec.

Figure 8.23: End elevation of Foothill Communities Law and Justice Centre, San Bernardino, California (courtesy Base Isolation Consultants, Incorporated)

Figure 8.24: Foothill Communities Law and Justice Centre (photograph courtesy Base Isolation Consultants, Incorporated)

263

8.4.3

Salt Lake City and County Building: Retrofit

This historic building, a massive 5-storey unreinforced masonry and stone structure with a 76 m high central clock tower, completed in 1894, is highly susceptible to earthquake damage, being 3 km from the Wasatch fault. It was retrofitted with seismic isolation, using a combination of lead rubber bearings and elastomeric bearings (Bailey & Allen, 1989) Figure 8.25 shows the façade of the building. The retrofitting project began with an analysis of possible seismic isolation systems, each of these to be carried out in conjunction with other structural changes such as a steel space truss within the clock tower, various plywood diaphragms, and anchorage of seismic hazards, such as chimneys, statues, gargoyles and balustrades, around the exterior of the building. The option of seismic isolation by means of a combination of elastomeric bearings and lead rubber bearings at the base of the building was chosen because it would be least disruptive to the interior of the building; other options required considerable demolition. Calculations indicated that this system would be adequate to withstand the design earthquake.

Figure 8.25: Salt Lake City and County Building, Utah; an historic building retrofitted with seismic isolation (photograph courtesy Dynamic Isolation Systems, Incorporated)

The task of retrofitting was complex, and was made more difficult by inaccurate detailing of the foundations on the original building plans, by variations in the level of the building foundation, and by the requirement that the building be damaged as little as possible, so that impact tools could not be used for cutting through the stone. The original plan had placed 500 isolators below existing foundations, but it was found that a massive concrete mat extended underneath the four main tower piers. Isolators were therefore installed on top of the existing footings, but the new first floor had to be raised 36 cm, and hundreds of slots had to be cut through existing walls above the footings in order to install the isolators. A major concern of the construction engineers was that an earthquake might occur during retrofit, when part of the building was isolated and part not, and when some walls had been removed. It was suggested (Bailey & Allen, 1989) that, in future, isolator locking mechanisms be employed during isolator installation in areas of high seismicity. A total of 443 isolators were used. All isolators were of the same size, approximately 43 cm square by 38 cm tall, to cut down on fabrication costs and to simplify installation. Not all the isolators had lead plugs, since computer analyses had indicated unacceptably high tower shear for certain earthquake records. The isolators with lead plugs, approximately half of the total, were located around the perimeter of the building to give high damping for rotational vibrations, and hence cut down on torsional response. 264

A retaining wall was constructed round the building's exterior to ensure a 400 mm seismic gap, this including a large safety factor as computer analysis had predicted only 12 cm lateral displacement of the building during the design earthquake. A bumper restraint system was also installed as a backup safety device. The project clearly demonstrated the feasibility of retrofitted isolation for a building of this kind, where: short periods result in high seismic forces the ratio of horizontal strength to weight is low ductility is low the risk of seismic collapse or cost of seismic repairs is unacceptable preservation has high cultural value the need to preserve exteriors and interiors limits scope for increasing strength and ductility it is practical to modify for inclusion of isolators the structural form and proportions do not give uplift for isolator-attenuated seismic forces adequate clearances for isolator and structure may be provided a practical isolation system gives an adequate reduction in seismic loads and deformations.

8.4.4

USC University Hospital, Los Angeles

This is an 8.storey, 35000 square-metre, steel-braced frame structure, with an asymmetric floor plan, scheduled for occupation in 1991 (Asher et al, 1990). It is a 275-bed teaching hospital, and is the first seismically isolated hospital in the world. The owner had been made aware of the potential benefits of seismic isolation and requested that it be considered as an alternative during the schematic design phase. As no consensus document for isolation design procedures existed, the structural engineer submitted proposed criteria for approval by the California Office of the State Architect. Issues addressed by the criteria were: seismic input, design force levels and essentially elastic behaviour, design displacement limits, and specific analysis requirements. The scope of the analysis was set by the approved criteria and extensive computation followed. The seismic isolation solution arrived at is shown schematically in Figure 6.26, namely a combination of lead rubber bearings at the exterior braced-frame columns, and elastomeric bearings at the interior vertical load-bearing columns. The completed hospital is seen in Figure 8.27.

Figure 8.26: Plan of USC Hospital, Los Angeles, showing positions of lead rubber bearings and elastomeric bearings (courtesy Dynamic Isolation Systems, Incorporated)

265

Figure 8.27: Completed USC Hospital, Los Angeles, California (photograph courtesy Dynamic Isolation Systems, Incorporated)

The Design Displacement arrived at was about 260 mm, a value in good accordance with those obtained by seismic isolation engineers in similar projects. All joints were detailed to allow a seismic gap 75 mm larger than the Design Displacement. Provision was made for inspection and replacement of the bearings if necessary. This is currently common practice throughout the world, although in the future, as experience with elastomeric bearings is gained, it will probably be found that these bearings do not need replacement during the life of a building. It was concluded (Asher et al, 1990) that, although the analysis procedures for a seismically isolated structure are more complex than for a conventional fixed-base structure, the actual design problems are no more complex than for an ordinary building.

8.4.5

Sierra Point Overhead Bridge, San Francisco

The Sierra Point Bridge was the first bridge in North America to be retrofitted using seismic isolation (Mayes, 1992). Originally built in 1956, it is 200 m long and 40 m wide on slight horizontal curvature (see Figure 6.28). Dynamic analysis indicated the bridge would sustain damage during a large design earthquake with horizontal acceleration of 0.6 g. The solution was to seismically isolate the bridge by replacing the existing steel spherical pin type bearings with lead rubber bearings. It was calculated that, in an earthquake of magnitude Richter 8.3 on the San Andreas Fault 7 km from the site, these bearings would lengthen the natural period of vibration of the structure so as to produce a six-fold reduction in real elastic forces to a level within the elastic capacity of the columns. Restraining bars were added to prevent the stringers from falling off their connections to the transverse girders. All work was done with no interruption of traffic on or under the bridge. The bridge is expected to remain in service during and immediately after the design event. (It did not receive a good test in the 1989 Loma Prieta earthquake, since the maximum ground acceleration was 0.09g.)

266

Figure 8.28: Sierra Point Overhead Bridge, San Francisco, seismically isolated by retrofitting with lead rubber bearings (photograph courtesy Dynamic Isolation Systems, Incorporated)

8.4.6

Sexton Creek Bridge, Illinois

This structure, carrying Illinois Route 3 over Sexton Creek near the town of Gale in Alexander County, is the first new bridge in North America to be seismically isolated (1988). It was designed by the Illinois Department of Transportation Office of Bridges and Structures. It is a 3-span continuous composite steel plate girder superstructure on slightly curved alignment, supported on wall piers and seat type abutments. There are five 1.4 m deep girders in the 13 m wide cross-section, and the spans are 40-50-40 m. The piers and abutments are founded on piled footings (see Figure 8.29) (Mayes, 1992).

Figure 8.29: Sexton Creek Bridge, Illinois, fitted with lead rubber bearings (Photograph courtesy Dynamic Isolation Systems, Incorporated)

Feasibility studies were conducted, leading to alternative solutions. The solution selected achieved the objective of reducing the seismic and non-seismic loads on the piers as much as possible, because of the poor foundation conditions. Seismic criteria for Sexton Creek included an acceleration coefficient of 0.2g and a Soil Profile Type III, in accordance with the AASHTO Guide Specifications for Seismic Design of Highway Bridges. The scheme chosen distributed the seismic load demands to the abutments using twenty lead rubber bearings, with twenty elastomeric bearings at the piers ("Force Control Bearings"). Seismic and wind forces at the piers were minimised through adjustments in bearing stiffness at the piers and abutments. The real elastic base shear was reduced to 0.13 W. 267

8.5

STRUCTURES ISOLATED IN ITALY

8.5.1

Introduction

The concept of seismic isolation has been enthusiastically applied to bridges in Italy, but there are far fewer examples of seismically isolated buildings. Available information (Parducci, 1992) on housing constructions is given in (b) below, while (c) describes the Mortaiolo Bridge, a new 9.6 km two-way bridge in Livorno-Cecina. The earliest records of bridges built in Italy go back two thousand years or more. A wooden bridge is described in Caesar's Gallic Wars, Book 4, but bridges spanning powerful rivers were usually built with stone piers and wooden superstructures, such as the Flavian Rhine Bridge at Moguntiacum, or Trajan's Danube Bridge, some 1120 m long (Cary, 1949). The modern technology of seismic isolation has been incorporated into the Italian bridge-building tradition since 1974, as shown in Table 8.8 (Parducci, 1992), in which details are given of over 150 bridges seismically isolated in Italy. A wide variety of isolating systems has been used, as seen in Table 8.8, although the earliest applications were designed without modern isolation criteria, certainly without official guidelines; a preliminary design guideline was published by Autostrade Company in 1991. Generally, elastic-plastic systems based on flexural deformations of steel elements of various shapes ('EP' in Table 6.8) were chosen. One such device is seen in Figure 8.30, while a device used in the Mortaiolo Bridge is described in detail below. Table 8.8 shows that, even when 2-way bridges are regarded as single structures, over 100 km of bridge in Italy has been seismically isolated in some way.

Figure 8.30: An elastic-plastic device used in the seismic isolation of bridges in Italy (Photograph courtesy A Parducci).

8.5.2

Seismically isolated buildings

To date, only few seismically isolated housing constructions have been designed or built in Italy (Parducci, 1992). These are detailed below. Vulcanised rubber-steel multi-layer pads are the seismic isolation system used.

268

(i)

SIP Regional Administration Centre, Ancona Five seven-storey seismically isolated buildings 61 isolators Type 'A': Isolated mass = 7.0 x 106 kg, 36 isolators Type 'B': Isolated mass = 3.7 x 106 kg, Elastomeric bearing  = 600 mm, H = 190 mm Horizontal stiffness = 114, 65 MN/m Natural periods = 1.5, 1.6 s Design viscous damping = 0.06 (experimental  0.12) Maximum response spectrum acceleration= 0.5 g Maximum design displacement = 145 mm

A full scale test was carried out on a type 'A' building; imposed displacements were up to 107 mm, before instant release. (ii)

Nuovo Nucleo Arruolamento Volontari, Ancona Isolated mass Natural period = Equivalent damping Maximum ground acceleration Maximum design displacement

(iii)

Centro Medico Legale Della Marina Militare, Augusta, (designed) Isolated mass Natural period = Equivalent damping Maximum ground acceleration Maximum design displacement

(iv)

= 0.2 x 106 kg 2.0 s = 10% = 0.25 g = 180 mm

Buildings Della Marina Militare, Augusta, (designed) Isolated mass Natural period = Equivalent damping Maximum ground acceleration Maximum design displacement

8.5.3

= 0.5 x 106 kg 1.6 s = 10% = 0.5 g ('single shock' quake) = 85 mm

= 0.4 x 106 kg 2.0 s = 13% = 0.25 g = 180 mm

The Mortaiolo Bridge

The Mortaiolo Bridge, a major 2-way bridge in the Livorno-Cecina section of the Livorno-Civitavecchia highway, was completed in 1992. The bridge crosses the large plain composed of deep soft clay stratifications lying near Livorno, in a region of seismic risk. The bridge is 9.6 km long, with typical spans of 45 m (see Figure 8.31(a)), made of pre-stressed reinforced concrete slab, with elastic-plastic devices on all the piers, shock-transmitter systems in the longitudinal direction, and a designed peak ground acceleration of 0.25 g. The elastic stiffness of the isolating device, in a typical section, is 135 MN/m, the yield/weight ratio is 0.11 and the maximum seismic displacement of the isolating system is + 80 mm (Parducci & Mezzi, 1991; Parducci, 1992).

269

(a)

(b) Figure 8.31: (a) Schematic of Mortaiolo Bridge (b) Schematic of one of the isolation devices used in the Mortaiolo Bridge (courtesy A Parducci)

Two equivalent isolating systems, manufactured by Italian firms, have been utilised in the bridge. Although they are based on different mechanical systems, they respond in the same elastic-plastic way. In both the devices the dissipating behaviour is based on the hysteretic flexural deformations of steel elements. Figure 8.31(b) illustrates the principle of operation of one of these devices. Provision for relative tilting between the piers and superstructure is provided by a spherical bearing. Damping is provided elasto-plastically by the deflection of numerous steel cantilevers arranged in a ring. A shock transmitter, a highly viscous device based on an oil-piston system, is in series with the isolator. The device is shown under test in Figure 8.32.

Figure 8.32: One of the isolation devices used in the Mortaiolo Bridge, under test (Photograph courtesy A Parducci)

270

Figure 8.33 shows the Mortaiolo Bridge during construction; further details are given by Parducci & Mezzi (1991), where it is also shown that the real incremental cost of the isolating systems was only 4.8% of the bridge cost. Figure 8.34 shows the nearly completed bridge.

Figure 8.33: Mortaiolo Bridge near completion (photograph courtesy A Parducci).

271

272

Table 8.8: Bridges Seismically Isolated in Italy KEY

EP EL OL SL ST RB LRB RC PCB

= = = = = = = = =

Elastic-plastic behaviour Elastic Oleodynamic system (EP equivalent) Sliding support Shock transmitter system associated with SL Rubber bearings Lead rubber bearings Reinforced concrete Prestressed concrete beams

273

NOTES

Where bridges are two-way, they have been regarded as a single bridge in estimating the length. The total length of isolated bridges is thus greater than 100 km. Of the more recent bridges (1985-1992), typical design values of the parameters are: • Yield/weight ratio: 5 to 28%, with a representative value of 10% • Maximum seismic displacement: + 30 to + 150 mm, with a representative value of + 60 mm • Peak ground acceleration: 0.15 to 0.40 g, with a representative value of 0.25 g. Known retrofits are indicated with an asterisk (*).

8.6

ISOLATION OF DELICATE OR POTENTIALLY HAZARDOUS STRUCTURES OR SUBSTRUCTURES

8.6.1

Introduction

Seismic problems arise with light-weight, delicate or potentially hazardous structures and substructures, such as life-support equipment in hospitals, important works of artistic or religious significance, e.g. the big statue of Buddha at Kamakura, Japan, equipment sensitive to vibration, and the radioactive components and associated support systems of nuclear reactors. An example of such a structure, where seismic isolation was installed because the cost of the contents far exceeds that of the building, is the Evans and Sutherland Building in Utah, which manufactures computerised flight simulator equipment (Mayes, 1992). Another example is the Mark II detector for the Stanford Linear collider at Stanford University, Palo Alto, California, which was provided with seismic isolation in 1987 (Mayes, 1992). Four lead rubber bearings were installed under the detector, also supporting the 1500 tonne mass of the collider. The isolation system was designed to reduce seismic forces by a factor of 10 and provide seismic protection of this sensitive and expensive equipment at less than 0.4% of its cost. The detector was not damaged during the 1989 Loma Prieta earthquake (Richter magnitude 7.1). Approximately bilinear isolators, which usually provide most of the mode-1 damping, have been found to be practical and convenient for the large-scale isolation of buildings and bridges as such. However, when an aseismic design is critically controlled by the responses of relatively light-weight substructures it is often appropriate to restrict the isolators to moderate or low levels of non-linearity. For such isolators it will sometimes be appropriate to provide a substantial part of the mode-1 damping by approximately-linear velocity dampers. These restrictions would not preclude the use of moderate levels of bilinear damping by means of metal yielding or by low sliding-friction forces. For example, the weight of an isolated structure might be carried on lubricated PTFE bearings. However, to minimize resonant-appendage effects during relativelyfrequent moderate earthquakes, such PTFE bearings should be supported by flexible mounts, as in the laminated-rubber/lead-bronze bearings pioneered by Jolivet & Richli (1977). Further isolator components should include flexible elastic components to provide centring forces, and sometimes substantial velocity damping. Both the latter components reduce the maximum extreme-earthquake base movements for which provision must be made. Nuclear power plants contain critical light-weight substructures essential for their safe operation and shut-down, including control rods, fuel rods and essential piping. These can be given a high level of protection by appropriate seismic isolation systems, designed to give low levels of seismic response for higher vibrational modes of major parts of the power plants. Further serious seismic problems arise with fast-breeder reactors in which critical components are given low strength by measures designed to give high rates of heat transfer. For some breeder-reactor designs it may be desirable to attenuate vertical as well as horizontal seismic forces. In this case it may be practical to provide horizontal attenuation for the overall plant and vertical attenuation for the reaction vessel only. 274

Since the dominant vertical earthquake accelerations have considerably shorter periods than the associated horizontal accelerations, displacements associated with vertical attenuation should be much smaller than those for horizontal attenuation. Early papers on nuclear power plant isolation, (Skinner et al, 1976a, 1976b), concentrated on the protection of the overall power plant structure but did not treat the problems with light-weight substructures, which arise from the seismic responses of higher modes of structural vibration. Structural protection may now be achieved with simpler alternative isolator components; for example the use of lead rubber bearings may remove the need for installing steel-beam dampers.

8.6.2

Seismically Isolated Nuclear Power Stations

Seismic isolation of nuclear structures is seen as a way to simplify design, to facilitate standardisation, to enhance safety margins and possibly to reduce cost (Tajirian et al, 1990); for example, it has been demonstrated that the weight of a pool-type Fast Breeder Reactor can be reduced by half if horizontal isolation is used. By 1990 it was reported (Tajirian et al, 1990) that six large Pressurised Water Reactor units had been installed, with seismic isolation, in France and South Africa and that several advanced nuclear concepts in the USA, Japan and Europe had also incorporated this approach. The design concepts for seismic isolation of two Liquid Metal Reactors, with the acronyms PRISM and SAFR, have been carried out in the USA. For the PRISM design, horizontal protection, for the reactor module only, is provided by 20 high-damping elastomeric bearings, while the SAFR design is unique in providing vertical as well as horizontal isolation, by using bearings which are flexible, both horizontally and vertically, the entire SAFR building being supported on 100 isolators. The seismic design basis for both plants is expected to cover over 80% of potential nuclear sites in the USA, and options for higher seismic zones have also been investigated.

8.6.3

Protection of Capacitor Banks, Haywards, New Zealand.

The AC Filter Capacitor Banks at the Haywards HVDC Converter Station in the Hutt Valley, New Zealand were built in 1965. Their earthquake resistance was increased in 1988 to the current seismic design requirement using a base isolation method employing rubber bearings and hysteretic steel dampers (Pham, 1991). (See Figures 8.34 and 8.35).

Figure 8.34: Capacitor banks at Haywards HVDC converter station in the Hutt Valley, New Zealand, seismically isolated by retrofitting with segmented rubber bearings and steel dampers.

275

Figure 8.35: Detail of retrofitted seismic isolation system for Haywards, as seen on the left of Figure 8.34. Note the low-stiffness elastomeric bearing, the steel cantilever damper and the original concrete support.

Figure 8.36: End elevation of Press Hall for Wellington Newspapers, Petone.

Due to the light mass involved, lead rubber bearings were found to be inappropriate and specially-designed segmented rubber bearings were used. These bearings have rubber layers bonded alternatively with steel plates in the conventional manner. However the rubber layers are not continuous but divided into four discs at 110 mm diameter each, as shown in Figure 3.14. This is to reduce the rubber shear area, while maintaining stability, and hence to reduce the shear stiffness sufficiently to shift the natural periods of the relatively light AC Filter Capacitor Banks from 0.2-0.5 sec to 1.8 sec. Dynamic shaking tests were done on 1 tonne bearings and static shear tests were done on 5 tonne bearings of this design. Test results have indicated that the bearings met the design specifications. To limit the displacements during large earthquakes and provide lateral restraints during minor earthquakes and for wind loads, hysteretic steel dampers were provided (see Figure 3.3(b)). Even with the base isolation, it was found that the insulators supporting the capacitor stack would not have adequate seismic strength. To reduce the bending moment at the support insulators, the stacks are split into two halves, thus effectively reducing the bending moment at the support insulators by a factor of two.

276

The specifications are as follows: AC Filter Capacitor Banks: a total of 18 banks of three different types with individual masses varying from 20 000 kg to 32 000 kg. The heights of the banks vary from 6.6 m to 9.6 m. Rubber Bearings: each bank has four to six bearings rated at 5000 kg each. Each bearing has 19 layers with a total height of 254 mm and a plan dimension of 400 x 400 mm. The shear stiffness is rated at 0.06 kN/mm. Dampers: each bank is provided with two circular tapered steel dampers with a base diameter of 45 mm, a height of 500 mm and was designed for a yield force Qy of 10.6 kN.

8.6.4

Seismic Isolation of a Printing Press in Wellington, New Zealand

In 1988 Wellington Newspapers Ltd approached the DSIR seeking advice on earthquake protection for a proposed new printing press establishment to be built in the Wellington region at Petone (Dowrick et al, 1991). The need for special protection of brittle cast-iron press machines had been demonstrated by the vulnerability of paper machines in the 1987 Edgecumbe earthquake. The site for this project was chosen because of its ready access to rail and road transport, but turned out to be traversed by the Wellington fault. To give the printing presses maximum protection from earthquakes, the building required a seismic isolation system, and in addition the building had to be as stiff as possible up to the top of the presses to limit the horizontal deflections of the presses in all directions. The originally proposed concrete walls were therefore extended in height and length around the ends of the press hall, and the mezzanine floor was stiffened. Creating enough horizontal stiffness in the direction lateral to the presses at the top platform level proved to be particularly difficult because visibility required for operations necessitated the use of a horizontal steel truss at this level (rather than using an opaque concrete slab). It was not practicable to create a truss with the optimum desired stiffness, but a workable solution was found. (See Figure 8.37.)

Figure 8.37: Lead Rubber Bearings for Press Hall under test

The dynamic analyses were carried out using a computer program for analysing seismically isolated structures incorporating the non-linear behaviour of the special isolating and damping system introduced below the ground floor. 277

From the results of the first trial analysis, it was found that the horizontal accelerations applied to the isolated structure, due to the very strong shaking caused by a rupture on the Wellington fault, would be in the range approximately 0.4g to 0.6g. It would have been both expensive and physically very difficult to give a high level of protection to the press against damaging deflections under such accelerations, particularly at the upper platform level. An additional disadvantage arose from the fact that it was not feasible operationally to apply any lateral restraint to the press at a level midway between the top platform and the mezzanine floor. It was found practicable to provide protection against earthquake-generated accelerations, transmitted through the structure, of about 0.3g at the top of the press and 0.25g at the lower levels. The specially designed building housing the press was mounted on lead rubber bearings 460 mm thick. This reduced the estimated loads and deflections on the press by a factor of 8 to 10 compared with the non-isolated case. (See Figure 8.38). As a result, the press should suffer only modest damage in earthquake shaking somewhat stronger than that required by the New Zealand earthquake code for the design of buildings.

Figure 8.38: Lead Rubber Bearing in place in Press Hall.

278

CHAPTER 9:

IMPLEMENTATION ISSUES

9.1 INTRODUCTION Preceding chapters have described the theory and design procedures for seismic isolation systems. A number of practical issues arise in implementing seismic isolation for a specific project and this chapter discusses these issues. Guidance is supplied to help decide on the isolation plane, the isolator locations and the types of device used. Seismic input is a critical design parameter for isolation and this is discussed in some detail. The remainder of the chapter discusses other aspects of the design process – structural analysis, connection design, structure design and specifications.

9.2 ISOLATOR LOCATIONS AND TYPES 9.2.1

Selection of Isolation Plane

Buildings The paramount requirement for installation of a base isolation system is that the building be able to move horizontally relative to the ground, usually at least 100 mm and in some instances up to 1 meter. A plane of separation must be selected to permit this movement. Final selection of the location of this plane depends on the structure but there are a few items to consider in the process. See discussion later in this chapter on Structural Design, as there are design consequences of decisions made in the selection of the location of the isolation plane. The most common configuration is to install a diaphragm immediately above the isolators. This permits earthquake loads to be distributed to the isolators according to their stiffness. For a building without a basement, the isolators are mounted on foundation pads and the structure constructed above them, as shown in Figure 9.1. The crawl space is usually high enough to allow for inspection and possible replacement of the isolators, typically at least 1.2 m to 1.5 m.

Ground Floor Isolator

Crawl Space

Figure 9.1 Building with No Basement

279

If the building has a basement then the options are to install the isolators at the top, bottom or mid-height of the basements columns and walls, as shown in Figure 9.2. For the options at the top or bottom of the column/wall then the element will need to be designed for the cantilever moment developed from the maximum isolator shear force. This will often require substantial column sizes and may require pilasters in the walls to resist the face loading.

Figure 9.2 Installation in Basement

The mid-height location has the advantage of splitting the total moment to the top and bottom of the component. However, as discussed later in Connection Design there will be P moments in the column/wall immediately above and below the isolator. The demands on basement structural members can be minimized by careful selection of isolator types and by varying the isolator stiffness. For example, if a LRB system is used then large lead cores may be used in isolators at locations such as wall intersections where there is a high resistance to lateral loads. More vulnerable elements such as interior columns may have isolators with small cores or no cores. As the diaphragm will enforce equal displacements at all isolators this will reduce the forces on the interior columns. If structural elements below the isolation interface are flexible then they may modify the performance of the isolation system as some displacement will occur in the structural element rather than the isolator. They should be included in the structural model. (See discussion on bridge isolation where flexible substructures are common). Selection of the isolation plane for the retrofit of existing buildings follows the same process as for new buildings but usually there are more constraints. Also, many of the issues which are resolved during design for a new installation, such as secondary moments, diaphragm action above the isolators and the capacity of the substructure to resist to maximum isolator forces, must be incorporated into the existing building. Figure 9.3 shows conceptually some of the issues that may be faced in a retrofit installation of any isolation system. These are schematic only as most retrofit projects have unique conditions. Each project may encounter some of all of these and will most likely also need to deal with other issues.

280

Isolators loaded with flatjacks

Walls strengthened locally with pilasters

Portion of wall between isolators removed after isolators installed and pre-loaded with flatjacks

SECTION

ELEVATION

Figure 9.3 Conceptual Retrofit Installation

1.

The isolators must be installed into the existing structure. The existing structure must be cut away to permit installation. For column installation this will require temporary support for the column loads. For wall structures, it may be possible to cut openings in the wall for the isolators to be installed while the non-separated portion of the wall supports the load. The wall between isolators is removed after installation of the isolators.

2.

The gravity load must be distributed to the isolators. Usually this is accomplished with flatjacks, which are hydraulic capsules in the form of a flat double saucer. Thrust plates are placed top and bottom, as shown in Figure 9.4 (adapted from a PSC Freyssinet catalogue). When the jack is inflated hydraulically the upper and lower plates are forced apart. The jacks can be inflated with hydraulic oil but for most isolation projects an epoxy grout is used and the jacks are left in place permanently.

Inlet

PLAN

Before Pressurizing

After Pressurizing Figure 9.4 Flat Jack

281

3.

For installation in wall structures, the walls will be needed to be strengthened above and below the isolators to resist primary and secondary moments. Often, precast concrete horizontal needle beams are clamped to each side of the existing wall above and below the isolators. These needle beams are connected using stressed rods.

4.

The existing wall will usually need strengthening to transfer the bending moment arising from the isolator force to the foundation elements. This may require pilasters.

5.

The structure above the isolators must be able to move freely by the maximum displacements, usually in the range of 150 mm to 500 mm or more. This will require construction of a moat around the building and may influence selection of the isolation plane as installation at the bottom of the basement will require deep retaining walls to allow movement.

Architectural Features and Services Apart from the structural aspects, base isolation requires modifications to architectural features and services to accommodate the movements. Especially important are items which cross the isolation plane, which will include stairs, elevators, water, communications, waste water and power. Provision will also need to be made to ensure that the separation space does not get blocked at some future time. There are devices available to provide flexible service connections and these can generally be dealt with by the services engineers, who must be advised of the location of the isolation plane and the maximum movements. Elevators usually cantilever below the isolation plane. The portion below the isolation system will need to have separation all round so that the movement can occur. Stairs may cantilever from above the isolation plane or may be on sliding bearings. Most isolation projects will have some items such as stairs; shaft walls etc, which require vertical support but must move with the isolators. The most common support for these situations is small sliding bearings. As the vertical reaction is usually small the friction resistance will be negligible compared to the total isolation force. With sliding bearings, no matter how small the load the displacement will still be equal to the maximum displacements and so even though a small bearing pad is used the size of the slide plate will be as large as for a heavy load. Most of the problems you encountered will have been solved on previous isolation projects. It will be helpful to consult some of the published case studies from isolation projects world wide. Bridges As noted in Chapter 7 of these guidelines, the most common location for the isolation plane for bridges is at the top of bents, isolating the superstructure. If the bents are single column bents then the pier will function as a cantilever. Multi-column bents will function as cantilevers under longitudinal loads but will act as frames transversely if the isolators are placed above the top transverse beam. 282

The weight of the bents themselves is often a high proportion of the total bridge weight and it may be preferable to isolate this portion of the mass as well as the superstructure mass. This could be achieved by placing the isolators at the base rather than at the top of the bent columns. In practice, this is likely to be a problem as there will be large moments, which must be resisted by the bridge superstructure. There may be some bridge configurations where this is practical. An unusual form of isolation which has been used on the South Rangitikei Viaduct in New Zealand is a rocking isolation system. The 70 m tall twin column piers have a horizontal separation plane near the bottom of each column. When the bridge moves under transverse earthquake loads the piers will rock on one column. Steel torsion bar energy absorbers are used to control the upward displacements and absorb energy under each uplift cycle.

Other Structures Selection of the isolation plane for other types of structures will follow the same general principles as for buildings and bridges. Isolation reduces the inertia forces in all mass above the isolators and so the general aim is to isolate as much of the weight as possible, which usually means placing the isolators as close to the base as possible. Exceptions may be where a large mass is supported on a light frame, such as an elevated water tank. It may be possible to install the isolators under the tank at the top of the frame. This will isolate the majority of the mass and will minimize the overturning moments on the isolators, avoiding tension loads in the isolators. However, the frame base must be able to resist the overturning moments from the maximum isolator shear forces applied at the top of the frame. Buildings and bridges are all relatively heavy and most isolation devices are best suited to large loads. This is because for a given isolation period the displacement is the same regardless of mass and it is difficult to retain stability of small isolators under large displacements. Sliding devices work well under light loads and there has been some development work performed on other low mass devices. Systems based on elastomeric bearings are suitable for loads per device of at least 50 kN and preferably 200 kN. This may restrict options available for structures other than buildings and bridges.

9.2.2

Selection of Device Type

No one type of device is perfect. If it were, all projects would use the same type of device. Of the types available, following is a summary of their characteristics and advantages and disadvantages. Each project will have specific objectives and constraints and so devices will need to be selected as those best fitting specific project criteria. Mixing Isolator Types and Sizes Most projects use a single type of isolator although sliding bearings in particular are often used with lead rubber or high damping rubber bearings. As discussed below, sliding bearings provide good energy dissipation, can resist high compression loads and permit uplift should tension occur but have the disadvantages of sticking friction and not providing a restoring force. If used in parallel with bearing types that do provide a restoring force the advantages of sliding bearings can be gained without the disadvantages. 283

The UBC procedures can be used to determine the ratios of the two types of bearing. A rule of thumb is that the sliding bearings should support no more than 30% of the seismic mass and LRBs or HDR bearings the remainder. The most common use of sliding bearings is where shear walls provide high overturning forces. A sliding bearing can efficiently resist the high compression and the tension end of the wall can be permitted to uplift. For most bearing types the plan size required increases as vertical load increases but the height (of LRB and HDR bearings) or radius (of FPS bearings) is constant regardless of vertical load as all bearings will be subjected to the same displacement. Therefore, the bearings can be sized according to the vertical load they support. In practice, usually only a single size or two sizes are used for a particular project. This is for two reasons: 1. For most applications, each different size of bearing requires two prototypes, which are extra bearings used for testing and not used in the finished structure. If the plan size is reduced for some locations with lower loads then the cost savings are often not enough to offset the extra prototype supply and testing costs. If there are less than 20 isolators of a particular size then it is probably more economical to increase them to the next size used. 2. For high seismic zones, a minimum plan size of LRB or HDR isolators is required to ensure stability under maximum lateral displacements. As all bearings have the same displacement, a reduced vertical load may not translate into much reduction, if any, in plan size. The design procedures can be used to decide whether several sizes of isolator are economically justified. Sort the isolator locations according to maximum vertical loads and then split them into perhaps 2, 3 or more groups, depending on the total number of isolators. Design them using first the same size for all groups and then according to minimum plan size. Check the total volume required for each option, including prototype volume. Price is generally proportional to total volume so this will identify the most economical grouping. Elastomeric Bearings An elastomeric bearing consists of alternating layers of rubber and steel shims bonded together to form a unit. Rubber layers are typically 8 mm to 20 mm thick, separated by 2 mm or 3 mm thick steel shims. The steel shims prevent the rubber layers from bulging and so the unit can support high vertical loads with small vertical deflections (typically 1 mm to 3 mm under full gravity load). The internal shims do not restrict horizontal deformations of the rubber layers in shear and so the bearing is much more flexible under lateral loads than vertical loads, typically by at least two orders of magnitude. Elastomeric bearings have been used extensively for many years, especially in bridges, and samples have been shown to be functioning well after over 50 years of service. They provide a good means of providing the flexibility required for base isolation. Elastomeric bearings use either natural rubber or synthetic rubber (such as neoprene), which have little inherent damping, usually 2% to 3% of critical viscous damping. They are also flexible at all strain levels and so do not provide resistance to movement under service loads. Therefore, for isolation they are generally used with special elastomer compounds (high damping rubber bearings) or in combination with other devices (lead rubber bearings).

284

As discussed later, the load capacity of an elastomeric bearing in an undeformed state is a function of the plan dimension and layer thickness. When shear displacements are applied to the bearing the load capacity reduces due to the shear strain applied to the elastomer and to the reduction of effective “footprint” of the bearing. Figure 9.5 provides an example of the load capacity of elastomeric bearings with a medium soft rubber and 10 mm layers.

30000 Gravity Moderate Seismic

25000 VERTICAL LOAD (KN)

High Seismic 20000

15000

10000

5000

0 400

500

600 700 800 BEARING DIAMETER (mm)

900

1000

Figure 9.5 Load Capacity of Elastomeric Bearings

The load capacity is plotted for gravity loads (assuming zero lateral displacements) and for two seismic conditions, the first a moderate displacement producing a shear strain of 150% and an effective area of 0.50 times the gross area. The second is for a very severe seismic displacement, producing a shear strain of 250% and an effective area of only 0.25 times the gross area. This latter case represents the extreme design limits for this type of bearing. As shown in Figure 9.5, the allowable vertical load reduces rapidly as the seismic displacement increases. This makes the sizing of these isolators complicated in high seismic zones. This is further complicated by the fact that vertical loads on the bearings may increase with increasing displacements, for example, under exterior columns or under shear walls. High Damping Rubber Bearings The term high damping rubber bearing is applied to elastomeric bearings where the elastomer used (either natural or synthetic rubber) provides a significant amount of damping, usually from 8% to 15% of critical. This compares to the more "usual" rubber compounds, which provide around 2% damping.

285

The additional damping is produced by modifying the compounding of the rubber and altering the cross link density of the molecules to provide a hysteresis curve in the rubber. Therefore, the damping provided is hysteretic in nature (displacement dependent). For most HDR compounds the viscous component of damping (velocity dependent) remains relatively small (about 2% to 5% of critical). The damping provided by the rubber hysteresis can be used in design by adopting the concept of "equivalent viscous damping" calculated from the measured hysteresis area, as in done for LRBs. As for LRBs, the effective damping is a function of strain. For most HDR used to date the effective damping is around 15% at low (25% to 50%) strains reducing to 8%-12% for strains above 100%, although some synthetic compounds can provide 15% or more damping at higher strains. For design, the amount of damping is obtained from tabulated equivalent viscous damping ratios for particular elastomer compounds. The load capacity for these bearings is based on the same formulas used for elastomeric bearings.

Lead Rubber Bearings A lead rubber bearing is formed of a lead plug force-fitted into a pre-formed hole in an elastomeric bearing. The lead core provides rigidity under service loads and energy dissipation under high lateral loads. Top and bottom steel plates, thicker than the internal shims, are used to accommodate mounting hardware (Figure 9.6). The entire bearing is encased in cover rubber to provide environmental protection. When subjected to low lateral loads (such as minor earthquake, wind or traffic loads) the lead rubber bearing is stiff both laterally and vertically. The lateral stiffness results from the high elastic stiffness of the lead plug and the vertical rigidity (which remains at all load levels) results from the steel-rubber construction of the bearing.

Internal Steel Shims

Rubber Layers

Lead Core

Figure 9.6 Lead Rubber Bearing Section

At higher load levels the lead yields and the lateral stiffness of the bearing is significantly reduced. This produces the period shift effect characteristic of base isolation. As the bearing is cycled at large displacements, such as during moderate and large earthquakes, the plastic deformation of the lead absorbs energy as hysteretic damping. The equivalent viscous damping produced by this hysteresis is a function of displacement and usually ranges from 15% to 35%. 286

A major advantage of the lead rubber bearing is that it combines the functions of rigidity at service load levels, flexibility at earthquake load levels and damping into a single compact unit. These properties make the lead rubber bearing the most common type of isolator used where high levels of damping are required (in high seismic zones) or for structures where rigidity under services loads is important (for example, bridges). As for HDR bearings, the elastomeric bearing formulas are also applicable for the design of LRBs. Flat Slider Bearings Sliding bearings provide an elastic-perfectly plastic hysteresis shape with no strain hardening after the applied force exceeds the coefficient of friction times the applied vertical load. This is attractive from a structural design perspective as the total base shear on the structure is limited to the sliding force. An ideal friction bearing provides a rectangular hysteresis loop, which provides equivalent viscous damping of 2/ = 63.7% of critical damping, much higher than achieved with LRBs or HDR bearings. In practice, sliding bearings are not used as the sole isolation component for two reasons: 1. Displacements are unconstrained because of the lack of any centring force. The response will tend to have a bias in one direction and a structure on a sliding system would continue to move in the same direction as earthquake aftershocks occur. 2. A friction bearing will be likely to require a larger force to initiate sliding than the force required to maintain sliding. This is termed static friction, or “sticktion”. If the sliders are the only component then this initial static friction at zero displacement will produce the governing design force. The UBC and AASHTO codes require that isolation systems either have a specified restoring force or be configured so as to be capable of accommodating three times the earthquake displacement otherwise required. As maximum design earthquake displacements may be of the order of 400-500 mm this would require sliding systems to be designed for perhaps 1.5m of movement. This may be impractical for detailing movement joints, services, elevators etc. A hybrid system with elastomeric bearings providing a restoring force in parallel with sliding bearings may often be an economical system. Sliding bearings such as pot bearings using Teflon as a sliding surface can take much higher compressive stresses than elastomeric bearings (60 MPa or more versus 15 MPa or so for elastomeric). Also, the bearings can uplift without disengagement of dowels. Therefore, they are especially suitable at the ends of shear walls and were used at these locations for the Museum of New Zealand. The most common sliding surface is Teflon on stainless steel. This has a low static coefficient of friction, around 3%. However, the coefficient is a function of both pressure and velocity of sliding. With increasing pressure the coefficient of friction decreases. With increasing velocity the coefficient increases significantly and at earthquake velocities (0.2 to 1 m/sec) the coefficient is generally about 8% to 12%. For preliminary design a constant coefficient of friction of about 10% is usually assumed. For detailed analysis, the element model should include the variation with pressure and velocity.

287

Curved Slider (Friction Pendulum) Bearings Although a number of curved shapes are possible, the only curved sliding bearing which has been extensively used is a patented device in which the sliding surface is spherical in shape rather than flat, termed the Friction Pendulum System. The schematic characteristics of this device are shown in Figure 9.7.

R W

Articulated Slider

Spherical Surface Displacement W/R W

Force

Figure 9.7 Curved Slider Bearing

The isolator provides a resistance to service load by the coefficient of friction, as for a flat slider. Once the coefficient of friction is overcome the articulated slider moves and because of the spherical shape a lateral movement is accompanied with a vertical movement of the mass. This provides a restoring force, as shown in the hysteresis shape in Figure 9.7. The bearing properties are defined by the coefficient of friction, the radius of the sphere and the supported weight. The post-sliding stiffness is defined by the geometry and supported weight, as W/R. The total force resisted by a spherical slider bearing is directly proportional to the supported weight. If all isolators in a project are of the same geometry and friction properties and are subjected to the same displacement then the total force in each individual bearing is a constant times the supported weight. Because of this, the center of stiffness and center of mass of the isolation system will coincide and there will be no torsion moment. Note that this does not mean that there will be no torsion movements at all as there will likely still be eccentricity of mass and stiffness in the building above the isolators.

288

Ball and Roller Bearings Although roller bearings are attractive in theory as a simple means of providing flexibility there do not seem to be any practical systems based on ball or roller bearings available. A ball system is under development using a compressible material, which deforms as it rolls providing some resistance to service loads and energy dissipation (the Robinson RoBall). Preliminary results have been presented at conferences and the device appears to have promise, especially for low mass applications. More detail should become available in the near future. Solid ball and roller bearings constructed of steel or alloys usually have the problem of flattening of the contact surface under time if they are subjected to a high stress, as they would be under buildings and bridges. This appears to have restricted their use. Also, they do not provide either resistance to service loads or damping so would need to be used in parallel with other devices. Supplemental Dampers Systems which do not have an inherent restoring force and/or damping, such as elastic bearings, sleeved piles or sliding bearings, may be installed in parallel with dampers. These devices are in the same categories used for in-structure damping, a different form of passive earthquake protection. Supplemental damping may also be used in parallel with damped devices such as LRBs or HDR bearings to control displacements in near fault locations. External dampers are classified as either hysteretic or viscous. For hysteretic dampers the force is a function of displacement, for example, a yielding steel cantilever. For viscous dampers the force is a function of velocity, for example, shock absorbers in an automobile. For an oscillating system the velocity is out of phase with the displacement and the peak velocity occurs at the zero displacement crossing. Therefore, viscous damping forces are out of phase with the elastic forces in the system and do not add to the total force at the maximum displacement. Conceptually, this is a more attractive form of damping than hysteretic damping. In practice, if a viscous damper is used in parallel with a hysteretic isolator then there is a large degree of coupling between the two systems, as shown in Figure 9.8. The maximum force in the combined system is higher than it would be for the hysteretic isolator alone. If the viscous damper has a velocity cut-off (a constant force for velocities exceeding a pre-set value) then the coupling is even more pronounced.

289

DAMPING FORCE

Total Viscous Hysteretic DISPLACEMENT Figure 9.8 Viscous Damper in Parallel with Yielding System

Practically, it is difficult to achieve high levels of viscous damping in a structure responding to earthquakes. The damping energy is converted to heat and materials exhibiting highly viscous behavior, such as oil, tend to become more viscous with increasing temperature. Therefore, the dampers lose effectiveness as the earthquake amplitude and duration increases unless a large volume of material is used. These factors have restricted the number of suppliers of viscous dampers suited for earthquake type loads. Hardware tends to be declassified military devices and is expensive. For either viscous or hysteretic dampers, the damping contributed to the total isolation system is calculated from the total area of the hysteretic loop at a specified displacement level. This loop area is then added to the area from other devices such as lead rubber bearings. These concepts are the same as used for in-structure damping and energy dissipation. Advantages and Disadvantages of Devices Table 9.1 summarizes the advantages and disadvantages of the most commonly used device types. Note that although disadvantages may apply to a generic type, some manufacturers may have specific procedures to alleviate the disadvantage. For example, static friction is a potential disadvantage of sliding bearings in general but manufactures of devices such as the Friction Pendulum System may be able to produce sliding surfaces that are not subject to this effect. Some factors listed in Table 9.1 are not disadvantages of the device itself but may be a design disadvantage for some projects. For example, the LRBs and HDR bearings produce primary and secondary (P-) moments which are distributed equally to the top and bottom of the bearing and so these moments will need to be designed for in both the foundation and structure above the isolators. For sliding systems the total P- moment is the same but the sliding surface can be oriented so that the full moment is resisted by the foundation and none by the structure above (or vice versa). 290

The advantages and disadvantages listed in Table 9.1 are general and may not be comprehensive. On each project, some characteristics will be more important than others. For these reasons, it is not advisable to rule out specific devices too early in the design development phase. It is usually worthwhile to consider at least a preliminary design for several type of isolation system until it is obvious which system(s) appear to be optimum. It may be advisable to contact manufacturers of devices at the early stage to get assistance and ensure that the most up-to-date information is used.

Elastomeric

Advantages Low in-structure accelerations Low cost

High Damping Rubber

Moderate in-structure accelerations Resistance to service loads Moderate to high damping

Lead Rubber

Moderate in-structure accelerations Wide choice of stiffness / damping

Flat Sliders

Low profile Resistance to service loads High damping P- moments can be top or bottom

Curved Sliders

Low profile Resistance to service loads Moderate to high damping P- moments can be top or bottom Reduced torsion response No commercial isolators available. May be low cost Effective at providing flexibility

Roller Bearings Sleeved Piles

Hysteretic Dampers Viscous Dampers

Control displacements Inexpensive Control displacements Add less force than hysteretic dampers

Disadvantages High displacements Low damping No resistance to service loads P- moments top and bottom Strain dependent stiffness and damping Complex analysis Limited choice of stiffness and damping Change in properties with scragging P- moments top and bottom Cyclic change in properties P- moments top and bottom High in-structure accelerations Properties a function of pressure and velocity Sticking No restoring force High in-structure accelerations Properties a function of pressure and velocity Sticking Require suitable application Low damping No resistance to service loads Add force to system Expensive Limited availability

Table 9.1 Device Advantages and Disadvantages

291

9.3 9.3.1

SEISMIC INPUT Form of Seismic Input

Earthquake loads are a dynamic phenomenon in that the ground movements that give rise to loads change with time. They are also indeterminate in that every earthquake event will generate different ground motions and these motions will then be modified by the properties of the ground through which they travel. Efficient structural design requires a small number of defined loads so codes represent earthquake loads in a format more suited to design conditions. The codes generally specify seismic loads in three forms, in increasing order of complexity: Equivalent Static Loads These are intended to represent an envelope of the storey shears that will be generated by an earthquake with a given probability of occurrence. Most codes now derive these loads as a function of the structure (defined by period), the soil type on which it is founded and the seismic risk (defined by a zone factor). The static load is applied in a specified distribution, usually based on an assumption of inertia loads increasing linearly with height. This distribution is based on first mode response and may be modified to account for structural characteristics (for example, an additional load at the top level or use of a power function with height). Base isolation modifies the dynamic characteristics of the structure and usually also adds damping. These effects are difficult to accommodate within the limitations of the static load procedure and so most codes impose severe limitations on the structures for which this procedure is permitted for isolated structures. Response Spectrum A response spectrum is a curve that plots the response of a single degree of freedom oscillator of varying period to a specific earthquake motion. Response spectra may plot the acceleration, velocity or displacement response. Spectra may be generated assuming various levels of viscous damping in the oscillator. Codes specify response spectra which are a composite, or envelope, spectrum of all earthquakes that may contribute to the response at a specific site, where the site is defined by soil type, and zone factor. The code spectra are smooth and do not represent any single event. A response spectrum analysis assumes that the response of the structure may be uncoupled into the individual modes. The response of each mode can be calculated by using the spectral acceleration at the period of the mode times a participation factor which defines the extent to which a particular mode contributes to the total response. The maximum response of all modes does not occur at the same time instant and so probabilistic methods are used to combine them, usually the Square Root of the Sum of the Square (SRSS) or, more recently, the Complete Quadratic Combination (CQC). The latter procedure takes account of the manner in which the response of closely spaced modes may be partially coupled and is considered more accurate than the SRSS method. The uncoupling of modes is applicable only for linear elastic structures and so the response spectrum method of analysis cannot be used directly for most base isolated structures, although this restriction also applies in theory for yielding non-isolated structures. Most codes permit response spectrum analysis for a much wider range of isolated structures than the static load procedure. 292

In practice, the isolation system is modeled as an equivalent elastic system and the damping is implemented by using the appropriately damped spectrum for the isolated modes. The analyses described in Chapter 6 suggest that this procedure may underestimate floor acceleration and overturning effects for non-linear systems. Time History Earthquake loads are generated in a building by the accelerations in the ground and so in theory a load specified as a time history of ground accelerations is the most accurate means of representing earthquake actions. Analysis procedures are available to compute the response of a structure to this type of load. The difficulty with implementing this procedure is that the form of the acceleration time history is unknown. Recorded motions from past earthquakes provide information on the possible form of the ground acceleration records but every record is unique and so does not provide knowledge of the motion which may occur at the site from future earthquakes. The time history analysis procedure cannot be applied by using composite, envelope motions, as can be done for the response spectrum procedure. Rather, multiple time histories that together provide a response that envelopes the expected motion must be used. Seismology is unlikely ever to be able to predict with precision what motions will occur at a particular site and so multiple time histories are likely to be a feature of this procedure in the foreseeable future. Codes provide some guidance in selecting and scaling earthquake motions but none as yet provide specific lists of earthquakes with scaling factors for a particular soil condition and seismic zone. The following sections discuss aspects of earthquake motions but each project will require individual selection of appropriate records. 9.3.2

Recorded Earthquake Motions

Pre-1971 Motions The major developments in practical base isolation systems occurred in the late 1960’s and early 1970’s and used the ground motions that had been recorded up to that date. An example of the data set available to those researchers is the Caltech SMARTS suite of motions (Strong Motion Accelerogram Record Transfer System) which contained 39 sets of three recorded components (two horizontal plus vertical) from earthquakes between the 1933 Long Beach event and the 1971 San Fernando earthquake. A set of these records was selected for processing, excluding records from upper floors of buildings and the Pacoima Dam record from San Fernando, which included specific site effects. Response spectra were generated from the remaining 27 records, using each of the two horizontal components, and the average values over all 54 components calculated. The envelope and mean 5% damped acceleration spectra are shown in Figure 9.9 and the equivalent 5% damped displacement spectra in Figure 9.10.

293

A curve proportional to 1/T fits both the acceleration and the displacement spectra for periods of 0.5 seconds and longer quite well, as listed in Table 9.2. This shows that: 1.

If it is assumed that the acceleration is inversely proportional to T for periods of 0.5 seconds and longer, the equation for the acceleration coefficient is Sa = C0/T. The coefficient C0 can be calculated from the acceleration at 0.5 seconds as C0 = 0.5 x 0.278 = 0.139. The accelerations at periods of 2.0, 2.5 and 3.0 seconds calculated as Sa = 0.139/T match the actual average spectrum accelerations very well.

2.

The spectral displacements is related to the spectral acceleration as Sd = SagT2/42. For mm units, g = 9810 mm/sec2 and so Sd = 248.5SaT2. Substituting Sa = 0.139/T provides for an equation for the spectral displacement Sd = 34.5 T, in mm units. The values are listed in Table 9.2 and again provide a very close match to the calculated average displacements.

These results show that the code seismic load coefficients, defined as inversely proportional to the period, had a sound basis in terms of reflecting the characteristics of actual recorded earthquakes. Figures 9.11 and 9.12, from the 1940 El Centro and 1952 Taft earthquake respectively, are typical of the form of the spectra of the earlier earthquakes. For medium to long periods (1 second to 4 seconds) the accelerations reduced with increased period and the displacement increased with increasing period. However, as discussed in the following sections later earthquake records have not shown this same trend. Period Period Period Period 2.0 2.5 3.0 0.5 Seconds Seconds Seconds Seconds Acceleration (g) Average Values Calculated as 0.139/T Displacement (mm) Average Values Calculated as 34.5T

0.278 0.278

0.074 0.070

0.057 0.056

0.048 0.046

17 17

73 69

89 86

106 104

Table 9.2: Average 5% Damped Spectrum Values

1.40

ACCELERATION (g)

1.20 Envelope Average

1.00 0.80 0.60 0.40 0.20 0.00 0.00

0.50

1.00

1.50 2.00 2.50 PERIOD (Seconds)

3.00

3.50

Figure 9.9: SMARTS 5% Damped Acceleration Spectra

294

4.00

1000 900 DISPLACEMENT (mm)

800

Envelope Average

700 600 500 400 300 200 100 0 0.00

0.50

1.00

1.50 2.00 2.50 PERIOD (Seconds)

3.00

3.50

4.00

Figure 9.10: SMARTS 5% Damped Displacement Spectra

EL CENTRO SITE IMPERIAL VALLEY IRRIGATION DISTRICT S90W IMPERIAL VALLEY MAY 18 1940

EL CENTRO SITE IMPERIAL VALLEY IRRIGATION DISTRICT S00E IMPERIAL VALLEY MAY 18 1940

1.00

500

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0

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ACCELERATION (g)

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0 1.00

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PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.11: 1940 El Centro Earthquake

295

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DISPLACEMENT (mm)

1.00

TAFT LINCOLN SCHOOL TUNNEL S69E KERN COUNTY 1952

TAFT LINCOLN SCHOOL TUNNEL N21E KERN COUNTY 1952 0.60

300

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ACCELERATION

200

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0.00 0.00

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PERIOD (Seconds)

Figure 9.12: 1952 Kern County Earthquake

Post-1971 Motions Since 1971 the number of seismic arrays for recording ground motions has greatly increased and so there is an ever increasing database of earthquake records. As more records are obtained it has become apparent that there are far more variations in earthquake records than previously assumed. In particular, ground accelerations are much higher and near fault effects have modified the form of the spectra for long period motions. The following Figures 9.13 to 9.18, each of which are 5% damped spectra of the two horizontal components for a particular earthquake, illustrate some of these effects: 1.

The 1979 El Centro event was recorded by a series of accelerographs that straddled the fault. Figure 9.13 shows the spectra of Array 6, less than 2 km from the fault. This shows near fault effects in the form of a spectral peak between 2 seconds and 3 seconds and a spectral displacement that exceeded 1 m for a period of 3.5 seconds. For this record, an isolation system would perform best with a period of 2 seconds or less. If the period increased beyond two seconds, both the acceleration and the displacement would increase.

296

1979 Imperial Valley CA El Centro Arr #6 140

1200

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1.40

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Acceleration

1.20

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DISPLACEMENT (mm)

1979 Imperial Valley CA El Centro Arr #6 230 1.40

0 6.00

5.00

PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.13: 1979 El Centro Earthquake: Bonds Corner Record

2.

The 1985 Mexico City earthquake caused resonance at the characteristic site period of 2 seconds, as shown clearly in the spectra in Figure 9.14. An isolated structure on this type of site would be counter-effective and cause damaging motions in the structure.

1985 MEXICO CITY SCT1850919BT.T N90W

1985 MEXICO CITY SCT1850919BL.T S00E 1.00

1250

1.00

1000

0.80

1250

Acceleration

0.40

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Displacement 0.80

0 1.00

2.00

3.00

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PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.14: 1985 Mexico City Earthquake

3.

The 1989 Loma Prieta earthquake produced a number of records on both stiff and soft sites. Figure 9.15 shows a stiff site record. This record shows the characteristics of decreasing acceleration with period but the stronger component has a constant displacement for periods between 2 seconds and 4 seconds. Within this range, isolation system flexibility could be increased to reduce accelerations four-fold (from 0.4 to 0.1) with no penalty of increased displacements.

297

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Loma Prieta 1989 Hollister South & Pine Component 000 Deg 700 Acceleration

1.20

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ACCELERATION (g)

ACCELERATION (g)

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0 6.00

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Displacement

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Loma Prieta 1989 Hollister South & Pine Component 090 Deg 700

DISPLACEMENT (mm)

1.40

0 6.00

PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.15: 1989 Loma Prieta Earthquake

The 1992 Landers earthquake produced records with extreme short period spectral accelerations (Figure 9.16), exceeding 3g for the 5% damped spectra, and constant acceleration in the 2 second to 4 second range for the 270 component. For this type of record isolation would be very effective for short period buildings but the optimum isolation period would not exceed 2 seconds. For longer periods the displacement would increase for no benefit of reduced accelerations. 1992 Landers Earthquake Lucerene Valley 270 Degree Component 1800

1992 Landers Earthquake Lucerene Valley 000 Degree Component 3.00 1800

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Acceleration

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PERIOD (Seconds)

Figure 9.16: 1992 Landers Earthquake

5.

The Sepulveda VA record of the 1994 Northridge earthquake, Figure 9.17, produced very high short period spectral accelerations, exceeding 2.5g, but the 360 component also had a secondary peak at about 2 seconds. For this component, the displacement would increase extremely rapidly for an isolated period exceeding 2 seconds.

298

1994 Northridge st=LA Sepulveda V.A. 270 corrected

1994 Northridge st=LA Sepulveda V.A. 360 corrected 600

3.00

500

2.50

600

Acceleration

2.00

400

1.50

300

1.00

200

0.50

100

0.00 0.00

1.00

2.00

3.00

4.00

5.00

ACCELERATION (g)

ACCELERATION (g)

Acceleration DISPLACEMENT (mm)

Displacement

2.50

0 6.00

500

Displacement

2.00

400

1.50

300

1.00

200

0.50

100

0.00 0.00

1.00

2.00

3.00

4.00

5.00

DISPLACEMENT (mm)

3.00

0 6.00

PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.17: 1994 Northridge Earthquake

1994 NORTHRIDGE SYLMAR-COUNTY HOSP. PARKING LOT 90 Deg 900 Acceleration Displacement

ACCELERATION (g)

2.50

750

2.00

600

1.50

450

1.00

300

0.50

150

0.00 0.00

1.00

2.00

3.00

4.00

5.00

ACCELERATION (g)

3.00

3.00

1994 NORTHRIDGE SYLMAR-COUNTY HOSP. PARKING LOT 360 deg 900

2.50

750

2.00

600

1.50

450 Acceleration Displacement

1.00

300

0.50

0 6.00

0.00 0.00

DISPLACEMENT (mm)

The Sylmar County Hospital record, also from the 1994 Northridge earthquake (Figure 9.18) also produced short period spectral accelerations exceeding 2.5g for one component. This record was unusual in that both components produced very high spectral accelerations at longer periods, exceeding 0.5g for 2 second periods. An isolation system tailored for this earthquake would use an isolated period exceeding 3 seconds as beyond this point both displacements and accelerations decrease with increasing period.

DISPLACEMENT (mm)

6.

150

1.00

2.00

3.00

4.00

5.00

0 6.00

PERIOD (Seconds)

PERIOD (Seconds)

Figure 9.18: 1994 Northridge Earthquake

One common factor to all these earthquakes is that the particular characteristics of each earthquake suggest an optimum isolation system for that earthquake. However, an optimum system selected on the basis of one earthquake would almost certainly not be optimal for all, or any, of the other earthquakes.

299

Code requirements for time history selection require use of records appropriate to fault proximity and so often one or more records similar to those shown in Figure 9.13 to 9.18 will be used for a project. The manner of scaling specified by codes such as UBC and FEMA-356 also result in relatively large scaling factors. Naeim & Kelly [1999] discuss this in some detail. 9.3.3

Near Fault Effects

Near fault effects cause large velocity pulses close to the fault rupture. Effects are greatest within 1 km of the rupture but extend out to 10 km. The UBC requires that near fault effects be included by increasing the seismic loads by factors of up to 1.5, depending on the distance to the nearest active fault and the magnitude of earthquake the fault is capable of producing. The current edition of the UBC does not require that this effect be included in the design of non-isolated buildings. There has been some research in New Zealand on this effect and recent projects for essential buildings have included time histories reflecting near fault effects. Figure 9.19 shows one such record used for the Parliament project. Between 6 and 9 seconds relatively large accelerations are sustained for long periods of time, causing high velocities and displacements in structures in the medium period range of 1.5 to 3.0 seconds. This type of accelerogram will affect a wide range of structures, not just isolated buildings. 0.40 0.30 ACCELERATION (g)

0.20 0.10 0.00

-0.10

0

2

4

6

8

10

12

14

16

-0.20 El Centro, 1979 Earthquake : Bonds Corner 230 deg.

-0.30 -0.40 -0.50

TIME (Seconds) Figure 9.19: Acceleration Record With Near Fault Characteristics

9.3.4

Variations in Displacements

Figure 9.20 shows the variation in maximum displacements from 7 earthquakes each scaled according to UBC requirements for a site in California. Displacements range from 392 mm to 968 mm, with a mean of 692 mm. If at least 7 records are used, the UBC permits the mean value to be used to define the design quantities. The mean design displacement, 692 mm, is exceeded by 4 of the 7 earthquake records. These records, from Southern California, were selected because each contained near fault effects. Each has been scaled to the same amplitude at the isolated period. The scatter from these earthquakes is probably greater than would be obtained from similarly scaled records that do not include near fault effects.

300

Available options to the designer are: 1. Use the mean of 7 records, a displacement of 692 mm. 2. Select the three highest records and use the maximum response of these, 968 mm. 3. Select the three lowest records and use the maximum response of these, 585 mm.

1200

968

DISPLACEMENT (mm)

1000

846

811

839

800 692 585

600

407 400

392

Maximum Displacement 200

Mean Displacement

0 Hollister Lucerene

Sylmar

El Centro NewHall Supulveda

Yermo

Figure 9.10: Variation between Earthquakes It is difficult to rationalize a design decision where the majority of earthquakes will produce displacements greater than the design values. However, the requirements of any code which requires a minimum of 3 time histories could also be satisfied using the 3rd, 4th and 6th records from Figure 9.20, resulting in a design displacement of 585 mm as in option 3. above. There is clearly a need to develop specific requirements for time histories to ensure that anomalies do not occur and that the probability of maximum displacements being exceeded is not too high. One procedure, which has been used on several projects, is to use at least one frequency scaled earthquake in addition to the scaled, actual earthquakes. A frequency scaled record has the frequency content of the record altered so that it produces a spectrum which is a close match (usually within 5%) of the design spectrum at all periods. This ensures that the full frequency range of response is included in the analysis.

301

9.3.5

Time History Seismic Input

A major impediment to the implementation of seismic isolation is that the time history method is the only reliable method of accurately assessing performance but code requirements for selecting time histories result in much higher levels of input than alternative methods such as the response spectrum procedure. Overly conservative seismic design input for base isolation not only results in added costs but also degrades the performance at the more likely, lower levels of earthquake. All practical isolation systems must be targeted for optimum performance at a specified level of earthquake. This is almost always for the maximum considered earthquake as the displacements at this level must be controlled. This results in a non-optimum system for all lower levels of earthquake. Regardless of this, it is mandatory to use records scaled in accordance with the applicable code requirements. Wherever possible, a site specific seismic study by a seismological consultant should be used to define near fault effects and both the return period for earthquake magnitude and the probability of the site being subjected to near fault effects. It is also preferable that the seismologist provide appropriate time histories, with scaling factors, to use to represent both the DBE and MCE events. 9.3.6

Selecting and Scaling Records for Time History Analysis

As noted above, the best method of selecting time histories is to have the seismologist supply them. However, this option is not always available and, if not, some guidance can be obtained from codes as to means of selecting and scaling records. The UBC and FEMA-356 Guidelines are explicit and generally follow the same requirements. These sources require a minimum of three pairs of time history components. If seven or more pairs are used then the average results can be used for design else maximum values must be used. The records are required to have appropriate magnitudes, fault distances and source mechanisms for the site. Simulated time histories are permitted. The UBC provides an explicit method of scaling records: For each pair of horizontal components, the square root of the sum of the squares (SRSS) of the 5% damped spectrum shall be constructed. The motions shall be scaled such that the average value of the SRSS spectra does not fall below 1.3 times the 5% damped spectrum of the design basis earthquake by more than 10% for periods from 0.5TD to 1.25TM. In this definition, TD is the period at the design displacement (DBE) and TM the period at the maximum displacement (MCE). It is generally interpreted that average value of the SRSS is the average at each period over all records. In this case, the scaling factor for any particular record depends on the other records selected for the data set. The ATC-40 document provides 10 records identified as suitable candidates for sites distant from faults (Table 9.3) and 10 records for sites near to the fault (Table 9.4). In the absence of other records, these may be useful. 302

No. 1 2 3 4 5 6 7 8 9 10

M 7.1 6.5 6.6 6.6 7.1 7.1 7.5 7.5 6.7 6.7

Year 1949 1954 1971 1971 1989 1989 1992 1992 1994 1994

Earthquake Western Washington Eureka, CA San Fernando, CA San Fernando, CA Loma Prieta, CA Loma Prieta, CA Landers, CA Landers, CA Northridge, CA Northridge, CA

Station Station 325 Station 022 Station 241 Station 241 Hollister, Sth & Pine Gilroy #2 Yermo Joshua Tree Moorpark Century City LACC N

File wwash.1 eureka.9 sf241.2 sf458.10 holliste.5 gilroy#2.3 yermo.4 joshua.6 moorpark. 8 lacc_nor.7

Table 9.3: Records at Soil Sites > 10 km From Sources

No. 1 2 3 4 5 6 7 8 9 10

M 6.5 6.5 7.1 7.1 6.9 6.7 6.7 6.7 6.7 6.7

Year 1949 1954 1971 1971 1989 1989 1992 1992 1994 1994

Earthquake Imperial Valley, CA Imperial Valley, CA Loma Prieta, CA Loma Prieta, CA Cape Mendocino, CA Northridge, CA Northridge, CA Northridge, CA Northridge, CA Northridge, CA

Station El Centro Array 6 El Centro Array 7 Corralitos Capitola Petrolia Newhall Fire Station Sylmar Hospital Sylmar Converter Stat. Sylmar Converter St E Rinaldi Treatment Plant

File ecarr6.8 ecarr7.9 corralit.5 capitola.6 petrolia.1 0 newhall.7 sylmarh.4 sylmarc.2 sylmare.1 rinaldi.3

Table 9.4: Records at Soil Sites Near Sources

9.3.7

Selecting Records from a Set

Although the UBC and FEMA documents specify the end product of the scaling of earthquake records, they do not provide guidance in selecting particular records from a set of calculating scaling factors for the individual records. The recent revision to the New Zealand Loadings Code, NZS 1170, provides a procedure which can be adopted for other codes. In this procedure, there are two steps, scaling of individual records and then scaling of the family of records: 1.

Determine the record scale factor, k1, for each of the horizontal ground motion components where k1 = scale value which minimises in a least mean square sense the This can be function log(k1SAcomponent/SAtarget) over the period range of interest. implemented using design tools such as spreadsheets by computing the factor D1 as: D1 

1 ( 1.5  0.4 )T1



1.5T

[ log ( 0.4T

k1SA component SA target

303

) ] 2 dT

(9.1)

A solver is then used to select k1 so as to minimise D1. This is the scale factor for the particular record. 2.

The second step of is to ensure that the envelope of the scaled records exceeds the target spectrum. The procedure is to determine the record family scale factor, k2, which such that for every period in the period range of interest, the principal component of at least one record spectrum scaled by its record scale factor k1, exceeds the target spectrum.

When selecting a subset of records from a larger set, the value of D1 is calculated for all records and those producing the smallest values are used as the subset. The New Zealand code scales on the principal component of the record and applies the scaling factor to both components.

For UBC or FEMA scaling, SAcomponent  SA12  SA22 where

SA1 and SA2 are the two components of the individual earthquake record. SAtarget is then set at 1.3 times the design spectrum. 9.3.8

Comparison of Earthquake Scaling Factors

The FEMA and UBC documents specify a procedure for selecting scale factors for time histories which differs in two main respects from the procedure of NZS1170: 1.

The individual UBC scaling factors are based on the ratio of the SRSS of the two components to 1.3 C(T), rather then the ratio of the primary component to C(T) as for NZS1170.

2.

The UBC family scaling factor is calculated so that the average of the three records exceeds the target spectrum at each period point. The NZS1170 family scaling factor if selected so that at least one record exceeds the target.

The net effect of these two differences is that the UBC scaling factors resulting in a 15% higher spectral response than the NZS1170 factors, as shown in Table 9.5 for an isolated building with a 2 second period. The spectral displacement at the two second period is 469 mm, and this is approximately the isolation system displacement which would be determined from a response spectrum analysis. The time history analysis would produce displacements 12% higher (NZS 1170) or 29% higher (UBC). As the response spectrum and time history methods have the same acceptance criteria in the UBC, it is unlikely that the time history procedure would be used for projects evaluated to these guidelines.

Record Mexico, UNIO, La Union Michoacan (Mexico) 1985 S00E Iran, Tabas Tabas (Iran) 1978 N74E Iran, Tabas Tabas (Iran) 1978 N90E Spectral Acceleration at 2.0 seconds (C(T) = 0.48) Spectral Displacement at 2.0 seconds (C(T) = 469 mm) Table 9.5: Comparison of Scaling Factors

304

NZS 1170 4.01 0.96 1.01 0.54 526

UBC 5.42 1.03 0.96 0.62 605

4.0 C(T) NZ Scaling UBC Scaling

Acceleration (g)

3.5 3.0 2.5 2.0

Isolated Period 2 seconds

1.5 1.0 0.5 0.0 0.0

1.0

2.0

3.0

4.0

Period (Seconds) Figure 9.21: 5% Damped Acceleration Spectra

1200

Acceleration (g)

1000

C(T) NZ Scaling UBC Scaling

800 600 400

Isolated Period 2 seconds

200 0 0.00

1.00

2.00

3.00

Period (Seconds) Figure 9.22: 5% Damped Displacement Spectra

305

4.00

9.4

DETAILED SYSTEM ANALYSIS

The design procedure described elsewhere in this book is based on the response of the isolation system alone, without accounting for the flexibility of the structure itself. The flexibility of the structure above the bearings (or the substructure below bridge bearings) will modify the response because some of the displacement will take place in the structure. The extent of this variation from the assumed response will depend on the flexibility of the structure or substructure relative to the isolation system. It is possible to modify the design procedure to take account of substructure flexibility, as for bridge structures. In this modification, the stiffness of the bearings is calculated as the combined stiffness of the isolators and the bent acting in series. However, most design offices have computers with structural analysis programs and it is generally more efficient to include structural flexibility at the analysis phase rather than as part of the design process. There is a hierarchy of analysis procedures, as listed in Table 9.6 in order of complexity. Each procedure has its role in the design and evaluation process. The analysis options are not mutually exclusive and in fact all methods are usually performed in sequence up to the most complex procedure appropriate for a project. In this way, each procedure provides benchmark results to assess the reasonableness of the results from the next, more complex procedure. 1. SINGLE DEGREE OF FREEDOM NONLINEAR Isolation System Design 2. PLANE FRAME / PLANE WALL 2D BRIDGE MODELS NONLINEAR Design Level vs. Damage Studies Effect of Bent Flexibility 3. THREE DIMENSIONAL LINEAR Member Design Forces 4. THREE DIMENSIONAL LINEAR SUPERSTRUCTURE NONLINEAR ISOLATORS Isolation System Properties 5. THREE DIMENSIONAL NONLINEAR SUPERSTRUCTURE NONLINEAR ISOLATORS Isolation System and Structure Performance

Table 9.6: Analysis of Isolated Structures

306

9.4.1

Single Degree-of-Freedom Model

A simple model is often used at the preliminary design phase, especially for hybrid systems. The superstructure is assumed rigid and the total weight modeled as a single mass. A number of elements in parallel are then used to model the isolators. For example, all elastomeric bearings are represented as a single elastic element, the lead cores as an elasto-plastic element and the sliding bearings as a single friction element. Viscous damping would be included in the elastic element but not the yielding elements. This model provides maximum isolator displacements and forces and acts as a check on the design procedure used. This model will produce results equivalent to those produced by the design procedure but with more accuracy in two areas: 1. The input for this model is a series of time histories and so this procedure quantifies the difference in results that will be produced by time history analysis compared to the response spectrum analysis method used in the design procedure. 2. The mass can be excited by two components of earthquake simultaneously, which will provide displacements and base shear forces which incorporate the interaction of isolator yield in the two directions. A number of programs are available for this type of analysis, including NONLIN or DRAIN-2D for single component analysis and 3D-BASIS, SAP2000, ETABS or ANSR for concurrent analyses. 9.4.2

Two Dimensional Nonlinear Model

Two-dimensional models of a single representative frame or shear wall from the building are an effective way of assessing the effects of superstructure / substructure response and yielding. The structural elements are represented as bilinear yielding elements and the isolators as for the single degree of freedom model. For bridge structures, two separate 2D models are usually developed, one to model longitudinal response and the other to model transverse response. The DRAIN2D2 program is typical of the type used for these analyses. This type of analysis is rarely used for buildings as computer hardware is such that three-dimensional non-linear analyses are practical in almost all cases. It is still used for bridges as the final analyses for bridges can be performed separately for the longitudinal and transverse directions. 9.4.3

Three dimensional Equivalent Linear Model

A linear elastic model using a building analysis program such as ETABS (or STRUDL for bridges) is sufficient for final design for some structures. A response spectrum analysis is performed to obtain earthquake response. In this type of analysis the isolators are represented as short column or bearing elements with properties selected to provide the effective stiffness of the isolators. Damping is incorporated by reducing the response spectrum in the range of isolated periods by the B Factor. As described earlier, there are some doubts about a possible under-estimation of the overturning moments for most non-linear isolation systems if this procedure is used. 307

Pending resolution of this issue, it seems advisable that a time history analysis always be performed on this model. Note that in ETABS and other programs the same model can be used for both response spectrum and time history analyses. 9.4.4

Three Dimensional Model - Elastic Superstructure, Yielding Isolators

This type of model is appropriate where little yielding is expected above or below the isolators. Some programs, for example 3D-BASIS, represent the building as a "super-element" where the full linear elastic model of the fixed base structure is used to reduce the superstructure to an element with three degrees of freedom per floor. This type of analysis provides isolator displacements directly and load vectors of superstructure forces. The critical load vectors are applied back to the linear elastic model to obtain design forces for the superstructure. As the isolators are modeled as yielding elements the response spectrum method cannot be used and so a time history analysis must be performed. ETABS has non-linear isolator elements and it is recommended that this option be used for all structures. 9.4.5

Fully Nonlinear Three Dimensional Model

Full non-linear structural models have become more practical as computer hardware in design offices has improved although they remain time consuming and are generally only practical for special structures. The Museum of New Zealand nonlinear model with 2250 degrees of freedom and over 1500 yielding elements was analyzed on MS-DOS 486 computers and provided full details of isolator forces and deformations, structural plastic rotations, drifts, floor accelerations and in-structure response spectra. Current desktop computers are capable of analyzing models in excess of 20,000 degrees of freedom. 9.4.6

Device Modeling

For nonlinear analysis the yield function of the devices is modeled explicitly. The form of this function for a particular element depends on the device modeled: 1. HDR bearings are modeled as either a linear elastic model with viscous damping included or with the hysteretic loop directly specified. 2. LRBs are modeled as either two separate components (rubber elastic, lead core elastoplastic) or as a single bi-linear element. 3. For sliding bearings, an elastic-perfectly plastic element with a high initial stiffness and a yield level which is a function of vertical pressure and velocity. If uplift can occur this is combined with a gap element so that the shear force is zero when uplift occurs. The modeling must be such that damping is not included twice, with both viscous and hysteretic formulations. This is why LRBs are often better modeled as two components. Element damping is applied to the rubber component, which has some associated viscous damping, but not to the lead component. For the Museum of New Zealand, a series of Teflon material tests were used to develop the dependence on pressure and velocity of the coefficient of friction. This was used to calibrate an ANSR-II model. The model was then used to correlate the results of shaking table tests for a concrete block mounted on Teflon pads. 308

ETABS has a sliding element which incorporates velocity effects and can also be used for curved sliding systems. 9.4.7

ETABS Analysis for Buildings

Versions 6 and above of the ETABS program have the capability of modeling a base isolated building supported on a variety of devices. The ETABS manual provides guidance for developing an isolated model. An isolation design spreadsheet, such as the example provided with this book, can be used to calculate properties to use for the ETABS analysis. This section describes the basis for the calculation of these properties and procedures to analyze the isolated building using ETABS. Isolation System Properties The devices isolation system designs will most commonly be one or more of lead rubber bearings (LRB), elastomeric bearings (ELAST), high damping rubber bearings (HDR) or Teflon flat or curved sliding bearings (PTFE and FPS). These are modeled as springs in ETABS. The appropriate spring types are as follows: Lead Rubber Bearings (LRB) LRBs are modeled as an equivalent bi-linear hysteresis loop with properties calculated from the lead yield stress and the elastomeric bearing stiffness. This is modeled as type ISOLATOR1 in ETABS. Elastomeric Bearings (ELAST) Plain elastomeric bearings are modeled as type LINEAR. Sliding Bearings (PTFE and FPS) Sliding bearings are modeled as type ISOLATOR2 with properties for the coefficient of friction at slow and fast velocities as developed from tests. The coefficient of friction is a function of pressure on the bearing as well as velocity. ETABS incorporates the velocity dependence but not the pressure dependence. Table 9.7 lists the measured coefficients of friction for a series of tests performed at the State University of New York, Buffalo. These are for unfilled Teflon (UF) and 15% and 25% glass filled (15GF and 25GF respectively). Tests on the UF material were performed both parallel to the lay (P) and perpendicular to the lay (T).

309

Pressure

Type of Teflon

Sliding Direction

psi

MPa

UF UF UF UF 15GF 15GF 15GF 15GF 25GF 25GF 25GF 25GF UF UF UF UF

P P P P P P P P P P P P T T T T

1000 2000 3000 6500 1000 2000 3000 6500 1000 2000 3000 6500 1000 2000 3000 6500

7 14 21 45 7 14 21 45 7 14 21 45 7 14 21 45

High Low Exponent Velocity Velocity a Coefficient Coefficient 0.027 0.018 0.015 0.009 0.040 0.043 0.043 0.022 0.055 0.049 0.044 0.032 0.024 0.017 0.029 0.011

0.119 0.087 0.070 0.057 0.146 0.101 0.085 0.053 0.132 0.112 0.096 0.059 0.142 0.105 0.082 0.055

0.60 0.60 0.80 0.50 0.60 0.55 0.60 0.70 0.65 0.65 0.32 0.90 0.45 0.70 0.55 0.45

Table 9.7: PTFE Properties

Table 9.7 shows considerable variations with pressure, velocity and material. Most isolation systems use unfilled Teflon and so only the UF values are of interest. From Table 9.7, reasonable analysis values for unfilled Teflon would be as listed in Table 9.8: Vertical Pressure on PTFE < 5 MPa 5 - 15 MPa > 15 MPa

Friction Coefficient at Low Velocity 0.03 0.025 0.02

Friction Coefficient at High Velocity 0.14 0.10 0.08

Coefficient Controlling Variation 0.55 0.65 0.60

Table 9.8: Analysis Values for PTFE

For curved slider bearings (FPS) the radius of curvature is also specified. To use this type of isolator, it is recommended the supplier be consulted for appropriate friction values. High Damping Rubber Bearings (HDR) Although the elastomer used for these bearings is termed "high damping" the major energy dissipation mechanism of the elastomer is hysteretic rather than viscous, that is, the force deflection curves form a nonlinear hysteresis. The UBC code provides a procedure for converting the area under the hysteresis loop to an equivalent viscous damping ratio to be used for equivalent linear analysis. For nonlinear analysis it is more accurate to model the force deflection curve directly and so include the hysteretic damping implicitly. This avoids the approximations in converting a hysteresis area to viscous damping. 310

The second data line for the ETABS input file contains the bilinear properties for a nonlinear time history analysis. The procedure for deriving these properties is based on the following methodology: 1.

The effective stiffness at the design displacement is known from the design procedure and the stiffness properties of the elastomer. This provides the force in the bearing at the design displacement.

2.

An equivalent "yield" strain is defined in the elastomer. displacement.

3.

From the elastomer shear modulus at the assumed "yield" strain the yield force can be calculated and the hysteresis loop constructed.

4.

The area of this hysteresis loop is computed and, from this and the effective stiffness, the equivalent viscous damping is calculated.

5.

If necessary, the assumed "yield" strain is adjusted until the equivalent viscous damping at maximum displacement equals the damping provided by the elastomer at that strain level.

This defines a "yield"

Procedures for Analysis The ETABS model can be analyzed using a number of procedures, in increasing order of complexity: 1.

Equivalent static loads.

2.

Linear response spectrum analysis.

3.

Linear Time History Analysis.

4.

Nonlinear Time History Analysis.

The UBC provides requirements on the minimum level of analysis required depending on building type and seismicity: The equivalent static analysis is limited to small, regular buildings and would almost never be sufficient for isolation projects. A linear response spectrum analysis is the most common type of analysis used. sufficient for almost all isolation systems based on LRB and/or HDR bearings.

This is

The response spectrum analysis procedure uses the effective stiffness of the bearings, defined as the force in the bearing divided by the displacement. Therefore, it is iterative in that, if the analysis produces a displacement which varies from that assumed to calculate stiffness properties, the effective stiffness must be adjusted and the analysis repeated.

311

In practice, the single mass approximation used for system design usually gives a good estimate of displacement and multiple analyses are not required. However, if the ETABS analyses produce center of mass displacements above the isolators which are significantly different from the design procedure values (variation more than about 10%) then the properties should be recalculated. The effective stiffness at a specified displacement, , can be calculated from the data on the second line of the ISOLATOR1 input as:

KE2 

FY2(1 RK2)  K2.RK2 

(9.2)

The effective damping can be calculated as:

DE2 

2.FY2.(1 RK2)(   .KE2. 2

FY2 ) K2

(9.3)

This is the total damping - as discussed below, this must be reduced by the structural damping, typically 0.05, specified in ETABS. Linear time history analysis provides little more information than the response spectrum analysis for a much greater degree of effort and so is rarely used. Nonlinear time history analysis is required for (1) systems on very soft soil (2) systems without a restoring force (e.g. sliding systems) (3) velocity dependent systems and (4) systems with limited displacement capability. In practice, nonlinear time history has been used in many projects even where not explicitly required by the UBC. This is largely because most isolated projects have been especially valuable or complex buildings. As discussed earlier, there are some concerns about the accuracy of equivalent stiffness analysis results. Input Response Spectra The response spectrum analysis calculates the response of each mode from the spectral ordinate at that period. For the isolated modes the damping must include the equivalent viscous damping of LRB and HDR bearings. Therefore, a series of response spectra must be input covering the full range of damping values for all modes. These spectra are calculated by dividing the spectral values by the B factor for each damping factor, as specified in the UBC:

B

50% 2.0

The time history solution applies the modal damping to the response calculated for each mode during the explicit integration. Therefore, the input time history does not need to be modified to reflect damping.

312

Damping The ETABS program is relatively straightforward for modeling stiffness properties of the isolators, both for effective stiffness analysis and nonlinear time history analysis. However, the manner in which damping is applied is more complex. The aim for most analyses is to use 5% damping for the structural modes, as is assumed in the codes, but to use only the damping provided by the isolation system in the isolated modes. The procedure used to implement this in each type of analysis is as described below. Response Spectrum Analysis For the response spectrum analysis, a value of 0.05 is specified for DAMP in the Lateral Dynamic Spectrum Data section. This applies damping of 5% to all modes, including the isolated modes. To avoid including this damping twice, the value of both DE2 and DE3 in the Spring Properties section is reduced by 0.05. The example spreadsheet calculations include this reduction. Linear Time History Analysis The linear time history analysis uses the effective stiffness and damping values as for the response spectrum analysis and so the same procedure for specifying damping as used above is applicable, that is, reducing DE2 and DE3 by 0.05. An alternative method for specifying damping is available in time history analysis by providing data lines to override the modal damping value specified. In this procedure, NDAMP is specified as 3 in the Lateral Dynamic Time History Data section and modes 1 to 3 are specified to have 0.0 damping. Nonlinear Time History Analysis For nonlinear time history analysis the hysteretic damping is modeled explicitly and the values of DE2 and DE3 are not used. The only procedure available to avoid "doubling up" on damping is to specify viscous damping as 0.0 in the first three modes, the second method listed above for linear time history analysis. This slightly underestimates total damping. The procedures used to specify damping for the different analysis types are generally based on an assumption of hysteretic damping only in the isolators, with no viscous damping. This is a conservative approach. From tests on these bearings at different frequencies, the damping may be increased by about 20% by viscous effects. In some types of analysis, this increase can be incorporated by increasing the size of the hysteresis loop. 9.4.8

Concurrency Effects

The design procedure for isolation systems is based on a single degree of freedom approximation which assumes a constant direction of earthquake loads. The evaluation of the structural system requires that earthquake motions be applied concurrently along both horizontal axes. 313

For the response spectrum method of analysis UBC requires that the spectrum be applied 100% along one direction and 30% of the ground motion along the orthogonal axis. The time history method of analysis requires that two horizontal components of each earthquake record be applied simultaneously. The yield function for bi-linear systems such as lead rubber bearings is based on a circular interaction formula:

Vax2  Vay2 Vy

 1.0

(9.4)

where Vax and Vay are the applied shears along the two horizontal axes and Vy is the yield strength of the isolation system. If concurrent shear forces are being applied along each axis then the effective yield level along either axis will be less than the design value based on non-concurrent seismic loads. For the case where equal shear forces are applied in both directions simultaneously, the shear force along each axis will be equal to

VY 2

.

The reduced yield force along a particular direction will result in the equivalent viscous damping being less than the value calculated from the design procedure. This will produce a performance different from that calculated. In some circumstances, it may be desirable to increase the yield level so that under concurrent action the response will closer match that calculated from non-concurrency. As an example of the effects of concurrency, an isolated building was analyzed for seven near fault earthquake records, each with two horizontal components scaled by the same factor. Maximum displacements and base shear coefficients were obtained for three cases: 1. The isolation system as designed, maximum vector response when both components were applied simultaneously. 2. The isolation system as designed, maximum vector response of the components applied individually. 3. The isolation system with the yield level increased by 2 , then evaluated as for 1. above, the maximum vector response with both components applied simultaneously. Figures 9.23 and 9.24 plot the resulting displacements and shear coefficients respectively for the three cases for each earthquake. Also plotted are the mean results, which would be used for design if 7 earthquakes were used for analysis.

314

VECTOR DISPLACEMENT (mm)

1000 Concurrent

900

Unidirectional

Concurrent Incr Fy

800 700 600 500 400 300 200 100 MEAN

YER

SEP

NEW

ELC

SYL

LUC

HOL

0

Figure 9.11: Displacements with Concurrent Loads

The results show that there is a consistent effect of concurrent versus non-concurrent applications of the two earthquake components in that the concurrent components always produced higher displacements and higher shear forces than the non-concurrent case. However, the difference was very much a function of the earthquake records. Displacements were higher by from 2% to 57% and shears higher by from 1% to 38%. The average displacement was 15% higher, the average shear 11% higher.

0.50 Concurrent

Unidirectional

Concurrent Incr Fy

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05

Figure 9.12: Shears with Concurrent Loads

315

MEAN

YER

SEP

NEW

ELC

SYL

LUC

0.00 HOL

BASE SHEAR COEFFICIENT

0.45

Increasing the yield strength of the isolation system generally, but not always, reduced concurrent displacements and shears to values less than the non-concurrent values with the lower yield strength. In this example, an increase in yield level would reduce the mean displacement to less than the non-concurrent value and reduce the base shear to only slightly more than the non-concurrent value.

Concurrent Unidirectional Concurrent with Increased Fy

Mean Mean Displacement Base Shear (mm) Coefficient 706 0.320 615 0.289 570 0.292

Although in this example an increase in yield level was effective in counteracting concurrency effects the results were not consistent enough to demonstrate that this will always be an effective strategy. It is recommended that the effects of concurrency be assessed on a project specific basis to check whether an increase in yield level is justified. An increase in yield level may require higher design forces for the structure above the isolation system if design is governed by the requirement for design base shear being at least 1.5 times the yield level of the system. If design is governed by this criterion then it may be preferable to accept higher displacements and shears from concurrency effects rather than re-design for a higher yield level.

9.5

CONNECTION DESIGN

9.5.1

Elastomeric Based Isolators

Early seismic isolation bearings used load plates bolted to a steel plate bonded internally in the bearing. Manufacturing technology has now improved such that the majority of seismic isolation bearings are manufactured with flange plates, or load plates, bonded to the bearing top and bottom during manufacture. These plates are larger in plan dimension than the isolator and are used to connect the bearing to the foundation below and the structure above. The load plates may be circular, square or rectangular, depending on project requirements. The amount of overhang depends on the bolt sizes and the seismic displacement. The bolts must be located far enough from the isolator such that they do not damage the cover rubber during maximum seismic displacements. Square load plates allow a smaller plan dimension than circular plates and so are often used for this reason. The isolators are installed between the foundation and the structure, as shown conceptually in Figure 9.25. The connection design must ensure that the maximum forces are safely transferred from the foundation through the bearing to the structure above.

316

Top Fixing Plate with Couplers and HD Bolts to suit

Concrete Floor Beams

Lead Rubber Bearing Pressure Grout under Bottom Fixing Plate to allow for levelling

Bottom Fixing Plate with Concrete Foundation Beams and Pads

Couplers and HB Bolts to suit

Figure 9.13: Typical Installation in New Building

Design Basis The connection of the isolation bearing to a structure must transmit shear forces, vertical loads and bending moments. Bending moments are due to primary (VH) and secondary (P) effects (Figure 9.26). Design for shear is relatively straightforward. Design for bending moments is complicated by the unknown shape of the compressive block, especially under extreme displacements. It is recognized that the design approach used here is simplistic and not a true representation of the actual stress conditions at the connection interface. However, the procedure has been shown to be conservative by prototype testing which has used less bolts, and thinner plates, than would be required by the application of this procedure.



P

V H V

Figure 9.14: Forces on Bearing in Deformed Shape

317

Bearing design includes the mounting plate and mounting bolts. The design basis depends on project specifications, but generally is either AASHTO allowable stress values, with a 4/3 stress increase factor for seismic loads, or AISC requirements.

Design Actions Connections are designed for two conditions, (1) maximum vertical load and (2) minimum vertical load, each of which is concurrent with the maximum earthquake displacement and shear force. The bearing is bolted to the structure top and bottom and so acts as a fixed end column for obtaining design moments. Figure 9.27 shows how the actions shown in Figure 9.26 may be transformed to an equivalent column on the centerline of the bearing.

P

M V M

Figure 9.15: Equivalent Column Forces

The total moment due to applied shear forces, VH, plus eccentricity, P, is resisted by equal moments at the top and bottom of the isolator. These design moments are equal to:

1 M  (VH  P) 2

(9.5)

Connection Bolt Design The design procedure adopted for the mounting plate connection is based on the simplified condition shown in Figure 9.28, where the total axial load and moment is resisted by the bolt group. In Figure 9.28, the area used to calculate P/A is the total area of all bolts and the section modulus used to calculate M/S is the section modulus of all bolts. Figure 9.28 is for a circular load plate. A similar approach is used for other shapes.

318

VERTICAL LOAD STRESS = P / A

COMPRESSION TENSION

BENDING MOMENT STRESS = M / S

COMPRESSION TENSION

TOTAL STRESS = VERTICAL + BENDING

COMPRESSION TENSION

Figure 9.16: Assumed Bolt Force Distribution

It is recognized that in reality the compression forces will be resisted by compressive stresses in the plate rather than by the bolts. However, the bearing stiffness to calculate the modular ratio, and so the neutral axis position, is unknown. This is why the bolt group assumption is made. This assumption is conservative as it underestimates the actual section modulus and so is an upper bound of bolt tension. The procedure for bolt design is: 1. Calculate the shear force per bolt as V/n, where n is the number of bolts. 2. Calculate the axial load per bolt as P/A 3. Calculate the tension per bolt due to the moment as M/S where S is the section modulus of the bolt group. 4. Calculate the net tension per bolt as P/A – M/S 5. Check the bolt for combined shear plus tension. This is done for maximum and minimum vertical loads.

319

Load Plate Design For a circular load plate, the assumed force distribution on which load plate calculations are based is shown in Figure 9.29. Bending is assumed to be critical in an outstanding segment on the tension side of the bearing. The chord defining the segment is assumed to be tangent to the side of the bearing. This segment is loaded by three bolts in the example displayed in Figure 9.29. Conservatively, it is assumed that all bolts (three in this example) have the maximum tension force and also that all three bolts have the lever arm of the furthest bolt.

RISE b

RADIUS r CHORD c

DISTANCE TO BOLT 1

COMPRESSION

TENSION

Figure 9.17: Circular Load Plate

The design procedure adopted for a square load plate connection is based on the condition shown in Figure 9.30. Loading is assumed along the direction of the diagonal as this is the most critical for the bolt layout used with this type of load plate. 320

Axis of Bending Critical Section for Cantilever Dim 'X'

150 Typ. (6")

60 Typ. (2 1/2")

Dim 'Y'

Isolator Diameter

Load Plate Dimension

Figure 9.18 Square Load Plate

9.5.2

Sliding Isolators

For sliding isolators the eccentricity of the load at maximum displacements depends on the orientation of the bearing. If the slide plate is at the top then under maximum displacements the vertical load will apply a P- moment which must be resisted by the structural system above the isolators. If the slide plate is at the bottom then the eccentricity will load the foundation below the isolator but will not cause moments above. For this reason, most seismic applications of sliding isolators are more effective if the slide plate in located at the bottom. Most sliding bearings are designed with a low coefficient of friction at the sliding interface. In theory, they do not require any shear connection. The friction at the interface of the bearing to the structure above and to the foundation below, usually steel on concrete will have a higher coefficient of friction and so slip will not occur. In practice, bolts are usually used at each corner of the slide plate and the sliding component is bolted to the structure above, also usually with four bolts. Most types of sliding bearings, such as pot bearings and friction pendulum bearings, are proprietary items and the supplier will provide connection hardware as part of supply. 321

9.5.3

Installation Examples

Figure 9.31 to 9.36 are example installation details which have been used on completed isolation projects. These include both new and retrofit projects. Although these details cannot be used directly for other projects, they provide an indication of installation methods and the extent of strengthening associated with installation.

Figure 9.19: Example Installation: New Construction

322

Figure 9.20 Example Installation: Existing Masonry Wall

323

Figure 9.21: Example Installation: Existing Column

324

Figure 9.22: Example Installation: Existing Masonry Wall

325

Figure 9.23: Example Installation: Steel Column

326

Figure 9.24: Example Installation: Steel Energy Dissipator

9.6

STRUCTURAL DESIGN

9.6.1

Design Concepts

The isolation system design and evaluation procedures produce the maximum base shears, displacements and structural forces for each level of earthquake, usually the DBE and MCE. These represent the maximum elastic earthquake forces that will be transmitted through the isolation system to the structure above. Even though isolated buildings have lower seismic loads than non-isolated buildings, it is still not generally cost effective to design for elastic performance at the MCE level and sometimes yielding may be permitted at the DBE level. Most building isolation projects have been designed elastically to the DBE level of loading with some ductility demand at the MCE level. This is because of the nature of buildings isolated so far, which have been either older buildings with limited ductility or buildings providing essential services where a low probability of damage is required. For new buildings in the ordinary category, design forces are usually based on the DBE level of load reduced to account for ductility in the structural system. This is the approach taken by the UBC for new buildings. An isolated building, if designed elastically to the DBE, will likely have higher design forces than a ductile, non-isolated building which would be designed for forces reduced by ductility factors of 6 or more. These higher forces, plus the cost of the isolation system, will impose a significant first cost penalty on the isolated building. 327

Total life cycle costs, incorporating costs of earthquake damage over the life of the building, will usually favor the isolated building in high seismic regions. However, life cycle cost analysis is rare for non-essential buildings and few owners are prepared to pay the added first cost. The UBC addresses this issue by permitting the structural system of an isolated building to be designed as ductile, although the ductility factor is less than one-half that specified for a nonisolated building. This provides some added measure of protection while generally reducing design forces compared to an equivalent non-isolated building. 9.6.2

UBC Requirements

The UBC requirements for the design of base isolated buildings differ from those for nonisolated buildings in three main respects: 1. The importance factor I, for seismic isolated buildings is taken as 1.0 regardless of occupancy. For non-isolated buildings I = 1.25 for essential and hazardous facilities. As discussed later, a limitation on structural design forces to the fixed base values does indirectly include I in the derivation of design forces. 2. The numerical coefficient, R, which represents global ductility, is different for isolated and non-isolated buildings. 3. For isolated buildings there are different design force levels for elements above and elements below the isolation interface. Elements below the Isolation System The isolation system, the foundation and all structural elements below the isolation system are to be designed for a force equal to:

V B  k D max DD

(9.6)

Where kDmax is the maximum effective stiffness of the isolation system at the design displacement at the center of mass, DD. All provisions for non-isolated structures are used to design for this force. In simple terms, this requires all elements below the isolators to be designed elastically for the maximum force that is transmitted through the isolation system at the design level earthquake. One of the more critical elements governed by elastic design is the total moment generated by the shear force in the isolation system plus the P- moment. As discussed previously, the moment at the top and bottom of an elastomeric type isolation bearing is:

1 M  (VB H  PDD ) 2

(9.7)

where H is the total height of the bearing and P the vertical load concurrent with VB. The structure below and above the bearing must be designed for this moment. For some types of isolators, for example sliders, the moment at the location of the slider plate will be PDD and the moment at the fixed end will be VH.

328

Elements Above the Isolation System The structure above the isolators is designed for a minimum shear force, VS, using all the provisions for non-isolated structures where:

VS 

k D max D D RI

(9.8)

This is the elastic force in the isolation system, as used for elements below the isolators, reduced by a factor RI that accounts for ductility in the structure. Table 9.9 lists values of RI for some of the structures included in UBC. For comparison the equivalent ductility factor used for a non-isolated building, R, is also listed in Table 12-1. UBC includes other structural types not included in this table so the code should be consulted for structural systems not listed in Table 12-1. All systems included in Table 9.9 are permitted in all seismic zones. The values of RI are always less than R, sometimes by a large margin. The reason for this is to avoid high ductility in the structure above the isolation system as the period of the yielded structure may degrade and interact with that of the isolation system. Structural System Bearing Wall System Building Frame System

Moment Resisting Frame System

Dual Systems

Cantilever Column Buildings

Lateral Force Resisting System

Concrete Shear Walls Masonry Shear Walls Steel Eccentrically Braced Frame (EBF) Concrete Shear Walls Masonry Shear Walls Ordinary Steel Braced Frame Special Steel Concentric Braced Frame Special Moment Resisting Frame (SMRF) Steel Concrete Intermediate Moment Resisting Frame (IMRF) Concrete Ordinary Moment Resisting Frame (OMRF) Steel Shear Walls Concrete with SMRF Concrete with steel OMRF Masonry with SMRF Masonry with Steel OMRF Steel EBF With Steel SMRF With Steel OMRF Ordinary braced frames Steel with steel SMRF Steel with steel OMRF Special Concentric Braced Frame Steel with steel SMRF Steel with steel OMRF Cantilevered column elements

Fixed Base R 4.5 4.5 7.0 5.5 5.5 5.6 6.4

Isolated

8.5 8.5

2.0 2.0

5.5

2.0

4.5

2.0

8.5 4.2 5.5 4.2

2.0 2.0 2.0 2.0

8.4 4.2

2.0 2.0

6.5 4.2

2.0 2.0

7.5 4.2 2.2

2.0 2.0 1.4

Table 9.9: Structural Systems above the Isolation Interface

329

RI 2.0 2.0 2.0 2.0 2.0 1.6 2.0

There are design economies to be gained by selecting the appropriate structural system. For example, for a non-isolated building the design forces for a special moment resisting steel frame are only about 53% of the design forces for an ordinary steel moment resisting frame. However, for an isolated moment frame the design force is the same regardless of type. In the latter case, there is no benefit for incurring the extra costs for a special frame and so an ordinary frame could be used. Care needs to be exercised with this approach because, as discussed later, there may be some penalties in structural design forces if the ratio of R/RI is low. Table 9.9 also shows that some types of building are more suited to isolation, in terms of reduction in design forces, than others. For bearing wall systems the isolation system needs to reduce response by a factor of only 4.5 / 2 = 2.25 or more to provide a net benefit in design forces. On the other hand, for an eccentrically braced frame the isolation system needs to provide a reduction by a factor of 7.0 / 2.0 = 3.5 before any benefits are obtained, a 55% higher reduction. The value of VS calculated as above is not to be taken as lower than any of: 1. The lateral seismic force for a fixed base structure of the same weight, W, and a period equal to the isolated period, TD. 2. The base shear corresponding to the design wind load. 3. The lateral force required to fully activate the isolation system factored by 1.5 (e.g. 1½ times the yield level of a softening system or static friction level of a sliding system). In many systems one of these lower limits on VS may apply and this will influence the design of the isolation system. Fixed Base Structure Shear In general terms, the base shear coefficient for a fixed base structure is:

C

CV I RT

(9.9)

and for an isolated structure

CI 

CVD RI BT

(9.10)

There is a change in nomenclature in the two sections and in fact CV = CVD and so to meet the requirements of Criterion 1 above, CI  C, the two equations can be combined to provide:

B

R RI I

(9.11)

Therefore, the limitation that forces be not lower than the fixed base shear for a building of similar period effectively limits the amount of damping in the isolation system, measured by B, which can be used to reduce structure design forces. The range of R/RI (Table 9.9) is from 1.57 to 4.25. Figure 9.37 shows the limitation on the damping that can be used to derive structure design forces for this range of factors.

330

Maximum Damping

60% 50% 40% 30% I=1 I=1.25

20% 10% 0% 1.50

1.75

2.00

2.25

2.50

2.75

3.00

Ratio R / RI Figure 9.25: Limitation on B

Most systems target 15% to 35% equivalent damping at the design basis earthquake level. As seen from Figure 9.37, this damping may not be fully used to reduce design forces where the ratio of R/RI is less than about 1.8, or less than 2.2 for a structure with an importance factor I = 1.25. This limitation on design base shears will generally only apply when you have a structure with a relatively non-ductile lateral load system (low R) and/or an importance factor greater than 1.0. Design Wind Load Most isolation systems are installed in relatively heavy buildings because isolation is most effective for high mass structures. The yield level selected for optimum damping, usually 5% to 15% of the weight of a structure, is generally much higher than the wind load, which is usually less than 2% of the weight. Because the isolation system yield level is always set higher than the wind load, then the third criterion discussed below, will govern rather than wind. Factored Yield Level The requirement that the design lateral force be at least 1½ times the yield force will govern in many isolation designs and will be a factor in selection of the isolator properties. High yield forces are used to increase the amount of damping in a system to control displacements. Generally, the higher the seismic load and the softer the soil type the higher the optimum yield level. Design is often a process of adjusting the yield level (for example, lead core size in LRBs) until the value of VS calculated from the isolation system performance is approximately equal to 1.5Fy. 331

The drift limitations for isolated structures may also limit the design of the structural system: Response Spectrum Analysis   0.015 / RI Time History Analysis   0.020 / RI These are more restrictive than for non-isolated buildings where the limits are: Period < 0.7 seconds Period  0.7 seconds

  0.025 / 0.7R   0.020 / 0.7R

Although the UBC is not specific in this respect, it can probably be assumed that the value of RI can be lower but not greater than the values specified in Table 9.9 above. If one of the three UBC lower limits applies to the design lateral force for the structure then the actual value of RI which corresponds to this force should be calculated. This will affect the calculation of the drift limit.

9.6.3

MCE Level of Earthquake

The UBC defines a total design displacement, DTD, under the design basis earthquake (DBE) and a total maximum displacement, DTM, under the maximum capable earthquake (MCE). The vertical load-carrying elements of the isolation system are required to be stable for the MCE displacements. The MCE displacements also define the minimum separations between the building and surrounding retaining walls or other fixed obstructions. There are no requirements related to the MCE level of load for design of the structural elements above or below the isolation interface. Presumably, it is assumed that the elastic design of elements below the isolation system produces sufficient over strength for MCE loads and that the limitations on RI provide sufficient ductility above the isolation system for MCE loads.

9.6.4

Non-Structural Components

The UBC requires components to be designed to resist seismic forces equal to the maximum dynamic response of the element or component under consideration but also allows design to be based on the requirements for non-isolated structures. For components, there are three aspects of the dynamic response which define the maximum force: 1. The maximum acceleration at the location of the component. UBC defines this for nonisolated components as a function of the ground acceleration, Ca, and the height of the component, hx, relative to the height of the structure, hr:

C  C a (1  3

hx ) hr

(9.12)

2. Component amplification factor, which defines the extent of amplification when flexible components are excited by structural motion. In UBC this is defined as ap. 3. The ductility of the part can be used to reduce the design forces in a similar manner to R is used for the structural system. UBC defines this as Rp.

332

UBC requires forces to be factored by the importance factor for the part, Ip, and a simplification also allows the component to be designed for the maximum acceleration (4Ca) and ignore both ap and Rp. For isolated structures, it is usual to replace the value of C calculated above with the peak floor accelerations obtained from the time history analysis. Values of ap and Rp as for nonisolated structures are then used with this value. As time history analyses are generally used to evaluate isolated structures it is possible to generate floor response spectra and use these to obtain values of ap, defined as the spectral acceleration at the period of the component. As this requires enveloping a large number of spectra, this procedure is usually only used for large projects. 9.6.5

Bridges

Although there are differences in detail, the same general principles for the structural design of bridges apply as for buildings: 1. The elastic forces transmitted through the isolation system are reduced to take account of ductility in the sub-structure elements. The 1991 AASHTO permitted use of R values equal to that for non-isolated bridges but in the 1999 AASHTO this has been reduced to one-half the value for non-isolated bridges. This provides a range of RI from 1.5 to 2.5, which implies relatively low levels of ductility. RI need not be taken less than 1.5. 2. A lower limit on design forces is provided by non-seismic loads, the yield level of a softening system or the friction level of a sliding system. AASHTO does not require the 1.5 factor on the yield level or friction level that is specified in the UBC. For buildings nonseismic lateral loads are usually restricted to wind but bridges have a number of other cases which may influence design (wind, longitudinal force, centrifugal force, thermal movements etc.). 3. Connection design forces for the isolators are based on full elastic forces, that is, R = 1.0. Although bridges do not generally use the DBE and MCE terminology typical of buildings, design of the structure is based on a 475 year return period earthquake and the isolators must be tested to displacement levels equivalent to that for a 2,400 year return period earthquake. The 2,400 year displacement is obtained by applying a factor of 2.0 to the design displacements for low to moderate seismic zones (accelerations  0.19g) and 1.5 for high seismic zones (accelerations > 0.19g).

9.7

SPECIFICATIONS

9.7.1

General

Sample specifications reflecting current US practice are provided in Naeim and Kelly [1999]. Figure 9.38 shows the major headings that are generally included in base isolation specifications.

333

1. 2. 3. 4. 5. 6. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 8. 9. 9.1. 9.2. 9.2.1. 9.2.2. 9.2.3. 9.3. 9.4. 9.4.1. 9.4.2. 9.4.3. 9.4.4. 9.4.5. 9.4.6. 9.5. 10.

PRELIMINARY SCOPE ALTERNATIVE BEARING DESIGNS SUBMITTALS REFERENCES BEARING DESIGN PROPERTIES BEARING CONSTRUCTION Dimensions Fabrication Fabrication Tolerances Identification Materials DELIVERY, STORAGE, HANDLING AND INSTALLATION TESTING OF BEARINGS General Production Testing Sustained Compression Tests Compression Stiffness Tests Combined Compression and Shear Tests Rubber Tests Prototype Testing General Definitions Prototype Test Sequence Determination of Force-Deflection Characteristics System Adequacy Design Properties of the Isolation System Test Documentation WARRANTIES

Figure 9.26: Specification Contents

Often, the specifications provide a particular bearing design which manufacturers can bid directly and also permit alternate systems to be submitted. Procedures need to be specified for the manner in which alternate systems are designed and validated. Generally, this will require specification of the seismic design parameters, the form of the analysis model and the performance requirements for the system. Performance requirements almost always include maximum displacements and maximum base shear coefficients and may also include limits on structural drifts, floor accelerations, member forces and other factors which may be important on a specific project. Care should be taken not to mix prescriptive and performance requirements. If performance requirements of the isolation system are specified, including the evaluation method to define this performance and the testing required to validate the properties, then the documents should not also specify design aspects such as the shear modulus of the rubber (for LRBs or HDR bearings) or the radius of curvature (for curved sliders). Even for the complying design, the onus should be placed on the manufacturer to verify the design because aspects of isolation system performance are manufacturer-specific, such as damping or lead core effective yield level. It is often useful to include a clause such as the following: 334

“The manufacturer shall check the bearing sizes and specifications before tendering. If the manufacturer considers that some alteration should be made to the bearing sizes and/or properties to meet the stated design performance requirements the engineer shall be advised of the alterations which the manufacturer intends making with the tender.” 9.7.2

Testing

Code requirements for base isolation require testing of prototype bearings, to ensure that design parameters are achieved, and additional production testing is usually performed as part of quality control. The UBC and AASHTO codes specify procedures for prototype tests and most projects generally follow the requirements of one of these codes. These require that two bearings of each type be subjected to a comprehensive sequence of tests up to MCE displacements and with maximum vertical loads. Because of the severity of the tests, prototype bearings are not used in the structure, with some exceptions in low seismic zones. The extra isolators can add significantly to the costs of projects that have a small number of bearings, or a number of different types. Production tests usually include compressive stiffness testing of every bearing plus combined shear/compression testing of from 20% to 100% of isolators. Compression testing has been found difficult to use as a control parameter to ensure consistency. This is because typical vertical deflections are in the order of 2 mm to 5 mm whereas for large bearings the out of parallel between top and bottom surfaces will be of the same order. This distorts apparent compressive stiffness. On recent projects, these difficulties have lead to a preference for the measurement of shear stiffness on all production bearings to ensure consistency. Testing requirements in the UBC have become more stringent in later editions of the code. In particular, the 1997 edition requires cyclic testing to the MCE displacements whereas earlier editions required a single loading to this displacement level. This requires high capacity test equipment because MCE displacements may be 750 mm or more. Test equipment that can cycle to this magnitude of displacement is uncommon. Where a project is not required to fully comply with UBC it may be cost-effective to use the earlier UBC requirement of a simple stability test to the MCE displacement. This may allow manufacturers to bid who would not otherwise bid because of insufficient test capacity. This option needs to be assessed on a project by project basis.

335

Chapter 10:

10.1

FEASIBILITY ASSESSMENT, EVALUATION AND FURTHER DEVELOPMENT OF SEISMIC ISOLATION

DECISION-MAKING IN A SEISMIC ISOLATION CONTEXT

10.1.1 Seismic Isolation Decisions to be made Chapters 1 to 9 of this book have shown that many engineers and contractors all over the world have used seismic isolation, as an integral part of their designs or as a retrofit, in order to provide a bridge or building or their contents with passive protection against a recognised natural hazard – earthquake damage. These chapters of this book have shown:    

that seismic isolation can be installed; that seismic isolation has been installed; that techniques are available to enable an engineer to calculate the necessary parameters for installation of a seismic isolation system; and that devices such as Lead Rubber Bearings can be fabricated, tested and installed to provide seismic isolation.

However the chapters above do not address the key question: 

Should seismic isolation be installed in a bridge or building in a particular case?

There are several elements to this key question:   

What are the benefits and costs of installing seismic isolation in this case? (This will depend on the geographical location of the site, the nature of the site, the probability of an earthquake occurring and the likely magnitude and type of the earthquake). How is the structure likely to perform in the event of an earthquake? (And how would it compare to the likely performance of an unisolated structure). At what stage in the design process should the feasibility study be undertaken? (This should be done as early as possible in the design process, bearing in mind that the installation of seismic isolation can radically affect all aspects of the construction process.).

This chapter aims to provide some answers to these questions. It draws on our lifetime experience as active practitioners in the field of seismic isolation design, assessment and installation and indicates some of the considerations that must be taken into account in assessing whether seismic isolation is appropriate for a given construction project. The stakes (loss of human life, property damage) are so high that processes must be in place to manage and reduce the risk that the assessment, design, installation or components are not fit for purpose in the event of an earthquake.

337

The elements of these processes are feasibility assessment, evaluation, and response to the results of the evaluation process by planning improvements in the system. This chapter presents   

an example of a feasibility assessment (that used prior to the installation of seismic isolation in Te Papa Tongarewa in Wellington); a record of the known performance of seismically isolated structures in real earthquakes to date; a report on two new devices designed to provide large design displacements as required in near-fault situations.

This chapter concludes with a cautionary note; decisions on seismic isolation should not be made in isolation by an engineer or a designer, but require input from a team of interdisciplinary experts. 10.1.2 Seismic Isolation Decisions in the Wellington Area This chapter uses some of the seismic isolation construction projects that have been undertaken in Wellington, New Zealand, to illustrate some of the issues and decisions that must be made regarding the design, assessment and installation of seismic isolation. Some of these projects in Wellington are included in Chapter 8 and we detail below some more work that has been done since Chapter 8 was written. We also give some detail about one of the major construction projects (completed in 1998), namely the Museum of New Zealand, Te Papa Tongarewa. Wellington is sited in an area that is geologically active, with the fault line running along the harbour. There is clear evidence of previous movement along the fault since this provided a convenient site on which to build the north-south motorway into Wellington. There are also plaques on the pavements in the city to mark the water-line before the 1840 earthquake); the streets along the earlier waterfront are called ‘quays’; and the old cricket ground on one of the hills is called the Basin Reserve as it was intended for ships. Wellington residents and visitors may not be generally aware of the seismic isolation that has been provided to bridges and buildings in the region, many of which are described in Chapter 8 and several more in the next section. However, there are two seismically isolated facilities at which the Lead Rubber Bearings are on display, one of these being the retrofitted Parliamentary Buildings and the other Te Papa, the Museum of New Zealand on the waterfront, which was built on Lead Rubber Bearings. Te Papa is such an important icon in New Zealand that we reproduce on page 341, the feasibility study that was carried out before the decision was made to include seismic isolation.

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10.2

CONSTRUCTION PROJECTS IN NEW ZEALAND AND INDIA 1992 TO 2005

10.2.1 Introduction Some of the buildings and bridges built in New Zealand are detailed in Chapter 8. New Zealand continues to build seismically isolated structures and some of these are detailed here. It is interesting to note that a study has been carried out (Carden, Davidson & Buckle, 2001) to consider whether to redesign the isolation system, and if necessary to retrofit additional seismic features on the William Clayton Building (see Chapter 8), which was completed in 1981 as the first building to be seismically isolated on Lead Rubber Bearings. This proposal was made as a result of two factors. First, new information is now to hand about the displacements that can occur near an earthquake fault; in this case it might be necessary to design for two or three times the original 300 mm displacement and seismic gap. Secondly the technology of seismic isolation has matured over the intervening twenty years so that techniques are available for finetuning the original system to provide more protection. 10.2.2 Retrofits Since 1992 seismic isolation has been retrofitted in four historic buildings in Wellington. Two of these were seismically vulnerable masonry buildings of historic interest, namely the adjacent landmarks, the old Parliament Building and the Assembly Library. Seismic isolation of these buildings was completed in 1996; using 514 individually tested Lead Rubber Bearings. The retrofit involved re-piling the building with LRBs and rubber bearings in the supports as well as cutting a seismic gap in the 500 mm thick concrete walls. During an earthquake the building will be able to move in any direction on a horizontal plane up to distances of 300 mm. Seismic isolation has also been retrofitted in the Maritime Museum, the former Head Office of the Wellington Harbour Board, and the former BNZ building, built in 1885 and one of Wellington’s oldest masonry buildings. The building has a classical Victorian style and façade and is richly decorated with fine plasterwork. It now has been retrofitted with a Lead Rubber Bearing seismic isolation system. 10.2.3 Te Papa Tongarewa The Museum of New Zealand, Te Papa Tongarewa, situated on the Wellington waterfront, is a New Zealand icon in many ways. It is a repository of New Zealand national treasures (taonga) and a conference, exhibition, research and learning centre that attracts huge numbers of national and international visitors every year. It is also seismically isolated.

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Figure 10.1: Te Papa Tongarewa, Museum of NZ under Construction

Figure 10.2: Installation of Lead Rubber Bearing – Te Papa, Museum of NZ

The public is obviously interested to learn that the Museum is seismically isolated and to visit the technical display that is on view down a set of stairs that provide access to two of the 152 Lead Rubber Bearings on which the building is mounted. The display includes an audiovisual presentation and other information about the Museum’s ‘base isolation’. The display makes it clear that the seismic isolation system is there to improve safety, much in the same way as the compaction of the ground beneath the building was carried out to reduce the risk of fluidisation of the ground beneath. None of the measures to improve safety are guarantees of perfect safety, and this cannot be promised in any natural hazard situation (as has been shown so recently by the tsunami and Hurricane Katrina). We present in the next section some of the considerations and analyses that underpinned the decision to provide seismic isolation for Te Papa.

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10.2.4 Other Seismically Isolated Buildings Four important structures are being, or have recently been, seismically isolated in New Zealand. These are:    

a new Accident & Emergency Wing of the Wellington Hospital, the Christchurch Women’s Hospital; the Victoria University Rankine Brown Library Building (retrofit), and the new Wellington Central Hospital.

These were all isolated by combinations of LRBs and sliding bearings. Both of the Wellington buildings are close to the Wellington fault and need to be able to reduce the forces expected from ‘near fault fling’ effects resulting in maximum displacements of the isolators of up to 600mm. The retrofitted nine-floor Rankine Brown Library Building is of particular interest in that the library continued to operate while the 12 columns were cut one by one, the redundant concrete piece removed and the Lead Rubber Bearings inserted and bolted in place. This process required the three floors above the bearings to be carefully jacked thereby redistributing the vertical loads through the building. The customer was extremely pleased with the retrofit construction and the lack of interference to the normal working of the library. The savings in insurance premiums were more than enough to make this retrofit financially worthwhile. The new Wellington Central Hospital, the main hospital for the Wellington region, is mounted on 135 lead rubber bearings and 135 sliding bearings. The new Christchurch Women’s Hospital is mounted on a combination of 4 sliding bearings and 43 lead rubber bearings. The new patients moved in on 1 April 2005 with the first baby being born almost immediately. 10.2.5 Bhuj Hospital A recently completed example of seismic isolation is the 300-bed hospital at Bhuj, in the state of Gujarat, India. The original hospital was completely destroyed in the magnitude 7.6 Bhuj earthquake on 26 January 2001 that destroyed most of the town of Bhuj. When the hospital was rebuilt in January 2004, it was provided with seismic isolation to protect it from earthquakes in the future. Immediately after the Bhuj earthquake the Prime Minister of India decided that a new hospital should be built and that it should have the latest international earthquake-protection building technology. The New Zealand Government was asked to respond to a request for information on the design of the hospital. This entailed bringing two key Indian designers – an engineer and an architect – to New Zealand for training in the practical aspects of seismic isolation. The two designers spent several weeks visiting New Zealand engineering companies, architectural and engineering consultancies, and building sites that used New Zealand’s seismic isolation technologies. It was decided to use Lead Rubber Bearings plus slider bearings for the new Bhuj Hospital.

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The illustrations show installation of the Lead Rubber Bearings during construction of the new Bhuj hospital, and the completed hospital in January 2004. The bearings were placed on the top of columns so that the entire building was supported by the bearings together with a number of slider bearings. The seismically-isolated structure is designed to provide protection from damage to the contents or structure in a 1 in 2000 year earthquake.

Figure 10.3: The completed Bhuj Hospital mounted on Lead Rubber Bearings for seismic isolation, January 2004

Figure 10.4: Bhuj Hospital during construction. The circles on the photograph show where the Lead Rubber Bearings are mounted on top of the foundation columns

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10.3

A FEASIBILITY STUDY FOR SEISMIC ISOLATION

10.3.1 Te Papa Tongarewa, the Museum of New Zealand We present here some of the considerations and analyses that underpinned the decision to provide seismic isolation for Te Papa Tongarewa, The Museum of New Zealand. This section is based, without modernisation, on the paper presented by Kelly & Boardman in 1993. This paper summarises the design of the structure and the isolation system and the three-dimensional nonlinear analyses performed to evaluate the building performance. 10.3.2 Description The building design is monumental in nature with a total floor area of 35,000 square metres distributed over five floor levels. The design team headed by Jasmax Architects was selected in 1990 after an international competition. Seismic isolation was considered at the stage where design development had been completed and final design and production of working drawings was in progress. The new building approximates a triangle in plan with maximum dimensions of 120m x 190m and a height of 23m. Figure 1 shows the layout of the building at the isolation level. Total building cost was estimated to be $NZ130 million.

Figure 10.5: Floor plan of Te Papa from Boardman and Kelly paper

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A number of preliminary value engineering studies by the entire design team investigated alternatives of reinforced concrete and structural steel and also a number of floor span configurations. The optimum system selected was a reinforced concrete structure based on a rectangular grid of 17.4m x 8.7m with precast floor units. Ductile frames were selected in the direction of the 8.7m grids and shear walls in five locations in the 17.4m span direction. The frames are formed of pairs of columns/girders spaced 2.1m apart. The double frame system has the effect of reducing the span of the floor units from 17.4m to 15.3m and also providing a system of "tunnels" for the building services. The building site on the Wellington waterfront is on reclaimed land which has been in filled over the last 40 years using high quality fill material which is uncompacted. Approximately 12m of this fill material overlays up to 100m of dense sand and gravel. A number of alternate deep and shallow foundation schemes were investigated of which the most cost effective was found to be dynamic consolidation of the site and the use of pad footings without piles. A pilot study using dynamic consolidation (dropping a weight of 25 tonnes a height of 25m in a fine grid pattern) was performed over a portion of the site and demonstrated its effectiveness to a depth of 12m. The level of the site reduces approximately a metre as a result of the consolidation. 10.3.3 Seismic Design Criteria The site is in the most seismically active region of New Zealand and specific earthquake performance requirements were set as part of the design brief, in particular: 1.

Probability of significant damage less than 50% in 150 years, which corresponds to a 250year return period.

2.

Probability of collapse less than 7% in 150 years, corresponding to a 2000-year return period.

For the reinforced concrete structural system the onset of "significant damage" was defined as (1) displacement ductility less than 2 and (2) concrete strains less than 0.004, which correspond to plastic rotations of approximately 0.007 radians. The limit beyond which collapse could occur was set at a strain of 0.010, a plastic rotation of 0.020 radians. The analysis procedures were required to be such that these values could be quantified. Site specific earthquake acceleration time histories and response spectra were generated for each of the return periods using the SHAKE computer program to obtain surface records. Source time histories were based on 1.8 x El Centro 1940, 0.7 x Tabas 1978 and 1.3 x Llolleo 1986. An additional record was generated by frequency scaling the El Centro 1940 record to be compatible with the smoothed surface spectrum. The 250-year and 2000-year return period spectra were obtained by a linear scaling of the 500 year spectrum by factors of 0.8 and 1.3 respectively. The 250-year spectrum is about 50% higher than would be required by the loadings code for the Wellington region. In addition, the damage criteria restrict the ductility factor to 2 rather than the 6 permitted by the code for ductile concrete frames. The net result of this is that elastic design forces for the building are 4.5 times higher than would be required for a building designed to the code.

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This level of design load and the desire to restrict contents damage formed the basis for the decision to investigate a base-isolated structure for the museum. 10.3.4 Feasibility Study Seismic isolation was included in the initial concept development of the building but, as part of the value engineering requirements of the project, its cost effectiveness was to be justified at each stage of design. A two stage feasibility study was performed, the first investigating global response parameters (base shear and floor accelerations) and the second evaluating and costing various frame and shear wall designs (drifts and ductilities). The method used for the initial evaluation was based on a procedure developed by Ferrito (1984) where the cost of damage to the structure and contents is estimated as a fraction of the initial cost. Design base shear levels of 0.2g and 0.5g were assumed for both a fixed and isolated building configuration. Maximum drifts and floor accelerations were estimated for each level of design and the cost of structural damage and damage to components assessed for each option using Ferrito's tables. Bar charts were produced based on an assumed total building cost of $50 m and contents value of $200 m. The procedure was approximate but did enable some conclusions to be drawn: 1.

Total damage costs are 3 to 8 times higher for a fixed base building than for an isolated building, the actual factor depending on the design base shear level and magnitude of earthquake.

2.

For the fixed based building damage costs actually increase if the design base shear level is increased even though costs of structural damage are reduced. This is because of the high value of the contents which are damaged by floor accelerations. Accelerations increase with increasing design level.

3.

Even for an isolated building significant contents damage could occur at the 250 year earthquake level assuming a threshold of damage of 0.08g (as in the Ferrito study). Measures must be taken in the design and operation of the structure to raise the threshold for acceleration-related contents damage, for example by restraining exhibits.

In the second phase of the feasibility study representative frames and shear walls were designed for base shear levels corresponding to varying levels of ductility at the 250-year level, from fully elastic to fully ductile. A time history analysis using the DRAIN-2D2 program was then used to compute the response at the 250-year and 2000-year return period earthquakes for each design. Each design was evaluated for acceptability in terms of the criteria limits on damage and for each design the quantity surveyors for the project estimated the structural construction cost. From a structural performance perspective both the fixed base and isolated schemes were able to be designed to achieve the criteria objectives limiting damage at the 250-year level and avoiding collapse for the 2000-year earthquake. This required that the frames be designed for a minimum of 50% of the 250 year elastic forces and the walls and coupling beams for 100% of the 250 year elastic forces. The fixed base configuration required 8 shear walls versus 5 shear walls for the isolated design and also required larger column and girder sections.

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The effect of these increases in the structural system sizes was to counteract the cost of the isolation system so that the two configurations produced similar structural costs, $14.5 million for the fixed base building and $15.1 million for the isolated building. Extra costs to accommodate the larger drifts in the fixed base building were not quantified. The design options had demonstrated approximately equal costs for the two systems but of more importance for a building of this function is the cost of non-structural damage (related to drift and floor accelerations) and especially contents damage (a function of floor accelerations). As Table 10.1 shows, the fixed base options produced drifts and accelerations several times as high as the isolated alternative. These results led to a decision to proceed with the isolation system design. 10.3.5 Isolation System Design As part of the feasibility studies varying isolation system parameters were studied but specific hardware was not designed. It was assumed that the system would contain the two essential elements of a practical isolation system in a high seismic zone, flexibility and added damping. Both hysteretic and viscous forms of damping were evaluated. It was decided that devices to provide hysteretic damping were more readily available than viscous dampers and so the design was based on hysteretic damping. After evaluating a number of systems, elastomeric bearings with lead cores to provide hysteretic damping were chosen. These bearings were not suitable for the wall locations where high compression and tension forces occurred. At these locations PTFE (Teflon) sliding bearings were used, the bearings uplifting when earthquakeinduced axial loads exceeded the gravity load. Architectural and services restrictions limited the maximum seismic gap around the building to 500 mm and so the isolation system design was required to produce displacements less than 500 mm at the 2000-year earthquake. This formed an upper bound on the flexibility of the isolation system. The design of the lead rubber bearings was based on procedures developed by Dynamic Isolation Systems, Inc. (1990). Different isolator location configurations were investigated and it was found that a single, large isolator at each column location was more economical than multiple smaller isolators because of the large displacements. The isolators as designed have a maximum size of 950 mm diameter x 300 mm height. 10.3.6 Evaluation of Structural Performance The final configuration of the structure and isolation system produced a very complex lateral load resisting system. To evaluate the performance a three-dimensional model of the structure and isolation system was developed using the ANSR-II computer program (Mondkar & Powell, 1979). The computer model of the building was developed in successively more complex stages with each step forming a check on the overall response produced by the succeeding step. Initial studies on a single degree-of-freedom model were extended to planar models of the frames and walls and then to a three-dimensional model with an elastic superstructure. The final model was a fully yielding model which reflected all the elements of the building:

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1.

Flexural bi-linear yielding elements to model the frame girders and columns and the shear walls and coupling beams.

2.

Special purpose gap-friction elements to model the Teflon bearings. The friction force for these elements was a function of the vertical pressure and velocity at each location at each time step of the analysis.

3.

Lead rubber bearings modelled as two components, a linear elastic element representing the elastomer and an elastic perfectly plastic element to represent the lead core.

4.

Horizontal movement buffers at the isolation level which engaged when displacements exceeded 500 mm.

5.

A rigid diaphragm at the North and South portions of the main building linked by truss elements to model the connection stiffness at the movement joints.

6.

A West Wing "stick" model mounted on the same isolation diaphragm as the Main Building but separated from it at upper levels.

As the ANSR-II model was developed, a concurrent equivalent elastic model using ETABS (Habibullah, 1986) was used to correlate the overall performance as much as possible. This model was used to check such effects as the distribution of shear forces between walls, structural deformations etc. The Teflon elements used for the program were based on a formulation of coefficient of friction developed at NCEER, New York (Mokha, Constantinou & Reinhorn, 1988). Further static and dynamic testing of a New Zealand produced PTFE material led to an upward adjustment of the coefficient of friction by 25% with a maximum coefficient of friction (at high velocities) of 0.12 at 15MPa decreasing to 0.09 at 30 MPa (Davidson & Smith, 1992). The geometry of the building is such that some frames and walls are based on a grid system rotated approximately 30 degrees from that of the remaining elements. The large difference in stiffness between the frames and walls coupled with this angular offset produced large opposing walls forces when deformations were in the frame direction. To reduce these secondary forces movement joints were introduced across the building between the two grid orientations. To reflect this, the ANSR-II model used two rigid diaphragms at each floor level with the two portions connected by truss elements with properties representing the reinforcing bars across the movement joint. Movement stops at the base had zero stiffness until translation exceeded 500 mm. At this point the gap elements engaged with a large stiffness, representing impact with the surrounding retaining wall. These elements were used to investigate the effects of designing a flexible isolation system to reduce earthquake response of the structure for smaller earthquakes and restrict maximum displacements by permitting impact to occur at higher earthquakes. When this occurred it was found that the impact transmitted very large accelerations into the diaphragm (in excess of 2g) and so the isolation system was stiffened so impact would not occur.

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The configuration of the building with a relatively small number of floors, a large number of column lines and interconnected diaphragms resulted in a large model for nonlinear analysis with a total of 2250 degrees of freedom, a maximum bandwidth of 1000 and approximately 1500 yielding elements. 10.3.7 Results of ANSR-II Analysis The ANSR-II model was used for a basic set of 16 analyses - 4 pairs of earthquake records, 2 orientations per record and 2 return periods for each orientation. For each analysis the two horizontal components of motions were applied simultaneously. The global results from these analyses are summarized in Table 10.2 which lists the maximum values from the two orientations. Maximum vector isolator displacements were 258 mm for the 250 year return period and 516 mm for the 2000 year earthquake. The overall structural deformations above the isolation system were 126 mm and 270 mm in the frame direction for the two return periods and 51 mm and 118 mm in the direction of the shear walls. The Teflon pads uplifted a maximum of 25 mm at the 250 year earthquake and 79 mm for the 2000 year earthquake. These uplift values were the maximum at any of the 36 Teflon pad locations. The larger uplift values tended to occur at 3 or 4 locations where the end of the wall did not connect to the framing girders and so supported very little gravity load. At other locations the uplift was much less. The results from the 16 analyses were used to evaluate the design of the structural elements and also to determine the most critical earthquake record and orientation for subsequent analyses. The reinforcing was refined based on the maximum plastic rotations from the analyses. The frequency-scaled El Centro record was used to evaluate the building with this refined strength and also to perform further analyses to evaluate P-delta effects (less than 5%), to obtain sets of vertical loads for foundation design and to obtain maximum inertia loads on the West Wing. 10.3.8

Conclusions

A series of feasibility and design studies performed for the Museum of New Zealand, Te Papa Tongarewa, have demonstrated that a seismic isolation system can be installed for almost the same first cost as a conventional, fixed base structural system. To obtain approximately similar levels of structural damage the conventional structure requires larger columns and beams and also a larger number of shear walls compared to the isolated structure. The consequences of designing a fixed base structure for very high levels of earthquake load are to increase the floor accelerations far above those of the seismically isolated scheme and so increase the potential for damage to non-structural components and contents. For a building such as a museum the values of the contents may be many times the value of the structure. When this is taken into account the total damage costs in a major earthquake in a fixed base building can be from 3 to 8 times those of an isolated building. This was the deciding factor in the selection of an isolated configuration for the building. The isolation system selected was a combination of elastomeric bearings with lead cores and PTFE (Teflon) sliding bearings. The elastomeric bearings are used at column locations and the Teflon bearings at shear walls where high overturning forces occur. A nonlinear analysis model was used to quantify the isolator forces and displacements and the ductility demands in the concrete superstructure. Some adjustments to the column reinforcing were made as a result of these analyses.

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The design and evaluation of earthquake response has demonstrated that, even with seismic isolation, the maximum earthquake motions to be expected in the high seismic Wellington region will cause relatively high in-structure accelerations. These will be of a level which could cause damage to contents and services unless mitigation measures are taken. Consideration of earthquake effects will need to be included in the initial design of all aspects of the building and also of the placement and fixing of contents during the operation of the building.

Maximum Floor Acceleration

Maximum Storey Drift

Fixed

Isolated

Fixed

Isolated

FRAMES 250 Year 2000 Year

0.81 1.14

0.33 0.48

0.6% 1.8%

0.2% 0.7%

WALLS 250 Year 2000 Year

1.02 1.69

0.27 0.38

0.5% 0.8%

0.1% 0.6%

Table 10.1: Structural Drifts and Accelerations

Figure 10.5 Museum of New Zealand, Te Papa Tongarewa

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250 - YEAR Displacements (mm) Frame Wall Isolator (Vector) Teflon Pad Uplift (mm) Compression (kN) 2000 - YEAR Displacements (mm) Frame Wall Isolator (Vector) Teflon Pad Uplift (mm) Compression (kN)

El Centro Frequency Scaled

El Centro SHAKE Output

Tabas SHAKE Output

Llolleo SHAKE Output

122 51 247

83 40 209

93 47 258

126 48 241

20 34,400

17 33,300

21 36,400

25 35,900

270 118 484

192 84 452

199 96 516

177 84 421

79 44,800

55 44,600

41 42,000

56 41,200

Table 10.2: Results of Nonlinear Analyses

10.4

PERFORMANCE IN REAL EARTHQUAKES

Examination of the actual performance of isolation systems in real earthquakes should ensure that we learn from these experiences. One of the most frequent questions asked by potential users of isolation systems is, Has it been proved to work in actual earthquakes? The short answer is a qualified no; no isolated building has yet been through “The Big One” and so the concept has not been tested to the limit but some have been subjected to earthquakes large enough to activate the system. Our buildings in New Zealand have not been subjected to any earthquakes yet, although four are located in Wellington so it is only a matter of time until this happens according to most seismologists. Two bridges on lead rubber isolation systems were subjected to strong motions during the 1987 Edgecumbe earthquake. One, Te Teko Bridge, had an abutment bearing roll out because the keeper plates were misplaced. This caused minor damage. This type of connection is no longer used. The other bridge was on a privately owned forestry road and, other than a report that there was no damage; there is no information on this. Table 10.3 summarizes the reported performance of structures world-wide during earthquakes. Many of the structures are not instrumented and so much evidence of performance is either indirect or anecdotal.

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There are features of observed response that can teach us lessons as we implement base isolation: 

Some structures performed well and demonstrated the reductions in response that base isolation is intended to achieve. The most successful is probably the USC Hospital in Los Angeles (see Chapter 8). Occupants reported gentle shaking during the main shock and after-shocks of the 1994 Northridge earthquake. The pharmacist reported minimal to no damage to contents of shelves and cabinets. Other successful installations were the Tohuku Electric Power building in Japan, the Stanford Linear Accelerator and Eel River Bridge in California and several bridges in Iceland.



At the LA County Fire Command Centre, the contractor had poured a reinforced concrete slab under the floor tiles at the main entrance to the buildings, preventing free movement in the E-W direction. Apparently the reinforcing was added after the contractor had replaced the tiles several times after minor earthquakes and did not realize that this separation was designed to occur. This emphasizes the importance of ensuring that building operational procedures are in place for isolated buildings.



The Seal Beach and Foothills (see Chapter 8) buildings demonstrate that accelerations will be amplified as for a fixed-base building for accelerations which do not reach the trigger point for the system.



The West Los Angeles residence used an owner-installed system of steel coil springs and dashpots without a complete and adequate plane of isolation. The springs allowed vertical movement and the building apparently responded in a pitching mode. The owner was satisfied with the performance.



The Matsumura Gumi Laboratory building in Japan did not amplify accelerations as for a fixed base building but also did not attenuate the motions as expected. The period of response was shorter than expected and a possible reason for this was the temperature of the isolators, estimated at 0C in the unheated crawl space. Potential stiffening of rubber as temperatures are reduced needs to be accounted for in design if isolators are in locations where low temperatures may occur.



Bridges in Taiwan and Kobe were partially isolated, a design strategy often used for bridges where the system provides energy dissipation but not significant period shift. The response of these bridges shows benefits in the isolated direction compared to the non-isolated direction but the reductions are not as great as for fully isolated structures.



The dissipators at the Bolu Viaduct in Turkey were severely damaged due to near-fault effects when the displacement caused impact at the perimeter of the dissipator. This appeared to be mainly due to large displacement pulses near the fault but may have been accentuated by use of an elastic-perfectly plastic system rather than the more common strain hardening system.

In all structural engineering, we need to learn from the lessons which earthquakes teach us. There is discussion throughout this book on aspects of isolation that can degrade performance if not properly accounted for. These earthquakes have shown the importance of attending to all these details.

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ACCELERATION SYSTEM TYPE

EQ

LRB

1994 Northridge

0.49

0.21

LA County Fire Command Center

HDR

1994 Northridge

0.22 E-W 0.18 N-S

0.35 E-W 0.09 N-S

Minor ceiling damage. Continued operation

Seal Beach Office

LRB

1994 Northridge

0.08

0.15

No damage. System not activated.

Foothills Law & Justice Centre

HDR

1994 Northridge

0.05

0.10

No damage. System not activated.

Springs

1994 Northridge

0.44

0.63

LRB Steel Dampers

1995 Kobe

0.31

0.11

Matsumura Gumi Laboratory

HDR

1995 Kobe

0.28

0.27

Stanford Linear Accelerator

LRB

1989 Loma Prieta

0.29

0.14

Bai-Ho Bridge

LRB PTFE

1999 Taiwan

0.17 L 0.18 T

0.18 L 0.26 T

Longitudinal isolation only.

Matsunohama Bridge

LRB

1995 Kobe

0.15 L 0.14 T

0.20 L 0.36 T

Longitudinal isolation only.

PTFE Crescent Moon Energy Dissipator

1999 Turkey

1.0 +

Eel River Bridge

LRB

1992 Cape Mendocino

0.55 L 0.39 T

Four bridges in Iceland

LRB

M6.6 and M6.5 in June 2000.

0.84

STRUCTURE

USC Hospital

West Los Angeles Residence

Tohuku Electric Power

Bolu Viaduct

Te Teko Bridge (NZ)

LRB

1987 Edgecumbe

FREE FIELD (G)

0.33

STRUCTUR E (G)

COMMENTS

Movement estimated at up to 45 mm. No damage Continued operation

No structural damage. Some damage at movement joint. Unusual isolation system. No damage. Movement estimated at 120mm. Isolators at 0C, may have stiffened. Not instrumented, estimated response. Movement estimated at 100mm

Displacements exceeded device limit of 500 mm, causing damage Not measured

Not measured

Estimated acceleration. Movement estimated at 200 mm L and 100 mm T. Minor joint spalling. No damage. Estimated acceleration. Estimated displacement 100mm. Abutment bearing dislodged caused minor damage.

Table 10.3: Earthquake Performance of Isolated Buildings

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10.5

NEW APPROACHES TO SEISMIC ISOLATION

10.5.1 Introduction In the last 10 years or so, many near source records have been obtained from large earthquakes, for example, the Lucene and Joshua Tree records from the 1992 Landers earthquake (Mw=7.2) and the Sylmar record from the 1994 Northridge earthquake (Mw=6.7). A common feature of several of these records is a long period velocity pulse of very large amplitude. Such a pulse can impose very large displacement demands on intermediate and long period structures, including base isolated buildings (Hall et al.1995). These results have encouraged design engineers to increase seismic gaps to 300 to 500mm. This increase in displacement is illustrated by the example of three seismic isolation projects completed in New Zealand during the 1990’s, viz: the new Wellington Central Police Station with a gap of 400mm (Charleson, et al 1987), the old NZ Parliament Buildings retrofit with a seismic gap of 300mm (Poole & Clendon, 1991) and the new Museum of NZ (Te Papa) with a seismic gap of 450mm (Kelly & Boardman, 1993). The lead rubber bearing has been a very useful isolator but like all rubber bearings it is limited by the behaviour of rubber at high strains. To satisfy the requirements of customers, isolation designers are now requiring strains in the rubber as high as 300 to 400%. In addition designers are asking for non-linear restoring forces together with very large displacements (~ 1 metre). Research and development into new approaches to seismic isolation continues with the manufacture of prototype ‘RoBall and RoGlider. The RoBall is a device suitable for use as a seismic isolator and the RoGlider is a sliding bearing which includes an elastic restoring force. The two devices promise to be economic alternatives to existing seismic isolation devices. Plans are now underway for the design and construction of a demonstration building seismically isolated by a system based on the RoGlider approach. 10.5.2 The RoBall A method of satisfying the demanding requirements of a very large displacement is to use a ‘friction device’ operating within an ‘inverted pendulum’ (Zayas, 1995). We have followed this approach with the invention and development of ‘friction balls’ or ‘RoBall’ moving between upper and lower spheroidal cavities or flat plates. The RoBall is filled with a material which is able to provide the friction forces required to absorb the energy from numerous earthquakes while supporting the structure. The RoBall promises to be an economical alternative to existing seismic isolation devices. It has no inherent displacement limit, provides a constant coefficient of friction, allows greater freedom in the choice of the restoring force and may also be used as a buffer. As a buffer the RoBall has two very desirable characteristics: it absorbs energy, and has gently increasing stiffness at large displacement amplitudes. The buffer action may also be useful for reducing the transmission of vertical earthquakes forces to the isolated structure. The RoBall technique is expected to enable light and in the future possibly heavy structures to be more economically seismically isolated.

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The latest version of the RoBallTM includes a restoring force. The top and bottom surfaces are flat and the sides are curved as shown in Figs. 10.5 and 10.6. Inside this version of the RoBall are seven solid balls (Robinson & Gannon, 2006). Other designs of the RoBall suitable for larger displacements could include 13, 19, 25 solid balls in a close packed array. The sides of the RoBall may be thicker than the top and bottom surfaces thereby contributing to a restoring force for small displacements (Figure 10.8) while for large displacements there is cyclic restoring with a wavelength approximately twice the diameter of the RoBall (Figure 10.9). The rolling action of the RoBall means that the device itself has no design displacement limit and so the maximum displacement is limited only by installation requirements. The dynamic behaviour of the device is independent of both frequency and ambient temperature within ranges that are applicable to most practical installations. The effective friction coefficient, i.e., the ratio of the nominal yield shear force to the compression force, of the prototypes, is ~0.1. The applications for the model of the RoBall containing solid spheres are expected to be for protecting light equipment and light structures from mechanically generated or earthquake induced vibrations.

Figure 10.6: RoBall under Vertical Load

Figure 10.7: RoBall with 7 Internal Balls being tested on Concrete Floor in RSL Laboratory

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Figure 10.9: RoBall – Large Displacement with Cyclic Shear Forces

Research and development into new approaches to seismic isolation continues with the manufacture of prototype ‘RoBall and RoGlider. The RoBall is a device suitable for use as a seismic isolator and the RoGlider is a sliding bearing which includes an elastic restoring force. The two devices promise to be economic alternatives to existing seismic isolation devices. Plans are now underway for the design and construction of a demonstration building seismically isolated by a system based on the RoGlider approach.

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10.5.3 The RoGlider The RoGlider is a sliding bearing which includes an elastic restoring force. The RoGlider is applicable for the seismic isolation of both light and heavy vertical loads and can be readily designed to accommodate extreme displacements. It is expected to perform significantly better than rubber bearings or lead rubber bearings in providing seismic isolation at large displacements (Robinson et al, 2006). The actual configuration is dependent on the details of the structure being isolated and the expected earthquake. The RoGlider presented here is a double acting unit with the restoring force provided by two rubber membranes (Figure 10.10). This double acting RoGlider consists of two stainless steel plates with a PTFE ended puck between the plates. Two rubber membranes are attached to the puck with each being joined to the top or bottom plates. When the top and bottom plates slide sideways with respect to each other diagonally opposite parts of the membrane undergo tension or compression. The tension components provide the restoring force between the plates while the compression parts buckle (Figures 10.10 and 10.11) and provide little or no restoring force. The particular double acting RoGlider described here has a maximum displacement of +/600mm, maximum vertical load of 1MN, with an outside diameter of ~900mm and a coefficient of friction of ~11%. Following this membrane approach it is expected that the elastic stiffness can be increased by a factor of four or more using our latest designs. The RoGlider has been chosen as the seismic isolation system for the two storey, three building Wanganui Hospital redevelopment in Wanganui, New Zealand. Each of these light buildings will have 30 RoGliders with each RoGlider able to support loads of 250 to 550kNs with a co-efficient of friction of approximately 10% and a maximum displacement of 450mm.

Figure 10.10: RoGlider ready for Testing Displacement 0mm – Load 850kN

Figure 10.11: RoGlider during Test Displacement ±150mm – Load 850kN

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Figure 10.12: RoGlider during Test Displacement ±575mm – Load 110kN

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Figure 10.13: RoGlider Force Displacement Curve – Vertical Load 850kN

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Figure 10.14: RoGlider Force Displacement Curve – Vertical Load 120kN

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10.6

PROJECT MANAGEMENT APPROACH

The importance of having a broad range of expertise in planning any seismic isolation project cannot be overemphasized. Again it is useful to use the Te Papa example as a model of good practice: This is a quote from the Feasibility study presented in 10.2 above, based on the paper by Kelly & Boardman (1993): “The adoption of a seismic isolation scheme requires the cooperation of all members of the design team to ensure an efficient and economic solution. The architects are required to detail for the 500 mm gap around the building and the building services engineers must ensure that all services crossing the isolation plane have sufficient flexibility to accommodate the movement.” The project members for this project were:        

Client: Project Manager: Architect: Structural Engineer: Mechanical Engineer: Electrical Engineer: Geomechanical Engineer: Peer Review.

The concept of requiring a wide range of inputs into the project at an early stage and if necessary during its implementation is also exemplified by a New Zealand business initiative that has been developed to provide earthquake engineering expertise to Oceania and to a number of countries including India, Nepal, Taiwan, South Korea and Turkey. This is called the New Zealand Earthquake Engineering Technology Business Cluster. The Cluster member companies have a combined resource of some 5,000 professional and technical personnel. All are independent consultants and have no ties to contractors. Although the focus of members of this Cluster is earthquake engineering, many of the members have a wide range of experience which allows them not only to deal with the detailed technical issues, but to set them in context of the whole building project. Members have a wide range of consultancy skills and experience including:     

Project appraisal, including earthquake hazards Design, including co-ordination of all disciplines Contract administration Construction monitoring Manufacture, including seismic isolation devices

In particular, the engineers have relevant and ongoing experience in retrofitting seismic isolation devices in heritage buildings.

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By working together, the Cluster is able to provide a totally integrated service taking care of all aspects required to identify the most appropriate structural and seismic solutions. The Cluster members are able to design the most economical and unobtrusive structural and overall solutions, prepare contract documentation suitable for tendering (or other project delivery methods such as design-build), and administer construction contracts. New Zealand is fortunate to have high standards of design and construction, where full compliance with codes is expected by the community and delivered by the professions. Standards are comparable to those in California and are among the best in the world. A number of our members in the Earthquake Engineering Cluster together with our colleagues in the Natural Hazards Cluster are overseas helping in the countries devastated by the 26 December 2004 Tsunami and the more recent Indonesian earthquake. The Earthquake Engineering and Natural Hazards Business Clusters are enabling the application of many of the results of our engineering experience and our research and developments to real structures in a number of countries.

10.7

FUTURE

Seismic isolation has now reached the stage where there is a range of devices suitable for providing adequate protection for most low-to-medium height buildings in earthquake zones. These same devices can be used to provide increased protection for bridges. The challenge now is to design and build structures which enable the attributes of the various seismic isolation devices to be used economically.

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REFERENCES Asher, J.W., van Volkinburg, D.R., Mayes, R.L., Kelly, T., Sveinsson, B.I. and Hussain, S. (1990), ‘Seismic isolation design of the USC University Hospital’, Proc. 4th US Nat. Conf. Earthq. Eng., Vol 3, May 1990, 529-538 Bailey, J. & Allen, E. (1989), ‘Seismic isolation retrofitting of the Salt Lake City and County building’, Post-SMIRT8 seminar, 1989, paper 14 Beck, J.L. & Skinner, R.I. (1972), ‘The seismic response of a proposed railway viaduct’, Tech. Rpt. No. 369, Physics and Engineering Laboratory, DSIR, NZ Beck, J.L. & Skinner, R.I. (1974), ‘The seismic response of a reinforced concrete bridge pier designed to step’, Int. J. Earthq. Engng. Struct. Dyn., 2, 343-358 Billings, I.J. & Kirkcaldie, D.K. (1985), ‘Base isolation of bridges in New Zealand’. Proc. Second Joint US-New Zealand Workshop on Seismic Resist. Highway Bridges ATC-121, May 1985, Applied Technology Council, California, USA Birchenall, C.E. (1959), Physical Metallurgy, London: McGraw-Hill Blakeley, R.W.G. (1979), ‘Parameter studies for (bridge) design’, Road Research Unit, National Roads Board, NZ, Bulletin 43, 117-42 Boardman, P.R., Wood, B.J. & Carr, A.J. (1983), ‘Union House – a cross-braced structure with energy dissipators’, Bull. NZ Nat. Soc. Earthq. Eng., 16, no. 2, 83-97 Bridge Engineering Standards (1976), Technical memorandum (Bridges), No. BE 1/76, ‘Design Requirements for Elastomeric Bridge Bearings’, Bridge Engineering (Design Standards) Division BES, Department of the Environment, London Buckle, I.G & Mayes, R.L (1990) ‘Theme issue: seismic isolation’, Earthquake Spectra, EERI, 6, no. 2, 161-201 Buckle, I.G. & Mayes, R.L. (1990), ‘Seismic isolation: history, application and performance: a world view’, Earthquake Spectra, 6, No. 2, 161-201 Cary, M. et al., (Eds), 1949 The Oxford Classical Dictionary, London: Oxford University Press Charleson, A.W., Wright, P.D. & Skinner, R.I. (1987), ‘Wellington Central Police Station: base isolation of an essential facility’, Proc. Pacific Conf. on Earthquake Eng., NZ, Vol. 2, 377-388 Clough, R.W. & Penzien, J. (1975), Dynamics of Structures, McGraw-Hill, USA Cormack, L.G. (1988), ‘The design and construction of the major bridges on the Mangaweka rail deviation’, Trans. IPENZ, 15, I/CE, March 1988, 16-23 Cottrell, A.H. (1961), Dislocations and Plastic Flow in Crystals, Oxford: Clarendon Press Cousins, W.J., Robinson, W.H. & McVerry, G.H. (1991), ‘Recent developments in devices for seismic isolation’, Proc. Pacific Conference on Earthquake Engineering, Auckland 20-23 November, New Zealand National Society for Earthquake Engineering, Volume 2, 221-232 Dowrick, D.J. (1987), ‘Edgecumbe earthquake of March 2, 1987’, NZ Engineering, 7-9 Dowrick, D.J., Babor, J., Cousins, W.J. & Skinner, R.I. (1991), ‘Design of a seismically isolated printing press’, Pacific Conf. on Earthq. Eng., NZ, 3, 35-44 Earthquake Engineering Research Laboratory (EERL) Reports (1972-5), e.g. ‘Volume III – Response Spectra, Parts A to Y’, California Institute of Technology, Pasadena, California, Occasional Reports from EERL 72-80 to EERL 75-83 Emi, S., Oshima, K., Takeda, T. & Nakayama, H.(1987), ‘Earthquake resistant design of cable-stayed bridges’, Proc. NZ-Japan Workshop on Base Isolation of Highway Bridges, Technology Research Centre for National Land Development, Japan, November 1987

361

Fan, F.-G. & Ahmadi, G. (1990), ‘Floor response spectra for base-isolated multi-storey structures’, Eng. Struct., 19, no. 3, 377-388 Fan, F.-G. & Ahmadi, G. (1992), ‘Seismic responses of secondary systems in base-isolated structures’, Earthq. Eng. Struct. Dyn., 14, no. 1, 35-48 Ferritto, JM. (1984) ‘Economics of seismic design for new buildings’ J. Struct. Engng, Vol 110, No. 12, December 1984, American Society of Civil Engineering Gent, A.N. & Lindley, P.B. (1959), ‘The compression of bonded rubber blocks’, Proc. Inst. Mech. Engrs., 173, 111-122 Huckelbridge, A.A. (1977), ‘Earthquake simulation tests for nine-storey steel frame with columns allowed to uplift’, Earthq. Eng. Res. Centre. College of Eng., University of California, Berkeley, Report no. UCB/EERG-77/23, 181 pages Jolivet, J. & Richli, M.H. (1977), ‘Aseismic foundation system for nuclear power stations’, Proc. SMIRT4, San Francisco 1977, Paper K.9/2 Jones, J.J., Sellars, C.M. & Tegard, W.J. McG. (1969), ‘Strength and structure under hotworking conditions’, Met. Rev., 130, 1-24 Kaneko, M., Tamura, K., Maebayashi, K. & Saruta, M. (1990), ‘Earthquake response characteristics of base-isolated buildings’, Proc. 4th US Nat. Conf. Earthq. Eng. Vol. 3, May 1990, 569-578 Kelly, J.M. (1986), ‘A seismic base isolation: review and bibliography’, Soil Dun. Earthq. Eng., 5, no. 3, 202-216 Kelly, J.M., Skinner, R.I. & Heine A.J. (1972), ‘Mechanisms of energy absorption in special devices for use in earthquake resistant structures’, Bull. NZ Nat. Soc. for Earthq. Eng., 5, no. 3, 63-88 Kelly, T.E. & Boardman, P.R. (1993) Seismic isolation of the Museum of New Zealand, Te Papa Tongarewa, Proceedings of ATC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, San Francisco, March 1993 Kobori, T., Yamada, T., Takenaka, Y., Maeda, Y. & Nishimura, I. (1988), ‘Effect of dynamic tuned connector on reduction of seismic response – application to adjacent office buildings’, Proc. 9th World Conf. on Earthq. Eng., Tokyo-Kyoto, Vol. V, 773-778 Lee, D.M. and Medland, I.C. (1978a), ‘Base isolation – an historical development, and the influence of higher mode responses’, Bull. NZ. Nat. Soc. Earthq. Eng., 11, no. 4, 219-233 Lee, D.M. & Medland, I.C. (1978b), ‘Estimation of base-isolated structure responses’, Bull. NZ. Nat. Soc. Earthq. Eng., 11, no. 4, 234-44 Malaysian Rubber Producers’ Research Association, Engineering design with natural rubber, NR Technical Bulletin Matsuo, Y. & Hara, K. (1991), ‘Design and construction of Miyagawa Bridge (first Menshin bridge in Japan)’, 1st US-Japan Workshop on Earthquake Protective Systems for Bridges, Buffalo, USA, Sept. 1991 Mayes, R.L. (1990-92), Dynamic Isolation Systems Incorporated, California, personal communications Mayes, R.L. (1992), ‘Current status and future needs of US seismic isolation codes’, Proc. Int. Workshop on Recent Developments in Base-isolation Techniques for Buildings, Tokyo, Japan, 27-30 April 1992, 321-34 McKay, G.R., Chapman, H.E. & Kirkcaldie, D.K. (1990), ‘Seismic isolation: New Zealand applications’, Earthquake Spectra, 6, no. 2, 203-222 Meggett, L.M. (1978), ‘Analysis and design of a base-isolated reinforced concrete frame building’, Bull. NZ Nat. Soc. for Earthq. Eng., 11, no. 4, 245-254 Mendelsson, A. (1968), Plasticity: Theory and Application, New York: MacMillan Miyazaki, M. (1991), Sumitomo Construction Co. Ltd, Japan, personal communication Mokha, A., Constantinou, M.C. & Reinhorn, A.M. (1988) ‘Teflon bearings in aseismic base isolation: Experimental studies and mathematical modelling’, State University of New York at Buffalo, Technical Report NCEER-88-0038

362

Mondkar, D.P. & Powell, G.H., (1979) ANSR II – Analysis of nonlinear structural response, users’ manual, Report No. UCB/EERC – 79/17, Earthquake Engineering Research Centre, University of California, Berkeley Mostaghel, N. & Khodaverdian, M. (1987), ‘Dynamics of resilient-friction base isolation 9R-FBI)’, Int. J. Earthq. Eng. Struct. Dyn., 15, 379-90 Nadai, A. (1950), Theory of Flow and Fracture of Solids, New York: McGraw-Hill Naeim, F. & Kelly, J.M. (1999), Design of seismic isolated structures: from theory to practice, New York: John Wiley & Sons Nakagawa, S., Kawamura, M. (1991), ‘Aseismic design of C-1 Building, the biggest base-isolated building in the world’, Post SMIRT11 Seminar, Seismic Isolation of Nuclear and Non-nuclear Structures, Aug. 26-27 1991, Japan Newmark, N.M. & Rosenblueth, E. (1971), Fundamentals of Earthquake Engineering, New Jersey: Prentice-Hall Parducci, A. (1992), Facoltá di Ingegneria, Instituto di Energetica, Universita’ degli studi di Perugia, personal communications Parducci, A. & Medeot, R. (1987), ‘Special dissipating devices for reducing the seismic response of structures’, Pacific Conference on Earthq. Eng., New Zealand, Vol. 2, 329-340 Parducci, A. & Mezzi, M (1991), ‘Seismic isolation of bridges in Italy’, Pacific Conf. on Earthq. Eng., New Zealand, Vol. 3, 45-56 Park, R. & Blakeley, R.W.G. (1979), ‘Seismic design of bridges’, Road Research unit, National Roads Board, New Zealand, Bull. 43, 101-105 Pearson, C.E. (1944), The Extrusion of Metals, New York: John Wiley and Sons Pham, T. (1991), AC Power Group Ltd, Wellington, personal communication Plichon, C., Gueraud, R., Richli, M. and Casagrande, J.F. (1980), ‘Protection of nuclear power plants against seisms’, Nuclear Technology, 49, 295-306 Poole, R.A. and Clendon, J.E. (1991), ‘NZ Parliament buildings: seismic protection by base isolation’ Pacific Conf. on Earthquake Eng., Auckland, NZ, Nov 1991, Vol. 3, p13 Popov, E.P. (1966), ‘Low cycle fatigue of steel beam to column connections’, Proc. International Symposium on the Effects of Repeated Loadings of Materials and Structures, Vol. VI, RILEM = Inst. Ing., Mexico Pugh, H.Ll.D. (1970), ‘Hydrostatic extrusion’ in Mechanical Behaviour of Materials under Pressure (Ed. H. Ll. D. Pugh), Applied Science, London Robinson, W.H. (1982), ‘Lead-rubber hysteretic bearings suitable for protecting structures during earthquakes’, Earthquake Eng. and Str. Dyn., 10, 593-604 Robinson, W.H. & Cousins, W.J. (1987), ‘Recent developments in lead dampers for base isolation’, Proc. Pacific Conference on Earthquake Engineering, 5-8 August 1987, Wairakei, New Zealand National Society for Earthquake Engineering, Volume 2, 279-284 Robinson, W.H. & Cousins, W.J. (1988), ‘Lead dampers for base isolation’, Proc. 9th World Conference on Earthquake Engineering, Tokyo and Kyoto, Japan, August 2-9, Vol 8, 427432 Robinson, W.H. & Greenbank, L.R. (1976), ‘An extrusion energy absorber suitable for the protection of structures during an earthquake’, Earthquake Eng. and Str. Dyn. 4, 251-9 Robinson, W.H. &Tucker, A. (1981), ‘Test results for lead rubber bearings for the Wm Clayton Bldg, Toe Toe and Waiotukupuna Bridges’, Bull. NZ Nat. Soc. Earthq. Eng., 14, 21-33 Saruta, M. (1991, 1992), Institute of Technology, Shimizu Corporation, Tokyo, personal communications Savage, J.L. (1939), ‘Earthquake studies for Pit River Bridge’, Civil Engineering, 9, no. 8, 470-2 Schey, J.A. (1970) in J.A. Schey, (Ed) Metal Deformation Processes, Friction and Lubrication, Amsterdam: Marcel Dekker

363

Seki, M. (1991, 1992), Technical Research Institute, Obayashi Corporation, Tokyo, personal communications Sharpe, R.D. & Skinner, R.I. (1983), ‘The seismic design of an industrial chimney with rocking base’, Bull. NZ Nat. Soc. for Earthq. Eng., 16, no. 2, 98-106 Shimoda, I. (1989-1992), Technology Development Division, Oiles Corporation, Tokyo, personal communications Shimoda,I., Nakano, S., Kitagawa, Y, & Miyazaki, M. (1991), ‘Experimental study on base-isolated building using lead-rubber bearing through vibration tests’, SMIRT11 Conference, Seismic Isolation of Nuclear and Non-nuclear Structures, 1991, Japan Skinner, R.I. (1964), ‘Earthquake-generated forces and movements in tall buildings’, Bull. 166, NZ Department of Scientific and Industrial Research Skinner, R.I. (1982), ‘Base isolation provides a large building with increased earthquake resistance: development, design and construction’, Int. Conf. Natural Rubber for Earthq. Prot. of Bldgs. and Vibration Isolation, Kuala Lumpur, Malaysia, Feb. 1982, 82-103 Skinner, R.I. & Chapman, H.E. (1987), ‘Edgecumbe earthquake reconnaissance report’, M.J. Pender and T.W. Robertson eds., Bull. NZ Nat. Soc. for Earthq. Eng., 20, no. 3, 239-240 Skinner, R.I. & McVerry, G.H. (1975), ‘Base isolation for Increased Earthquake Resistance’, Bull. NZ. Nat. Soc. Earthq. Eng., 8, no. 2. Skinner, R.I., Bycroft, G.N. & McVerry, G.H. (1976), ‘A practical system for isolating nuclear power plants from earthquake attack.’ Nucl. Eng. Design, 36, 287-297 Skinner, R.I., Kelly, J.M. & Heine, A.J. (1974), ‘Energy absorption devices for earthquake resistant structures’, Proc. 5th World Conf. on Earthq. Eng., Rome 1973, Vol. 2, 2924-2933 Skinner, R.I., Kelly, J.M. & Heine, A.J. (1975), ‘Hysteretic dampers for earthquake resistant structures’, Int. J. Earthq. Engng. Struct. Dyn., 3, 287-296 Skinner, R.I., Robinson, W.H. & McVerry, G.H. (1991), ‘Seismic isolation in New Zealand’, Nuclear Eng. Design, 127, 281-9 Skinner, R.I., Robinson, W.H. & McVerry, G.H. (1993), “An introduction to seismic isolation”, England: Wiley & Sons Inc Skinner, R.I., Tyler, R., Heine, A. & Robinson, W.H. (1980), ‘Hysteretic dampers for the protection of structures from earthquakes’, Bulletin NZ Nat. Soc. for Earthq. Eng., 13, 22-36 Skinner, R.I., Tyler, R.G. & Hodder, S.B. (1976b) ‘Isolation of nuclear power plants from earthquake attack’, Bull. NZ. Nat. Soc. Earthq. Eng., 9, no. 4 199-204 SMiRT-11, ‘Seismic isolation and response control for nuclear and non-nuclear structures’, Structural mechanics in Reactor Technology, August 18-23, 1991, Tokyo Teramura, A., Takeda, T. K, Tsunoda, T., Seki, M., Kageyama, M. & Nohata, A. (1988), ‘Study on earthquake response characteristics of base-isolated full scale building’, Proc. 9th World Conf. on Earthq. Eng., Aug 1988, Tokyo, Japan, Vol. V, 693-8 Turkington, D.H. (1987), ‘Seismic design of bridges on lead-rubber bearings’, Research Report 87/2 Department of Civil Engineering, University of Canterbury, NZ, Feb 1987, 172 pages Tyler, R.G. (1977), ‘Dynamic tests on PTFE sliding layers under earthquake conditions’, Bull. NZ Nat. Soc. Earthq. Eng., 10, no. 3 Tyler, R.G. (1978), ‘Tapered steel energy dissipators for earthquake resistant structures’, Bull.NZ Nat.Soc.Earthq.Eng., 11, no. 4, 282-294 Tyler, R.G. (1991), ‘Rubber bearings in base-isolated structures – a summary paper’, Bull. NZ Nat. Soc. Earthq. Eng., 24, no. 3, 251-274 Tyler, R.G. & Robinson, W.H. (1984), ‘High-strain tests on lead-rubber bearings for earthquake loadings’, Bull. NZ Nat. Soc. Earthq. Eng., 17, 90-105 Tyler, R.G. & Skinner, R.I. (1977), ‘Testing of dampers for the base isolation of a proposed 4-storey building against earthquake attack’, Proc. 6th Australasian Conf. on the Mechanics of Structures and Materials, University of Canterbury, NZ, 376-382

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van Vlack, L.H. (1985), Elements of Materials Science and Engineering, Addison-Wesley Publishing Co Way, D. (1992), Base Isolation Consultants Incorporated, California, personal communication Wulff, J., Taylor, J.F. & Shaler, A.J. (1956), Metallurgy for Engineers, New York: Wiley Zayas, V., (1995), ‘Application of Seismic Isolation to Industrial Tanks’, ASME/JSME Pressure Vessels & Piping Conf., Honolulu, Session 3.2H

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ADDITIONAL RESOURCES AASHTO (1991), ‘Guide Specifications for Seismic Isolation Design’, included in Standard Specification for Seismic Design of Highway Bridges, American Association of State Highway and Transportation Officials, Washington An Acceptable Procedure for the Design and Review of California Hospital Buildings using Base Isolation, California Office of Statewide Health Planning and Development, Building Safety Board, April 1989 Anderson, T.L. Ed. (1990), ‘Theme issue: seismic isolation’, Earthquake Spectra. EERI, 6, no. 2, 438 pp. Andriono, T. & Carr, A.J. (1991a), ‘Reduction and distribution of lateral seismic inertia forces on base-isolated multi-storey structures’, Bull. NZ Nat. Soc. Earthq. Eng., 24, no. 3, 225-237 Andriono, T. & Carr. A.J. (1991b), ‘A simplified earthquake resistant design method for base-isolated multi-storey structures’, Bull. NZ Nat. Soc. Earthq. Eng., 24, no. 3, 238-250 Auckland Uniservices Ltd (1992) Base isolation using stainless steel/teflon sliding bearings: Preliminary report on Teflon/steel interface friction characteristics, report prepared for Holmes Consulting Group Auckland Uniservices Ltd (1992) Shake table tests of an isolated system using PTFE/stainless steel bearings, report prepared for Holmes Consulting Group Auckland Uniservices Ltd (1992) Size effects of PTFE bearings for aseismic base isolation, report prepared for Holmes Consulting Group AUSTROADS Bridge design code section 4: bearings and bridge joints, AUSTROADS, Sydney, Australia, 1992 Blakeley, R.W.G. (1987), ‘Analysis and design of bridges incorporating mechanical energy dissipating devices for earthquake resistance’, Proc. NZ-Japan Workshop on Base Isolation of Highway Bridges, Technology Research Centre for National Land Development, Japan, November 1987 Blakeley, R.W.G., Charleson, A.W., Hitchcock, H.C., Meggett, L.M., Priestly, M.J.N., Sharpe, R.D. & Skinner, R.I. (1979), ‘Recommendations for the design and construction of base isolated structures’, South Pacific Regional Conference on Earthquake Engineering, Wellington, NZ Borg, S.F. (1962), Fundamentals of Engineering Elasticity, van Nostrand, Princeton N.J., p 40 British Standards Institution, Steel, concrete and composite bridges: Part 9A: Code of practice for design of bearings and Part 9B: Specification for materials, manufacture and installation of bearings, British Standard BS5400:1978 Chalhoub, M.S. (1988). ‘Response of fluids in cylindrical containers and applications to base isolation’, J. Appl. Mech. Trans. ASME Chalhoub, M.S. & Kelly, J.M. (1990), ‘Shake table test of cylindrical water tanks in base-isolated structures’, J. Eng. Mech., 116, no. 7, 1451-72 Cooke, N., Carr, A.J., Moss, P.J. & Kwai, T.F. (1986), ‘The influence of non-geometric factors on the seismic behaviour of bridges on isolating bearings’, Bull. NZ Nat. Soc. Earthq. Eng., 19, No. 4, 263-71 der Kiureghian, A. (1980a), ‘Structural response to stationary excitation’, J. Eng. Mech. Div., ASCE, 106, 1195-1213 der Kiureghian, A. (1980b), ‘A response spectrum method for random vibrations’, Earthq. Eng. Res. Centre. College of Eng., University of California, Berkeley, Report No. UCB/EERC-80/15, 31 pages der Kiureghian, A. (1981), ‘A response spectrum method for random vibration analysis of MDF systems’, Int. J. Earthq. Eng.Struct. Dyn., 9, no. 5, 419-35 Dowrick, D.J. (1987), Earthquake Resistant Design for Engineers and Architects, 2nd Edition, Chichester, England: John Wiley & Sons

367

Federal Emergency Management Agency, NEHRP guidelines for the seismic rehabilitation of buildings, FEMA-273, Washington D.C., October 1997 Gueraud, R., Noel-Leroux, J.-P., Livolant, M. and Michalopoulos, A.P. (1985), ‘Seismic isolation using sliding-elastomer bearing pads’, Nucl. Eng. Des., 84, 363-77 Habibullah, A. (1986), ETABS Three dimensional analysis of buildings systems – users manual, Computers and Structures, Inc. Berkeley, CA Highways Directorate, Dept of Environment, Great Britain, Design requirements for Elastomeric bridge bearings, Technical Memorandum BE 1/76, Feb. 1976 Holmes Consulting Group (1992), Skellerup Industries lead rubber isolation bearings: Experimental properties, Report No. 3373-01, July 1992 Holmes Consulting Group (2000), Performance based evaluation of buildings – nonlinear pushover and time history analysis, Revision 5, Nov. 2000 Holmes Consulting Group (2001) In-structure damping and energy dissipation design guidelines, Revision 0, July 2001 Hüffmann, G.K. (1985), ‘Full base isolation for earthquake protection by helical springs and visco-dampers’, Nucl. Eng. Design, 84, 331-8 Hurty, W.C. & Rubinstein, M.F. (1964), Dynamics of Structures, New Jersey: Prentice-Hall Igusa, T. (1990), ‘Response characteristics of inelastic 2DOF primary-secondary system’, J. Eng. Mech., 116, No. 5, 1160-74 Igusa, T. & der Kiureghian, A. (1983), ‘Dynamics of multiply-tuned and arbitrarily supported secondary systems’, Earthq. Eng. Res. Centre, College of Eng., University of California, Berkeley, Report No. UCB/EERC-83/07, 220 pages Igusa, T. & der Kiureghian, A. (1985a), ‘Dynamic characterisation of two-degree-offreedom equipment-structure systems’, J. Eng. Mech., 111, no. 1, 1-19 Igusa, T. & der Kiureghian, A. (1985b), ‘Dynamic response of multiply supported secondary systems’, J. Eng. Mech., 111, no. 1, 20-41 Igusa, T., der Kiureghian, A. & Sackman, J.L. (1984), ‘Modal decomposition method for stationary response of non-classically damped systems’, Int. J. Earthq. Eng. Struct. Dyn., 12, no. 1, 121-136 Ikonomou, A.S. (1984), ‘Alexisismon seismic isolation levels for translational and rotational seismic input’, 8th World Conf. Earthq. Eng. San Francisco, Vol. 5, 975-82 International Meeting on Base-isolation and Passive Energy Dissipation, Universita’ degli Studi di Perugia, Assist, June 8, 1989 Kanaan, A.E. and Powell, G.H., DRAIN 2D – A general purpose computer program for dynamic analysis of inelastic plane structures, Report No. EERC 73-6 and 73-22, University of California, Berkeley (revised Sept. 1973 and Aug. 1975) Katayama, T., Kawashima, K. and Murakami, Y. (1987), ‘Current design considerations for reducing seismic lateral force of highway bridges in Japan’, Proc. NZ-Japan Workshop on Base Isolation of Highway Bridges, Technology Research Centre for National Land Development, Japan, November 1987 Kawashima, K. and Aizawa, K. (1986), ‘Earthquake response spectra taking account of number of response cycles’, Int. J. Earthq. Eng. Struct. Dyn., 14, no. 2, 185-97 Kelly, J.M. & Tsai, H.-C. (1985), ‘Seismic response of light internal equipment in base-isolated structures’, Int. J. Earthq. Eng. Struct. Dyn., 13, no. 6, 711-32 Kwai, T.F. (1986), ‘Seismic behaviour of bridges on isolating bearings’, Research Report 86/13, Department of Civil Engineering, University of Canterbury, Christchurch, NZ, May 1986, 118 pages Lee, D.M. (1980), ‘Base isolation for torsion reduction in asymmetric structures under earthquake loading’, Earthq. Eng. Struct. Dyn., 8, 349-359 Li, Li (1984), ‘Base isolation measure for aseismic buildings in China’, 8th World Conf. Earthq. Eng. San Francisco, Vol. 6, 791-8 Mayes, R.L., Buckle, I.G., Kelly, T.E. & Jones, L.R. (1992), ‘AASHTO seismic isolation design requirements for highway bridges’, J. Struct. Eng., 118, No. 1, 284-304

368

Mayes, R.L., Button, M.R. & Jones, D.M. Design issues for base isolated bridges: The 1997 revised AASHTO code requirements, Structural Engineers World Congress, San Francisco, CA, 1998, Elsevier Moss, P.J., Carr, A.J., Cooke, N. & Kwai, T.F. (1986), ‘The influence of bridge geometry on the seismic behaviour of bridges on isolating bearings’, Bull. NZ Nat. Soc. Earthq. Eng., 19, No. 4, 255-62 New Zealand Ministry of Works and Development, Design of lead-rubber bridge bearings, Civil Engineering Division, publication CDP 818/a: 1983 Park, R., Chapman, H.E., Cormack, L.G. & North, P.J. (1991), ‘New Zealand contributions to the International Workshop on the Seismic Design and Retrofitting of Reinforced Concrete Bridges, Bormio, Italy, April 2-5, 1991’, Bull. NZ. Nat. Soc. Earthq. Eng., 24, No. 2, 139-201 Penzien, J. (1969), ‘Earthquake response of irregularly-shaped buildings’, proc. 4th World Conf. Earthq. Eng. Vol. II, A-3, 75-89 Penzien, J. & Chopra, A.K. (1965), ‘Earthquake response of appendage on a multi-storey building’, Proc. 3rd World Conf. Earthq. Eng. New Zealand, Vol 2, 471-86 Proceedings of International Workshop on Recent Developments in Base-isolation Techniques for Buildings, Architectural Institute of Japan, Tokyo, 27-30 April, 1992, 335 pages Proceedings of New Zealand-Japan Workshop on Base Isolation of Highway Bridges, 1987, Technology Research Centre for National Land Development, Japan, 183 pages Proceedings of the First US-Japan Workshop on Seismic Retrofit of Bridges, December, 1990, Public Works Research Institute, Tsukuba Science City, Japan, 441 pages Proceedings of the Fourth US National Conference on Earthquake Engineering, Palm Springs. CA, 1990, Earthquake Engineering Research Institute, CA, USA Proceedings of the Ninth World Conference on Earthquake Engineering, Tokyo, 1988, 9WCEE organising committee, Japan Association for Earthquake Disaster Prevention, Tokyo, Japan, Vols V and VIII Proceedings of the Pacific Conference on Earthquake Engineering, Auckland, NZ, 1991, NZ Nat. Soc, Earthq, Eng. 3 vols Proceedings of the Tenth World Conference on Earthquake Engineering, Madrid, Spain, 1992, A.A. Balkema, Rotterdam, Vol IV Read, W.T. (1953), Dislocations in Crystals, New York: McGraw-Hill Robinson, W.H. & Gannon, C.R. (2006)“A RoBall with an Elastic Restoring Force” Bulletin of the New Zealand Society for Earthquake Engineering , Vol 39, 2006 Robinson, W.H., Gannon, C.R. & Meyer, J. (2006), ‘The RoGlider: A sliding bearing with an elastic restoring force’, Bull. NZ Soc. for Earthq. Engng, vol 39, No. 1, March 2006 RRU, Road Research Unit, National Roads Board, Wellington, NZ, Bulls. 41-44, 1979 Siebel, E. & Fangmeier, E. (1931), ‘Researches on power consumption in extrusion and punching of metal’, Mitt. K.-Wilhem-Inst. Eisenforsch Skinner, R.I. & McVerry, G.H. (1992) Report on an Introduction to Seismic Isolation, Internal IGNS Report, Institute of Geological and Nuclear Sciences, Lower Hutt, New Zealand Skinner, R.I., Skilton, D.W.C. & Laws, D.A. (1965), ‘Unbalanced buildings and buildings with light towers, under earthquake forces’, Proc. 3rd World Conf. Earthq. Eng., January 1965, Auckland, NZ, Vol. II, 586-602 Soong, T.T. (1988), ‘Active structural control in civil engineering’, Eng. Struct., 10, 74-82 Standards New Zealand (1992), Concrete structures standard: Part 1 0 The design of concrete structures, NZS 3101: Part 1:1995 Stanton, J.F. & Roeder, C.W. (1982), ‘Elastomeric bearings design, construction and materials’, National Cooperative Highway Research Program, Report 248 Su, L., Ahmadi, G. & Tadjbakhsh, I.G. (1989), ‘A comparative study of performances of various base-isolation systems: Part I: Shear beam structures’, J. Eng. Mech. Div. ASCE, 115, 1976-92 T. Igusa, T. & der Kiureghian, A. (1985), ‘Dynamic response of multiply supported secondary systems’, J. Eng. Mech., 111, no. 1, 20-41 Tajirian, Frederick, Kelly, James & Aiken, Ian D. (1990), ‘Seismic isolation for advanced nuclear power stations’, Earthquake Spectra. 6, no. 2, 371-401

369

Takayama, M., Wada, A., Akiyama, H. & Tada, H. (1988), ‘Feasibility study on base-isolated building’, proc. 9th World Conf. on Earthq. Eng., Tokyo-Kyoto, Vol. V, 669-674 Tsai, H.-C. & Kelly, J.M. (1988), ‘Non-classical damping in dynamic analysis of base-isolated structures with internal equipment’, Int. J. Earthq. Eng. Struct. Dyn., 16, no. 1, 29-43 Tsai, H.-C. & Kelly, J.M. (1989), ‘Seismic response of the superstructure and attached equipment of a base-isolated building’, Int. J. Earthq. Eng. Struct. Dyn., 18, no. 4, 551564 Tyler, R.G. (1978), ‘A tenacious base isolation system using round steel bars’, Bull. NZ Nat. Soc. for Earthq. Eng., 11, no. 4, 273-281 Uniform Building Code (UBC) (1991), Earthquake Regulations for Seismic-isolated Structures, Chapter 23, Division 3, USA Uniform Building Code Appendix Division III Earthquake Regulations for seismic-isolated structures, UBC, American Association of Building Officials, Whittier, CA 1994 Veletsos, A.S. & Ventura, C.E. (1986), ‘Modal analysis of non-classically damped linear systems’, Int. J. Earthq. Eng. Struct. Dyn., 14, no. 2, 217-43 Wilson, E.L., der Kiureghian, A. & Bayo, E.P. (1981), ‘A replacement for the SRSS method in seismic analysis’, Short Communications. Int. J. Earthq. Eng. Struct. Dyn., 9, 187-94

370