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CHICAGO SPIRE Chicago, Illinois

2011 – 2012 ASPIRE Master of Engineering Structural Design Project

Cornell University Ithaca, NY May 2012

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ASPIRE PROJECT TEAM Joseph Beaudette Cornell University Canton, New York

J. David Muench University of Massachusetts – Amherst Medway, Massachusetts

Connor Bruns Project Leader Cornell University Potomac, Maryland

Catherine T. Mulhern Project Leader Smith College Winchester, Massachusetts

Joseph A. Caccio Jr Cornell University Monroe Township, New Jersey

Stephanie Richmond Cornell University Ellicott City, Maryland

Nicholas Chack Columbia University New York, New York

Kristy L. Scales Syracuse University Berkshire, New York

Katherine McEntee Coumes Cornell University Boston Heights, Ohio

Tom Shouler Project Leader Cornell University Smithtown, New York

Jonathan Dobrin Cornell University Montreal, Quebec

Neelang Tiwari MS Ramaiah Institute of Technology Indore, M.P., India

Diana Foster Cornell University Wilmette, Illinois

Alex Vandenbergh Cornell University State College, Pennsylvania

Jeffrey Liu Pennsylvania State University Staten Island, New York

Chung Yu Wang Cornell University Taipei, Taiwan

Dan Lu Cornell University Potomac, Maryland

Muzi Zhu Tianjin University Tianjin, China

Shideh Shadravan, Ph.D. Lecturer Cornell University

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ACKNOWLEDGEMENTS The 2011-2012 Master of Engineering project team, ASPIRE, would like to thank our professional advisors from Thornton Tomasetti, Chicago: John Peronto (Associate), and Mary Williams (Senior Engineer). Mr. Peronto and Ms. Williams volunteered significant time to provide guidance and structure to our project. Their technical knowledge of structural engineering specific to tall buildings played an instrumental role in our project. ASPIRE would also like to thank our faculty advisor, Dr. Shideh Shadravan, for her daily support. Dr. Shadravan provided both project team and individual guidance vital to our development as Masters students. The design team would also like to thank the support staff of MIDAS Information Technology Co. for the assistance and troubleshooting with the MIDAS GEN 3D structural modeling software. Finally, we would like to acknowledge the Cornell University Department of Civil and Environmental Engineering faculty and staff. In particular, we would like to thank Professor Christopher Earls, Professor Ken Hover, Professor T.D. O’Rourke, Cameron Wilkens, Paul Charles, and Karen Browning.

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EXECUTIVE SUMMARY ASPIRE designed the gravity, lateral, and foundation systems, utilized finite element software for structural optimization, designed steel and concrete connections, and studied the effects of creep and shrinkage during a year-long analysis of the Chicago Spire. Preliminary analysis included research of different lateral load resisting systems in order to select the system that would best suit the needs of the structure. The lateral system chosen was a central concrete core with outriggers and belt trusses connecting the core with the exterior steel columns. The gravity design of the structure explored the use of non-composite and composite beams and columns in the Spire. ASPIRE selected steel beams with a composite metal decking system. A column load takedown based on tributary areas was used for the preliminary column design. The Chicago Spire was modeled using MIDAS Gen, a structural finite element software, to accurately understand the lateral behavior of the building. A sensitivity analysis was performed to resize the concrete core, the outriggers, and the belt truss members from the initial hand calculation sizes. Core wall thicknesses were optimized across the height of the building. Vertical columns and transfer columns were redesigned as a series of steel built-up shapes through energy optimization methods. The foundation system featured the design of a seven level below-grade parking garage and a retaining wall along the site perimeter. Rock-socketed caissons were designed to support the tower, extending from the base of the building to the bedrock 119 feet below grade. There are hundreds of connections in the Chicago Spire ranging from standard steel connections to complex designs for the outriggers and the lobby level mega-columns. Several steel-to-steel and composite connections were designed throughout the tower. A study of concrete creep and shrinkage estimated differential settlement between the concrete core and the exterior steel columns using the GL2000 model. Creep and shrinkage are dependent on variables such as loading schedule, curing period, and material properties, making it difficult to predict the actual amount of creep and shrinkage. However, failure to acknowledge these effects leads to cracks in the concrete and uneven floors. Through the course of the project, ASPIRE faced many challenges that required the design team to seek guidance from outside sources, including weekly meetings with our faculty advisor and biweekly conference calls with our professional advisors from Thornton Tomasetti. The structural design of the Chicago Spire was a collaborative effort of eighteen students and the advisors. The project provided a realistic design experience incorporating team management, iterative design, and professional reporting. For the final deliverable ASPIRE has prepared a cumulative design narrative, calculation book, and final structural drawing set.

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TABLE OF CONTENTS ASPIRE PROJECT TEAM .......................................................................................................................................................... i ACKNOWLEDGEMENTS ........................................................................................................................................................ ii EXECUTIVE SUMMARY ........................................................................................................................................................ iii TABLE OF CONTENTS............................................................................................................................................................. v LIST OF FIGURES ............................................................................................................................................................... viii8 LIST OF TABLES ...................................................................................................................................................................... xi 1.0

Introduction ............................................................................................................................................................... 1

1.1

Chicago Spire: Background and Location ................................................................................................. 2

1.2

Project Scope ........................................................................................................................................................ 3

1.3

Design Process ..................................................................................................................................................... 4

2.0

Design Criteria .......................................................................................................................................................... 5

2.1

Tall Building Design........................................................................................................................................... 5

2.2

Lateral System Determination ...................................................................................................................... 6

2.3

Typical Floors and Column Layouts ........................................................................................................... 8

2.4

Gravity Design Loads ........................................................................................................................................ 9

2.5

Lateral Design Loads ....................................................................................................................................... 10

2.6

Load Combinations .......................................................................................................................................... 13

2.7

Serviceability Requirements ........................................................................................................................ 14

3.0

Gravity Design ......................................................................................................................................................... 16

3.1

Geometry and Loading ................................................................................................................................... 17

3.2

Core Slab Design ............................................................................................................................................... 21

3.3

Link Beam Design ............................................................................................................................................. 22

3.4

Composite Beam Design ................................................................................................................................ 23

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3.5

Façade Beam Design........................................................................................................................................ 27

3.6

Column Design ................................................................................................................................................... 28

4.0 4.1

Structural System Overview ........................................................................................................................ 34

4.2

Preliminary Core Wall Design ..................................................................................................................... 36

4.3

Auxiliary Lateral Systems ............................................................................................................................. 41

4.4

Finite Element Model ...................................................................................................................................... 45

4.5

Core Wall Reinforcement Design ............................................................................................................... 52

4.6

Energy Optimization ....................................................................................................................................... 53

4.7

Eigenvalue Analysis ......................................................................................................................................... 56

5.0

Steel and Concrete Detailing ............................................................................................................................. 59

5.1

Typical Connections ........................................................................................................................................ 60

5.2

Complex Connections ..................................................................................................................................... 65

6.0

Foundation Design and Detailing .................................................................................................................... 72

6.1

Soil Properties ................................................................................................................................................... 73

6.2

Retaining Wall Design..................................................................................................................................... 74

6.3

Parking Garage Slab Design.......................................................................................................................... 75

6.4

Bell Caisson Design .......................................................................................................................................... 76

6.5

Rock-Socketed Caisson................................................................................................................................... 77

7.0

Long-Term Deflection Effects ........................................................................................................................... 82

7.1

Conceptual Summary ...................................................................................................................................... 83

7.2

Creep and Shrinkage Analysis ..................................................................................................................... 84

7.3

Conclusion and Recommendations ........................................................................................................... 90

8.0

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Lateral Load Resisting System Design .......................................................................................................... 33

References ................................................................................................................................................................ 92

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9.0

Appendix ................................................................................................................................................................... 94

9.1

Gravity Design Loads ...................................................................................................................................... 95

9.2

RWDI Recommended Wind Load .............................................................................................................. 96

9.3

Seismic Load Summary ............................................................................................................................... 101

9.4

Core Slab Design Summary ....................................................................................................................... 105

9.5

Link Beam Summary .................................................................................................................................... 106

9.6

Beam Spans and Tributary Areas ........................................................................................................... 109

9.7

Slab and Decking Summary ....................................................................................................................... 110

9.8

Composite Beam Summary ....................................................................................................................... 111

9.9

Initial Gravity Design Column Comparison ........................................................................................ 112

9.10

MIDAS Gen Gravity Loads .......................................................................................................................... 113

9.11

Column Validation Summary .................................................................................................................... 117

9.12

MIDAS Sensitivity Analyses ....................................................................................................................... 118

9.13

Core Wall Reinforcement ........................................................................................................................... 121

9.14

Creep and Shrinkage .................................................................................................................................... 122

10.0

Drawings ..................................................................................................................................... C-2.001 - S-4.004

11.0

Calculations ................................................................................................................................................. C1-C297

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LIST OF FIGURES Figure 1.1: Chicago Spire ...................................................................................................................................................... 1 Figure 1.2: Chicago Spire Site Location .......................................................................................................................... 2 Figure 1.3: Bank Location .................................................................................................................................................... 4 Figure 2.1: Outrigger and Belt Truss System Sketch (Taranath 1988, 279) ................................................... 6 Figure 2.2: RWDI Wind Tunnel versus ASCE7 Directional Procedure Forces ............................................. 11 Figure 3.1: Structural Beam Labeling System ............................................................................................................ 18 Figure 3.2: Tributary Area Breakdown for External Bays .................................................................................... 19 Figure 3.3: Tributary Area for Joist 1 ............................................................................................................................ 19 Figure 3.4: Gravity Load Paths for Design Process .................................................................................................. 20 Figure 3.5: Core Slab Detail ............................................................................................................................................... 21 Figure 3.6: Core Slab Design Locations, Directions, and Numbering ............................................................... 21 Figure 3.7: Tributary Areas for Link Beam Design. ................................................................................................. 22 Figure 3.8:Typical Composite Beam and Decking System .................................................................................... 24 Figure 3.9: Tributary Areas for the HSS Beam .......................................................................................................... 27 Figure 3.10: Steel Column Load Paths .......................................................................................................................... 29 Figure 3.11: Bank 3 Steel Column Layout.................................................................................................................... 29 Figure 3.12: Bank 1 Steel Column Layout.................................................................................................................... 30 Figure 3.13: Typical Core Column Section, Banks 1-3............................................................................................ 31 Figure 3.14: Composite Column Section ...................................................................................................................... 32 Figure 3.15: Transfer Column Orientations................................................................................................................ 32 Figure 4.1: 3D model of Outrigger and Belt Truss Locations .............................................................................. 35 Figure 4.2: Typical Core Wall Stress Diagram ........................................................................................................... 37 Figure 4.3: Distributed Lateral Load for Core Wall ................................................................................................. 39

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Figure 4.4: Outriggers Spanning Two Mechanical Floors ..................................................................................... 41 Figure 4.5: Compression Block and Steel Strain from Weak Axis Bending ................................................... 47 Figure 4.6: Initial Discontinuity Check under Gravity Loads .............................................................................. 48 Figure 4.7: a) BU1 and b) BU2 .......................................................................................................................................... 49 Figure 4.8: Discontinuity Test Comparison between Original and Final Design ........................................ 50 Figure 4.9: Deformed Shape for 50 year MRI Wind Loads (NTS) ...................................................................... 51 Figure 4.10: Optimization Material Use versus % Reduction of Drift ............................................................. 55 Figure 4.11: From Left to Right: a) Mode Shape 1; b) Mode Shape 2; c) Mode Shape 3 .......................... 58 Figure 5.1: a) Elevation and b) Plan of Typical Welded Column Splice .......................................................... 60 Figure 5.2: Elevation of Floor Joist to Girder Connection ..................................................................................... 61 Figure 5.3: Elevation of HSS Beam to Cantilever Connection.............................................................................. 61 Figure 5.4: Elevation of Built-up Column to Radial Girder and Cantilever Connection ........................... 62 Figure 5.5: Elevation of Circumferential Girder to Column Plate Connection ............................................. 63 Figure 5.6: a) Elevation and b) Section of Radial Girder to Core Wall Connection .................................... 64 Figure 5.7: 3D Rendering of Base of Mega-Column to Caisson Connection .................................................. 66 Figure 5.8: Bottom of Outrigger Connection .............................................................................................................. 67 Figure 5.9: Elevation of Outrigger and Radial Girder Connection to Concrete Core ................................. 68 Figure 5.10: a) Embedded Steel Frame and b) Cross Bracing and Point Loads .......................................... 69 Figure 5.11: 3D Rendering of Mega-Column Connection...................................................................................... 70 Figure 5.12: Singular Transfer Column Connection Front and Side Elevation ............................................ 71 Figure 5.13: Split Transfer Column Connection Front and Side Elevation .................................................... 71 Figure 6.1: Provided Soil Profile for Foundation Design....................................................................................... 73 Figure 6.2: Failure Modes for Retaining Wall Design ............................................................................................. 74 Figure 6.3: Elevation of Bell Caissons ........................................................................................................................... 76

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Figure 6.4: Elevation of Rock-Socketed Caissons ..................................................................................................... 77 Figure 6.5: Detail of Caisson .............................................................................................................................................. 78 Figure 6.6: Limit states from Left to Right: a) Stress, b) Settlement and c) Uplift ...................................... 78 Figure 6.7: Elevation of Ring Beam ................................................................................................................................ 79 Figure 6.8: Plan View of Ring Beam Resistance to Soil Pressure ....................................................................... 79 Figure 6.9: a) Compression and b) Tension Stresses in Rock-Socketed Caisson ........................................ 80 Figure 7.1: Concrete Strength Gain with Time .......................................................................................................... 84 Figure 7.2: Concrete Elastic Modulus Gain with Time ........................................................................................... 84 Figure 7.3: Initial Strength Gain of Concrete for Various Cement Types........................................................ 87 Figure 7.4: Typical Strain Values for a Single Floor ................................................................................................ 88 Figure 7.5: Core Deformations per Floor ..................................................................................................................... 89 Figure 7.6: Total Core Displacement over Time ....................................................................................................... 91 Figure 9.1: Built Up Column Sensitivity Results to Dead Load ........................................................................ 119 Figure 9.2: Core Wall Thickness Sensitivity Results to Dead Load ................................................................ 120 Figure 9.3: Belt Truss and Outrigger Sensitivity ................................................................................................... 120

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LIST OF TABLES Table 1.1: Floor Bank Summary ........................................................................................................................................ 4 Table 2.1: Summary of Exterior Columns per Bank .................................................................................................. 8 Table 2.2: Unfactored Design Loads per ASCE 7-05 (psf)....................................................................................... 9 Table 2.3: Seismic Lateral Forces.................................................................................................................................... 12 Table 3.1: Typical Values for Vibrational Analysis Calculations ........................................................................ 26 Table 3.2: Summary of Estimated Vibrations ............................................................................................................ 26 Table 3.3: HSS Beam Design Summary ......................................................................................................................... 27 Table 3.4: Factored Loads from Gravity at Ground Level ..................................................................................... 31 Table 4.1: Critical Core Wall Unfactored Design Loads ......................................................................................... 36 Table 4.2: Controlling Stresses for Core Wall Design ............................................................................................. 38 Table 4.3: Initial Core Wall Reinforcement Requirements .................................................................................. 40 Table 4.4: Initial Core Thickness by Bank ................................................................................................................... 40 Table 4.5: Summary of Column Properties for each Column Section .............................................................. 43 Table 4.6: Stress Reduction in each Bank from Outriggers .................................................................................. 43 Table 4.7: Summary of Core Wall Thicknesses with Outriggers and Columns ............................................ 43 Table 4.8: System Stiffness Summary ........................................................................................................................... 44 Table 4.9: Initial MIDAS Model Element Properties ............................................................................................... 45 Table 4.10: Final MIDAS Model Element Properties ............................................................................................... 48 Table 4.11: Initial and Final MIDAS Results ............................................................................................................... 50 Table 4.12: Optimization Results for Δ = h/500 ...................................................................................................... 54 Table 4.13: Material Savings for Δ = h/500 ............................................................................................................... 55 Table 4.14: Natural Frequency and Period of first 15 mode shapes ................................................................ 56 Table 4.15: Modal Mass Participation ........................................................................................................................... 57

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Table 6.1: Critical Von Mises Stresses from ABAQUS Model ............................................................................... 81 Table 7.1: Cement Type Deformation Sensitivity Analysis .................................................................................. 86 Table 7.2: Core Total Deformations ............................................................................................................................... 88 Table 7.3: 20-Year Deformation Comparisons .......................................................................................................... 90 Table 9.1: RWDI Wind Load Combinations ................................................................................................................ 96 Table 9.2: RWDI Provided Wind Forces and Torsional Moments ..................................................................... 97 Table 9.3: Link Beam Dimensions ............................................................................................................................... 106 Table 9.4: Residential and Lobby Link Beam Summary ..................................................................................... 107 Table 9.5: Mechanical Floor Link Beam Summary ............................................................................................... 108 Table 9.6: Decking and Slab Thickness Summary for Composite Beam System ...................................... 110 Table 9.7: Unfactored Dead Load for Composite Beam System ...................................................................... 110 Table 9.8: Composite Beam Summary ....................................................................................................................... 111 Table 9.9: Initial Composite and Steel Column Comparison............................................................................. 112 Table 9.10: MIDAS Gen Unfactored Gravity Loads (kips / node) ................................................................... 113 Table 9.11: Composite and Steel Shapes for Lateral Design Column Validation...................................... 117 Table 9.12: Built-up Steel and Concrete Properties ............................................................................................. 118 Table 9.13: Sensitivity Analyses Element Properties .......................................................................................... 119 Table 9.14: Core Wall Reinforcement Details ......................................................................................................... 121 Table 9.15: Concrete Core Properties ........................................................................................................................ 126 Table 9.16: Steel Deflection Summary ....................................................................................................................... 126 Table 9.17: Humidity Data for Chicago ...................................................................................................................... 127 Table 9.18: Concrete Reinforcement Data ............................................................................................................... 127 Table 9.19: 20 Year Concrete Deflection................................................................................................................... 128

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1.0 INTRODUCTION

1.0 Introduction The 2011-2012 Master of Engineering Structural Design Project was the structural design of the Chicago Spire (Figure 1.1), located on the west side of Lake Shore Drive in Chicago, Illinois. The project was provided by John Peronto, P.E. and Mary Williams, P.E. of Thornton Tomasetti’s Chicago office. Cornell University Lecturer Dr. Shideh Shadravan was the project advisor. The project team consisted of sixteen Master of Engineering students and two undergraduates. The team members provided a unique assortment of design experience, academic specialty, and cultural background. This resulted in a realistic, professional experience similarly found at a design firm.

Figure 1.1: Chicago Spire

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1.0 INTRODUCTION

1.1 Chicago Spire: Background and Location The Chicago Spire is 2,000 ft tall on a strip of land between the Ogden Slip and the mouth of the Chicago River (Figure 1.2). The tower contains approximately 3 million square feet of upscale condominiums and amenities. The basement has 7 below-grade parking levels on top of rock socketed caissons. The structural engineer of record was Thornton Tomasetti. The project was put on hold in 2008 with only its foundation completed. Upon completion, the Chicago Spire would be the tallest building in the Western Hemisphere. Spanish architect Santiago Calatrava was the architect and engineer for the project. The design highlights a spiraling exterior supported by an exterior column grid and a concrete core. Calatrava compared the design to an imaginary smoke stack from a campfire lit by the indigenous Native American tribes of Chicago.

Figure 1.2: Chicago Spire Site Location

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1.0 INTRODUCTION

1.2 Project Scope The Master of Engineering team was charged with providing a complete structural design of the gravity and lateral system as well as foundation design, connections and details, and an analysis of the effects from creep and shrinkage. The project required the eighteen team members to collaborate as sub-teams to complete assigned deliverables, utilizing full engineering knowledge and experience. The design of the cylindrical superstructure entailed expanding design limits into unfamiliar areas through self-learning and provided resources. The design project was split into ten deliverables through the academic school year. Deliverables include submittal of white-paper reports, annotated engineering calculations, structural drawings, and finite element models. Local and professional advisors provided design support through biweekly teleconferences and daily correspondence. Structural design was supplemented by academic field trips pertinent to tall building design. ASPIRE traveled to New York City in November of 2011. This trip included a presentation by Silverstein Properties and a site tour of Four World Trade Center, a 72-story skyscraper designed by Leslie E. Robertson and Associates. In December 2011, team members visited the Rowan, Williams, Davies, Inc. (RWDI) wind tunnel testing facility in Guelph, Ontario, Canada. RWDI is a leader in the field of wind tunnel testing, and has performed dynamic analysis for some of the world’s tallest structures, including the Chicago Spire.

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1.0 INTRODUCTION

Bank 3

Initial design consisted of determining a lateral system and overall design criteria including serviceability limits and load conditions. The structure is split into four banks (Figure 1.3). The bottom of each bank consists of a lobby level and the top of each bank consists of two mechanical levels. Bank 1 is an exception where the ground floor lobby spans four floors for a large open space atrium. Bank 4 was further split into two sub-banks for design optimization as the structure’s tapering increases significantly at floor 139. Table 1.1 summarizes the floor breakup per bank.

Bank 2

The structural design process began in August of 2011. Thornton Tomasetti provided ASPIRE with architectural geometry and a structural elevation. A geotechnical report from STS Consultants, LTD and wind tunnel testing results from RWDI were also provided. Co-project managers were elected to oversee and organize the design approach for each deliverable. They held weekly meetings, compiled deliverable submissions, critiqued design tools, and served as the primary liaison to the project advisors.

Bank 4

1.3 Design Process

Bank 1 2 3 4.1 4.2

Floors 1-39 40-73 74-110 111-129 130-147

Revit Structure was used to construct a preliminary three dimensional model. Element shapes and sizes were updated throughout the design process. Initially, Revit was utilized to produce structural drawings; however, AutoCAD 2012 was ultimately used for the final drawings due to inadequate computer graphic and RAM resources for Revit.

Bank 1

Table 1.1: Floor Bank Summary

Figure 1.3: Bank Location

All structural elements were initially designed for gravity forces, and ultimately optimized using MIDAS Gen, a three dimensional structural software tool. The project highlighted team interaction and collaboration, and iterative design. Sub-group communication was a necessity as sizes, loads, and dimensions were continuously changing. Final element sizes and critical loads were used to design typical connections.

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2.0 DESIGN CRITERIA

2.0 Design Criteria Preliminary analyses required ASPIRE to study relevant tall building design. In adjunction with architectural constraints, this research was utilized to select specific structural systems for gravity and lateral systems.

2.1 Tall Building Design For years engineers have furthered the practice of structural engineering, designing increasingly taller skyscrapers to meet the demanding vision of architects and owners. As buildings grow, more efficient, specialized structural systems are needed to handle the loads. One of the first buildings to clearly demonstrate the potential of the skyscraper was the Empire State Building, reaching 1250 feet in 1931 through the use of a standard riveted steel frame with simple portal bracing (Binder 2006, 42). Engineering has progressed onward from this simple system, reducing the amount of material used while simultaneously increasing the height. One way of achieving this is through the use of a high-density concrete core with outriggers and belt trusses at mechanical floors. This strategy has allowed buildings like the Shanghai World Finance Center and the Burj Khalifa to soar to heights over one and two thousand feet, respectively. The Chicago Spire’s specifications are demanding, defining a building that is truly unique. Outriggers and belt trusses for lateral restraint are limited to the mechanical floors, isolated throughout the structures elevation. The residential floors contain spacious floor plans with evenly spaced columns in a ring around the core. Cantilever beams extend from the radial frame to the façade, allowing for unobstructed views in all directions. For a building as slender as the Chicago Spire, the lateral system is often the limiting factor in selecting a design. As buildings increase in height, the structural frames continue to decrease in average weight per square foot. This is possible due to interaction between interior/exterior components; high strength low-alloy steel; composite construction; wind tunnel tests; and concrete improvements in reinforcement and strength. A vital piece of the Chicago Spire’s design is a system to resist lateral loads. Lateral loads are more variable than gravity loads and increase significantly with building height. Lateral systems are designed with the tower’s strength, stability, and rigidity in mind. For tall buildings, serviceability usually controls the design. Inter-story deflection, also called floor-to-floor drift, and dynamic effects, such as vortex shedding and vibrations, are concerns for slender buildings.

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2.0 DESIGN CRITERIA

2.2 Lateral System Determination The Chicago Spire’s architecture plays a significant role in selecting a feasible lateral system. Clearance requirements in residential and lobby floors limit regions where the exterior column grid and concrete core can integrate to resist lateral forces. The two primary components of the chosen lateral system are the high-strength concrete core and the exterior column system.

2.2.1 Outriggers and Belt Trusses Mechanical floors will include outriggers and belt trusses to effectively stiffen the structure and incorporate the exterior column grid with the core. The outriggers will span from each exterior column to the core wall two floors above. Belt trusses will circle the structure at the same floors. Belt trusses enable the column grid to systematically resist induced shear forces and moments. The lack of architectural constraints in mechanical floors allows for large steel members to span in regions normally occupied in residential floors. The outriggers and belt trusses are effective in reducing both inter-story and global drift. Additionally, these transfer a 20-40% of the exterior axial forces into the concrete core. Outriggers and belt trusses are extremely difficult and timely to construct. However given the architectural constraints of the project, they are a necessity to meet serviceability requirements. Construction scheduling must consider the delay and dead time when outriggers floors are erected. Figure 2.1 shows an outrigger and belt truss system sketch for a typical lateral restraint system.

Figure 2.1: Outrigger and Belt Truss System Sketch (Taranath 1988, 279)

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2.0 DESIGN CRITERIA

2.2.2 Core and Shear Walls The core of the Chicago Spire will consist of thick concrete shear walls integrated through link beams and a reinforced concrete, two-way slab. Concrete is a versatile building material with its own strengths and weaknesses. Concrete is economic, fire-resistant, and long-lasting. Concrete walls can be almost any shape or size as long as they harden uniformly to limit cracking. A disadvantage of concrete is the increased section required to support a specified load. However, this larger section can increase structure stiffness, decrease global deflection, and minimize floor vibrations. Another weakness of concrete is the construction time involved with slip formwork erection, pumping, pouring, and curing. The increased construction time results in increased labor costs, which should be balanced by material savings. One important consideration for a concrete core is the effect of creep and shrinkage. With steel or composite columns, the vertical elements will ultimately experience differential settlement. This must be pre-calculated and accounted for during construction.

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2.0 DESIGN CRITERIA

2.3 Typical Floors and Column Layouts Four typical floors can be used to fully represent the loading in the Chicago Spire. These typical floors include the lobby and amenities, residential floors, mechanical floors, and the parking floors. The number of columns per bank decreases to optimize column sizing and spacing (Table 2.1). Load diagrams have been prepared for each of the typical floors selected and can be viewed in S0.001. Table 2.1: Summary of Exterior Columns per Bank Bank 1 2 3 4.1 4.2

8

Columns 21 21 14 14 14

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2.0 DESIGN CRITERIA

2.4 Gravity Design Loads Gravity loads include element self-weight as well as superimposed dead loads and live loads as defined by ASCE 7-05. Loading diagrams look specifically at loads acting on the floor slabs; detailing which load is applied in a certain area. This information is used to design beams, columns, and slabs for gravity loads. Loads from column self-weight, lateral forces, and façade line loads are not included in loading diagrams. Dead loads include self-weight of reinforced concrete slabs and composite decking when applicable. Values were updated throughout the design process once all slab thicknesses, concrete densities, and decking specifications were made. Table 2.2 summarizes the unfactored gravity forces used for design. Appendix 9.1 displays the calculations for the specific loads in Table 2.2. Table 2.2: Unfactored Design Loads per ASCE 7-05 (psf) Dead Load

Superimposed Dead Load

Live Load

Lobby Residential Mechanical Parking Mechanical Core

32 33 39 150 55

57 34 10 42 10

100 55 240 40 240

Residential and Lobby Core

55

57

100

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2.0 DESIGN CRITERIA

2.5 Lateral Design Loads Lateral loads are extremely important in the design of tall buildings, and they are the controlling factor the Chicago Spire design. Tall and slender structures such as the Spire are extremely susceptible to wind and seismic forces. ASCE 7-10 was used to estimate wind and seismic forces. Wind tunnel testing results were also provided and used in comparison to the code defined wind loads.

2.5.1 ASCE 7-10 Wind Loads Chapter 26 was utilized to calculate various factors, which include basic wind speed, wind directionality factor, exposure category, topographic factor, gust effect factor, and enclosure classification. Chapter 26 calculations can be found in Calculation 2.2.1. The following assumptions were made throughout the calculation. Basic wind speed, V = 120 mph

ASCE 7-10, 26.5-1B

Wind directionality factor, Kd = 0.85

ASCE 7-10, 26.2-1

Exposure Category D (Flat, unobstructed wind over water)

ASCE 7-10, 26.7

Building, Enclosed

ASCE 7-10, 26.2

Occupancy Category IV (Iconic structure)

ASCE 7-10, 1.5-1

These factors are then used in the Directional Procedure in Chapter 27 to calculate windward and leeward pressures. The main wind force-resisting system from 27.4 is used to calculate the wind pressures for windward and leeward walls. The code calculated wind pressures were multiplied by respective lateral tributary areas to produce a net wind force at each floor. Loads from ASCE 7-10 are very conservative and ambiguous for the Chicago Spire. The calculations were performed to provide baseline values to compare against wind tunnel data. For code calculations, the building is assumed to be prismatic and regular-shape, so that windward, leeward, and side walls can be identified. Effects like vortex shedding are not addressed. The ASCE 7-10 wind loads are calculated with basic wind speeds corresponding to a mean recurrence interval of 1700 years. These results should be considered for design only. ASCE 7-10, Figure CC-3 provides 50-year MRI basic wind speeds which can be used for serviceability criteria.

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2.0 DESIGN CRITERIA

2.5.2 RWDI Wind Tunnel Forces Thornton Tomasetti provided ASPIRE with a wind tunnel analysis of the Chicago Spire. The report, prepared by RWDI, contained forces (Fx and Fy) and torsional moments (Mz) for each floor. The report lists recommended wind load combinations which will be discussed in a later section. The maximum resultant of the combinations for Fx and Fy were plotted against the ASCE 7-10 directional procedure forces. Figure 2.2 shows these results and a confirmation that wind tunnel forces should be used for strength design and serviceability criteria. Appendix 9.2 shows all RWDI Wind Tunnel Data and recommended wind load combinations. The RWDI forces are for a 100-year MRI. For checking serviceability criteria, a reduction factor of 0.83 is used to estimate 50-year MRI forces.

Figure 2.2: RWDI Wind Tunnel versus ASCE7 Directional Procedure Forces

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2.0 DESIGN CRITERIA

2.5.3 ASCE 7-10 Seismic Load Calculations ASCE 7-10, Chapters 11 and 12 were used to estimate seismic loads for the Chicago Spire. The complete seismic calculations are in Calculation 2.3. The overall weight of the building was needed to perform seismic loading analysis. The building is broken down into 8 Mechanical floors, 8 Lobby floors, and 131 Residential floors for a total of 147 floors. The effective seismic weight, W, was calculated using an initial estimate for core wall, column, and cladding self-weight. Following the design of columns and core walls, the effective weight and resulting seismic forces were updated. The effective seismic weight was found to be 650,000 kips. The base shear was calculated assuming a seismic response coefficient, Cs, of 0.10. The following formulas were used to determine the seismic lateral loads at each floor. ASCE 7-10, 12.8-11 (

∑

∑

)

ASCE 7-10, 12.8-12 ASCE 7-10, 12.8-13

where Fx ,Fi = lateral seismic forces induced at any level i or x Cvx = vertical distribution factor V = total design lateral base shear wi , wx = portion of the total effective seismic weight of the structure located to level i or x hi , hx are the height from the base to level i or x k= exponent related to the structure period Vx = design story shear at any story Table 2.3 summarizes the results at the base and top floor of the structure. See Appendix 9.3 for all lateral forces, story shears, and moments.

Table 2.3: Seismic Lateral Forces

12

Floor Level, x

Lateral Force Fx, kips

Story Shear Vx, kips

Moment Mx, ft-kips

1

0.01

6,563

8.82 x 106

147

213.4

213

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2.0 DESIGN CRITERIA

2.6 Load Combinations The following load combinations from ASCE 7-05, 2.3.2 were used throughout the design process. Load combinations were used in both engineering hand calculations and in the MIDAS Gen 3D model. The RWDI wind tunnel recommended combinations from Appendix 9.2 were used as a sublevel of load combinations when wind applied. 1.4D 1.2D + 1.6L 1.2D + 1.6W + 1.0L 1.2D + 1.0E + 1.0L .9D + 1.6W .9D + 1.0E

The following load combinations from ASCE 7-05, CC.1.2 were used in for drift serviceability criteria. The RWDI wind tunnel recommended combinations from Table 9.1 were used as a sublevel of load combinations with a reduction factor of 1.20.

1.0D + .5L + .7W

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2.0 DESIGN CRITERIA

2.7 Serviceability Requirements Serviceability limit states are the conditions in which the routine functions of a structure are impaired because of local deformation of building components or because of occupant discomfort. These limit states are affected by static loads from the occupants and their possessions, snow or rain on roofs, temperature, dynamic loads from human activity, wind, or the operation of the building service equipment. Serviceability criteria for the Chicago Spire should be selected from the limits specified in design codes to ensure both functional as well as economical design when constructing a building with desirable retail space. Serviceability criteria for the Chicago Spire are controlled by:    

Excessive deflection or rotation Excessive vibrations Total and local (floor-to-floor) building drift Tower accelerations

The criteria used depend on the function of the building. General guidance on serviceability limits is provided in sections CC1.1, CC1.2, and CC1.3 of ASCE 7-10.

2.7.1 Deflection Vertical deflections arise primarily from:   

Gravity loads (dead loads and live loads) Effects of temperature, creep and differential settlement Construction tolerances and errors

For the Chicago Spire, the deflection limit for horizontal members is as follows: Δ ≤ L/360

ASCE 7-10, CC1.1

These limits will prevent any visible deflection or impairment of window and door operation. Snow loads are negligible in the Chicago Spire, thus only dead and live loads are considered when meeting deflection criteria. The suggested load combination is: D+L

ASCE 7-10, CC-1a

Member depths are often restricted due to architectural constraints. If these members are unable to stay within the serviceability requirements, a predetermined camber will be specified to counteract anticipated deflection. Camber will be a powerful tool when approaching the long spanning cantilever beams extending from the radial column grid.

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2.7.2 Vibration Analysis Intense floor or building vibrations can cause discomfort to the building occupants. Some ways to mitigate the vibrations include using a dampening system or limiting the deflection to an absolute value that is independent of span. The acceleration limit for continuous vibrations throughout the building will be the following: a ≤ 0.005*g

ASCE 7-10, CC1.3

where

a = continuous vibration acceleration g = gravity

2.7.3 Total and Story Drift Serviceability drift is a key component in the ultimate design of the Chicago Spire. At roughly 2,000 feet tall, the inter-story and total building drift can significantly affect occupant comfort, reducing high-end real estate rates. The total and local drift limit is of the following order: Δ ≤ h / 400

ASCE 7-10, CC1.2

where

h = building or story height Serviceability drift also depends on the mean recurrence interval (MRI) and the respective importance factor applied to the lateral loads. The design considers a 50-year MRI (annual probability of 0.01) because of the height and slenderness of the structure. A combination of geographical conditions, surveying data, and client preference will determine an importance factor for this 50-year MRI.

2.7.4 Other Considerations The design considers time dependent serviceability criteria. Structural elements are expected to show long term deformations due to creep and shrinkage, which occurs at a slow but persistent rate over a long period of time. The thick concrete core will ultimately lead to significantly more deflection than the exterior columns. This deformation can be limited and accounted for during construction.

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3.0 GRAVITY DESIGN

3.0 Gravity Design ASPIRE considered several alternatives for the Chicago Spire initial gravity design. Steel, concrete, and composite systems were compared using both qualitative and quantitative methods to determine an ultimate design. The final Chicago Spire gravity design includes composite steel floor deck systems, reinforced concrete slabs within the core structure, steel built-up columns, and reinforced concrete link beams. For floor beam design, both non-composite and composite systems were considered. The column design uses built-up steel columns. Built-up steel sizes vary as building height increases. Reinforced concrete was used for the core slab and core link beams, Initial gravity design does not consider the influence of lateral loads. The gravity system was designed using conservative approaches to account for future changes and the contribution from wind and seismic forces.

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3.1 Geometry and Loading The Chicago Spire geometry is based on provided architectural drawings as well as team assumptions based on design calculations and the elevation drawings. Assumptions for the Chicago Spire geometry and loading are listed below.      

Beam spans and associated tributary areas are calculated from the Revit model. Two cantilever beam spans (short and long) are considered for each typical floor plan. The spans are estimated from the provided structural elevation drawing. Exterior face consists of curved, load bearing HSS beams. Mechanical and lobby floor plans have three joists per internal bay. Residential floor plans have two joists per internal bay. Radial girders and cantilever beams are fixed-fixed to reduce net moment at the respective connection. All other beam connections are considered to be simply supported.

3.1.1 Tributary Areas Joists, circumferential girders, angled girders, and HSS beams bear loads from the design loads shown in Table 2.2 (pg 9). A floor beam denomination system is shown in Figure 3.1. Calculation 3.1 displays the calculation steps for gravity design tributary area. More specific assumptions for the tributary area calculations are listed below.   

  

Rectangular shapes are used to estimate all tributary areas. Column-to-façade distance is assumed to be constant throughout the rise of the tower. Typical floor plans are considered to have internal bays and external bays. o Internal bays consist of floor joists and radial girders. o External bays consist of cantilevers, HSS beams, and angled girders. HSS 1 extends from the short cantilever to the end of the long cantilever and back down to another short cantilever. HSS 2 spans between two short cantilevers. See Figure 3.2. In external bays bounded by HSS 1, the HSS beam bears ¼ of the area, the angled girder bears ½ of the area, and the circumferential girders bears ¼ of the area. See Figure 3.2. In external bays bounded by HSS 2, the HSS beam bears ½ of the area, and the column girder bears ½ the area. See Figure 3.2.

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3.0 GRAVITY DESIGN

HSS 1

HSS 2

Figure 3.1: Structural Beam Labeling System

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3.0 GRAVITY DESIGN

Figure 3.2: Tributary Area Breakdown for External Bays Figure 3.3 shows the tributary area for a typical joist. The base length is the average adjacent joist lengths, and the height is the beam spacing.

Figure 3.3: Tributary Area for Joist 1 Appendix 9.4 summarizes all design spans and tributary areas for the Chicago Spire.

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3.0 GRAVITY DESIGN

3.1.2 Loading and Load Paths The following equations are used for the deflection serviceability requirements and the gravity beam design. Serviceability:

D+L

Strength Design: 1.2D + 1.6L There are several load paths considered for the gravity design process. Figure 3.4 summarizes the paths for the gravity loads summarized in Table 2.2 (pg 9). The façade load was assumed to be 10 psf and the floor-to-floor height of 13 ft, 2 in. This results in a line load of 132 plf.

DL, LL, SDL (psf) Façade (plf)

HSS Beams

Angled Girders

Column Girders

Joists

Radial Girders

Cantilevers

Link Beams Columns

Core Walls Foundation

Figure 3.4: Gravity Load Paths for Design Process

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3.0 GRAVITY DESIGN

3.2 Core Slab Design The core slabs were designed as reinforced concrete floors. The core requires a large number of voids for elevator shafts and mechanical openings. ASPIRE used reinforced concrete instead of composite decks to account for these different span lengths and configurations. Slab thicknesses and reinforcement was determined to provide appropriate moment capacity. Loads for core slab design are shown in Table 2.2 (pg 9). For each bank, four typical slabs were designed. These slabs are labeled in Figure 3.6. The numbering is identical for the same locations on different banks. Slab design 4 is assumed to be typical for slab sections not included in the numbering or not identical to other numbered slabs. Appendix 9.4 summarizes the core slab reinforcement. Calculation 3.2.1 shows the design steps following ACI 318-08 for one-direction slabs.

Figure 3.5: Core Slab Detail

Figure 3.6: Core Slab Design Locations, Directions, and Numbering

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3.0 GRAVITY DESIGN

3.3 Link Beam Design Link beam sizes were determined by the loading condition from Table 2.2, pg 9. Five different link beams were selected from plan to be designed. These designs can then be extrapolated to size the remaining link beams within the core. The tributary areas were estimated fairly conservatively (Figure 3.7).

Figure 3.7: Tributary Areas for Link Beam Design. There were several assumptions used to carry out the design of the link beams within the core structure:    

Length of curved beams equal to length of arc centerline. Steel to concrete connections from radial girders fixed to curved beams act as point loads on the centerline of the beam. All beams are simply supported. Sand-lightweight concrete is used throughout.

Appendix 9.5 summarizes the link beam geometry and results. The curved beams were the most difficult to design given the amount of torsion induced by the radial shape. Calculation 3.2.2 shows the link beam design steps following ACI 318.

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3.0 GRAVITY DESIGN

3.4 Composite Beam Design Composite beam design was used for all above grade beam systems surrounding the concrete core. The initial gravity design compared a non-composite beam system to a composite system. The composite system required smaller W-shapes and less concrete for the slabs.

3.4.1 Slab and Decking Specific deck sizes were selected from the Vulcraft Steel Roof & Floor Deck, 2008 manual with respect to constructability as well as minimizing the material weight. Specific assumptions for the slab and decking calculations are listed below.    

Floor-to-ceiling heights must remain constant in all residential and lobby levels. When calculating weight of the steel, steel beam systems were modeled as a group of W12x29 shapes. Weight of steel is assumed to be 500 pcf. Decking system is simply supported over steel framing as a continuous beam.

Decking runs perpendicular to all floor joists and circumferential girders. Decking comes in 30 in or 36 in widths and can be either shop or field cut to meet the architectural requirements of the slab edge. Appendix 9.7 summarizes the decking and slab thickness used for composite beam design. Calculation 3.3.1 summarizes the composite deck sizing calculations.

3.4.2 Composite Beam Sizing The design procedure found in Bungale S. Taranath’s Steel, Concrete, & Composite Design of Tall Buildings was used in conjunction with Chapter I of the AISC Steel Construction Manual. Sample composite beam calculations can be found in Calculation 3.3.2. Assumptions for composite design are listed below.       

Unshored construction will be used and all pre-composite loading conditions must be considered. Area of corrugated steel decking and concrete between top of flange and top of decking will be considered negligible. All shear studs will be ¾ in. diameter and 3 in. long before welded to steel beam. Lateral-torsional buckling is not a concern for the completed structure. Angled girder design is assumed to be perpendicular to the decking direction. Lightweight concrete, ρc = 110 pcf, is used for all floor slabs. 28-day compressive strength of concrete, f’c = 4000 psi

A composite beam system integrates the steel W-shapes, metal decking, and concrete slab through shear studs. The addition of the concrete slab raises the neutral axis and increases the available system section modulus. Figure 3.8 shows a typical composite beam and decking system for decking perpendicular to the beam. ASPIRE

23

3.0 GRAVITY DESIGN The radial girders on mechanical floors were designed for weak axis bending. These girders are rotated 90 degrees to increase the constructability and strength of the outrigger connections. Appendix 9.5 summarizes the preliminary composite beam design

Figure 3.8:Typical Composite Beam and Decking System

3.4.3 Serviceability 3.4.3.1

Deflection

All beams were checked under pre-composite and post-composite load conditions against deflection requirements set in Section 2.7.1. For uniformly distributed beams modeled as simply supported, deflection was calculated using the following equation:

 max 

where

5wl 4 384 EI

I = Is for pre-composite I = Ieff for post-composite

The following checks were made against the pre- and post-composite deflection.  

24

If the pre-composite loading exceeded the allowable deflection, camber was specified for 75% of Δmax. If the post-composite loading exceeded the allowable deflection, a stiffer steel shape was chosen.

ASPIRE

3.0 GRAVITY DESIGN Cantilever beams and radial girders received point loads from adjacent beam members. Beam deflection was calculated using the principles of superposition from separate scenarios of single point loads.

3.4.3.2

Vibration Analysis

Vibration from human movement and walking excitation must be considered as a serviceability design requirement for the Chicago Spire’s gravity design. Serviceability loads and beam deflections are used to calculate the floor’s natural frequency per AISC Design Guide 11, equation 3.3:

f n  0.18

g total

AISC Design 11, 3.3

The following assumptions are made throughout the vibration analysis test.   

Vertical column frequencies are not taken into account Beam and decking are non-continuous over the bays. This assumes that each bay is independent from the others. Transformed moment of inertia must be used for deflection equations.

The natural frequency, fn, is used to calculate the ratio between the peak acceleration and gravity (ap/g), which is compared to the acceleration limit (ao/g) based on the type of occupancy. For the Chicago Spire, the occupancy condition is residential, and per AISC Design Guide 11, Table 4.1 the acceleration limit is 0.5%. The peak acceleration is calculated from equation 4.1:

ap g



Po  e0.35 fn  W

AISC Design 11, 4.1

where Po = excitation β = modal damping ratio W = effective weight supported by the component. Peak acceleration from Equation 4.1 is compared to the acceleration limits set in Section 2.7.2. The typical values that were used in calculations are shown in Table 3.1.

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3.0 GRAVITY DESIGN Table 3.1: Typical Values for Vibrational Analysis Calculations Residential

Mechanical

Lobby

2

3

3

1.5

2

1.5

1.78 0.253 60

3.29 0.292 65

1.78 0.253 60

0.2 65

0.2 65

0.2 65

Number of joists framing into girders Thickness of corrugation Weight of decking Theoretical volume of concrete Total Load

Units

in psf ft3/ft2 psf

From AISC Design Guide 11, Table 4.1

β Po

lbs

When a member or bay is subjected to excitation at its natural frequency, fn, the beam will reach its maximum vibrational displacements. The natural frequencies of members depend on their stiffness and mass. Members analyzed individually showed a natural frequency in the range of 3 Hz to 22 Hz; however, when analyzed as a combined system yielded natural frequencies between 3 Hz and 10 Hz. The peak acceleration for the Chicago Spire was found to be between 0.040% and 0.246%. See Table 3.2 for the full range of values. Table 3.2: Summary of Estimated Vibrations Type Residential Mechanical Lobby Residential Mechanical Lobby Residential Mechanical Lobby Residential -1 Residential -2

Bank

ap/g

ao/g

1 1 1 2 2 2 3 3 3 4 4

0.332% 0.099% 0.199% 0.246% 0.040% 0.086% 0.194% 0.043% 0.073% 0.146% 0.130%

0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50%

A vibration analysis for serviceability requirements can be found in Calculation 3.3.3.

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3.0 GRAVITY DESIGN

3.5 Façade Beam Design The beams running along the slab edge support the façade and design loads from Table 2.2. These beams were designed as hollow structural section (HSS) to account for large, curved spans. Section geometry of HSS beams allows for increased constructability and resistance to torsion. Blodgett’s Design of Welded Structures was used to calculate end torsion of the curved beams. The following assumptions were made throughout the HSS beam design process.  

Tributary area was calculated from the Revit model (Figure 3.9) Other than torsion at the beam ends and angular twist, all other calculations for bending moment and shear capacity assume that the beam is straight.

Figure 3.9: Tributary Areas for the HSS Beam

A preliminary section was chosen for all perimeter façade beams. Table 3.3 summarizes this design. Table 3.3: HSS Beam Design Summary Selected Section

HSS 20x12x1/2

Self-Weight

103.3 lb/ft

Span

78.7 ft

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3.6 Column Design Vertical columns and slanted transfer columns were selected given the gravity design load combination in Section 3.1.2. Axial loads for column design were calculated using a column load takedown. The structure was split fourteen subsections for the column schedule. Initial composite and steel shapes were chosen for these locations. These sizes serve as a baseline for structural software modeling and energy optimization. The column sizes are expected to change multiple times once lateral forces are analyzed for strength and serviceability. All vertical concrete has a 28-day compressive strength of 14,000 psi. High density concrete, ρc=160 pcf, is also used in all composite columns and the concrete core wall. Design tools for axial forces, vertical columns sizing and transfer columns sizing can be found in Calculation 3.4.

3.6.1 Column Load Takedown A column load takedown tool calculated axial forces given factored design loads and respective tributary areas. Axial forces were calculated for the exterior columns and the core bearing walls. Beam columns transfer eccentric loads at mechanical floors due to the chosen column grid summarized in Table 2.1. Two gravity load paths, shown in Figure 3.10, allow for the design of four types of columns. Column 1 extends the entire height of building while Column 2 of Banks 3 and 4 is transferred to two columns, 3a and 3b, for Banks 1 and 2. Figure 3.11 and Figure 3.12 display the typical column grid for Bank 1 and Bank 3, respectively. For constructability purposes the column details should be similar in each subsection.

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Figure 3.10: Steel Column Load Paths

Column 1 Column 2

Figure 3.11: Bank 3 Steel Column Layout

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3.0 GRAVITY DESIGN

Column 1 Column 3a/3b

Figure 3.12: Bank 1 Steel Column Layout Axial loads for the core were also found using the column load takedown. The core was not originally designed for solely gravity forces. The core loads from the column load takedown were utilized in the three dimensional finite element model as nodal forces. The core is divided into four shear walls, an East-West pair, and a North-South pair. The shear walls act as coupling units through the reinforced concrete link beams and slab. The column load takedown calculated axial forces for individual shear walls. Elevator shaft openings throughout the tower limit the core wall shapes. Generic core wall geometry was simplified to the cross section shown in Figure 3.13. In Bank 4 the reduced shaft opening space and the tapering of exterior columns leads to an exception to the typical core geometry.

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Figure 3.13: Typical Core Column Section, Banks 1-3 Calculations were performed at each level for each type of column. Tributary area was multiplied by the distributed load to get the resultant axial column load. In cases where there is more than one type of loading, the corresponding area is used. Cumulative axial loads at the ground level can be used for foundation and mega-column design (Table 3.4). Table 3.4: Factored Loads from Gravity at Ground Level

Column 1

DL (kips) 5,600

SDL (kips) 7,600

LL (kips) 7,600

Column 3a

4,200

5,800

5,800

Column 3b

4,200

5,800

5,800

E-W Core

9,700

13,100

24,200

N-S Core

12,100

14,200

43,400

Does not include column and core self-weight

3.6.2 Initial Vertical Column Design: Composite and Steel Shapes Axial forces from the column load takedown were used to optimize the column material and size for each sub-section. Steel columns were chosen for Bank 3 & 4 because of their ability to resist lateral loads. The preliminary steel column design included steel built-up columns at the lower floors. Although large composite columns were chosen in their stead, this possibility proved to be an effective means for later column design.

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3.0 GRAVITY DESIGN The initial column sections of the Chicago Spire were optimized for strength, economy, and architectural constraints. Composite columns were designed following AISC Chapters I, G1 and G2. Steel columns were designed using AISC Chapters H1. Column behavior from lateral load combinations was not considered for this deliverable. Figure 3.14 shows a typical composite column section with a W-shape and reinforcement encased in concrete.

Figure 3.14: Composite Column Section Appendix 9.9 summarizes the initial column sizes for each subsection of the Spire.

3.6.3 Transfer Column Design At mechanical floors, angled beam-columns transfer gravity loads from one bank to another. As the height of the structure increases, the building tapers and radial column grids reduce in diameter. Figure 3.15 shows the different transfer column configurations for each bank. The columns were designed in accordance with AISC Chapter H1 because they are subject to both axial and flexural forces. Using the loads from the column load takedown, nominal moments and compressive strengths were calculated. The columns were designed to satisfy flexural and axial limit states. Upon preliminary analysis, it was discovered that typical W-shapes were not sufficient for the combined loading criteria. Built up columns or W-shapes with cover plates are needed to fully satisfy the design loads.

Figure 3.15: Transfer Column Orientations

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.0 Lateral Load Resisting System Design ASPIRE conducted a three phase lateral system design for the Chicago Spire. First, a preliminary lateral analysis modeled the building as a cantilever tube representing the reinforced concrete core. Each bank was assigned an initial wall thickness and inner radius to optimize the critical tensile and compressive stresses at the base of the bank. The preliminary core thicknesses were very large and unfeasible for construction and design, so additional investigation was necessary. This deliverable incorporates the columns into the lateral design and assesses the need for additional lateral systems. Outriggers and belt trusses have been added to create an integrated system. The core and the columns act together to resist lateral forces and torsional moments from wind and seismic load combinations. A three-dimensional model was created with MIDAS Gen to run load cases in static and dynamic analyses. Core walls, outriggers, and belt trusses were sized using sensitivity analyses to meet serviceability requirements defined in Section 2.7. Critical moments and axial forces, taken from the finite element model, showed the preliminary sizing from the gravity design to be inadequate. Ultimately, column steel area was increased to improve the structure’s stiffness. This was critical to lateral deflection and gravity load shedding at outrigger levels.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.1 Structural System Overview The overall structural systems are critical to the lateral design of the Chicago Spire. The Chicago Spire includes a reinforced concrete core surrounded by radial exterior columns. In three isolated mechanical sections, two-story trusses span between the radial columns and the core, acting as outriggers that tie the movements and rotations of the columns to the core. Outriggers are also effective in shedding gravity loads from the columns to the concrete core. Belt trusses also surround these levels to tie the columns together into a cohesive unit. While the gravity system was designed for code defined loads and calculated tributary areas, lateral forces are both unpredictable and significant. Statistical analyses are typically performed to determine the critical wind and seismic lateral forces for both design and serviceability conditions. Wind tunnel loads and torsional moments were provided by RWDI and provide an accurate estimate of 100-year MRI forces on the Chicago Spire. ASCE 7 design procedures for wind loads produce extremely conservative results for tall, slender buildings. The core of the building is primarily designed to be a stiff lateral load-resisting system. Although size and openings are constrained by architectural specifications, the core still needs to resist critical wind and seismic forces. These forces develop an overturning moment in the core that induces tensile stresses on the windward side of the core and compression stresses on the leeward side. The moment induced in the core near the top of the building is fairly negligible, necessitating a core of only a few feet thick. However, near the base, this moment can be significant enough to control the overall core design. Concrete has a strong resistance to compressive stresses, yet is weak in tension. The core is heavily reinforced with flexural reinforcement to resist the tension stresses. Additionally, the outrigger and belt truss system helps reduce the overturning moment, thereby reducing the tensile stresses. Figure 4.1 shows the locations of the belt truss and outrigger system at mechanical floors.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

Belt Truss Outrigger

Figure 4.1: 3D model of Outrigger and Belt Truss Locations

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.2 Preliminary Core Wall Design Hand calculations were completed to estimate initial core wall thicknesses and reinforcement limits based on the compressive strength of concrete and the modulus of rupture. Wind tunnel testing provided by RWDI proved to be more accurate than ASCE design loads. All exterior framing, foundations, slabs, and columns are ignored in these calculations. The Chicago Spire’s core is assumed to act as a cantilever resisting lateral forces from seismic activity or wind and axial forces from self-weight, dead loads, and live loads. Calculations 4.2 and 4.3 summarize the engineering calculations used to develop baseline core wall thicknesses when considering both a system with and without outriggers.

4.2.1 Core Wall Design Loads A combination of wind tunnel data, ASCE 7-05 and ASCE 7-10 were used to find forces, stresses, and moments at each floor.    

ASCE 7-10 used for seismic load calculation ASCE 7-05 2.3.2 basic load combinations used for wind strength design ASCE 7-05 CC.1 basic load combinations used for wind serviceability verification RWDI 100 year MRI Wind Tunnel Testing Information Used for wind serviceability load calculation (Appendix 9.2).

The loads at the bottom floor of each bank were used to calculate controlling tensile and compressive stresses. The loads used in the calculations are in Table 4.1 below. The floor at the base of each bank was assessed for a conservative approach. Table 4.1: Critical Core Wall Unfactored Design Loads Core Gravity Loads

Bank 1 2 3 4a 4b

36

Floor 1 40 74 111 130

Total Dead Load (SDL + DL) kips 81,958 56,024 33,366 15,356 6,810

Total Live Load kips 84,464 59,908 37,076 21,238 13,496

Core Self Weight Above Floor kips 594,387 282,275 141,506 38,397 15,825

ASPIRE

Lateral Moments ASCE 7-10 Seismic k-ft 8.82E6 5.49E6 2.86E6 8.02E5 2.25E5

RWDI Wind Tunnel k-ft 9.41E6 5.16E6 2.42E6 5.70E5 1.20E5

4.0 LATERAL LOAD RESISTING SYSTEM DESIGN The loads in Table 4.1 have been determined from various design tools: 

Dead load, superimposed dead load, and live load are from a column load takedown created for the gravity design deliverable. The column load takedown calculated loads for each core wall section. These values were scaled to represent the total unfactored loading on the assumed tube for each floor.



Seismic moments were calculated as the sum of all moment arms from lateral seismic forces, Fx.



Wind moments were calculated as the sum of all moment from critical lateral wind forces. Recommended wind load combinations were considered. A critical resultant force from the effects of Fx and Fy at each floor was used for the preliminary design moments. Wind moment calculations ignore torsional moments provided by RWDI testing.

4.2.2 Core Wall Design The concrete cantilevered tube was designed to resist the previously calculated gravity and lateral loads. The inner radius and core wall thickness were adjusted at each bank to account for the varying loads throughout the building. The strength design load combinations from Section 2.6. The compressive stress block due to the gravity load was combined with the lateral stress diagram to calculate net compressive and tensile stresses at the extreme outer fiber of the core. Shear forces and moments were calculated from the distributed seismic and wind forces. Figure 4.2 displays a sample combination of gravity and lateral induced stresses.

Figure 4.2: Typical Core Wall Stress Diagram

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

The following equations were used:

 ( comp ,tens ) 

Pgravity A



M lateral  c I

where c = distance from center to extreme outer fiber I = second moment of area A = section area of concrete tube Pgravity = critical gravity load Mlateral = critical moment from lateral forces The controlling compressive and tensile stresses from the load combinations were compared to allowable stresses found in ACI 318. Table 4.2 summarizes the design comparison between the controlling stresses from the six load combinations to the allowable stress values. The reinforcement is designed assuming the steel yields first, allowing Φ = 0.90. Table 4.2: Controlling Stresses for Core Wall Design

Net Compression = Net Tension =

1 6.468 -3.610

Allowable Compression =

0.55*φ * f'c =

Allowable Tension =

2 4.647 -2.989

.5

7.5 * (f'c) =

3 3.552 -2.698

4a 2.066 -1.463

6.93 ksi -0.887 ksi

4b 1.050 -0.465

ksi ksi

ACI 318 (14.5.2) Φ = 0.90

The equations for net compression and tension are dependent on the cross sectional area of the core and the moment of inertia. The core thickness and inner radii were adjusted to meet the allowable compression constraint, as shown in the next section. The grey highlighted cells in Table 4.2 exceed the modulus of rupture; however, preliminary analysis ignores concrete reinforcement against tension.

4.2.3 Drift Hand Calculation The core wall was idealized as a series of stacked concrete tubes. Collectively the tubes acted as a cantilevered beam experiencing deflection from a distributed lateral load. Figure 4.3 shows the distributed load simplification as four sets of uniform loads acting on each bank. 38

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

Figure 4.3: Distributed Lateral Load for Core Wall Bernoulli’s equation was used to calculate the maximum tip deflection from the uniform loads calculated from the RWDI forces.

y

w 24 E I

4

x 

c1 3 c2 2 x   x  c3 x  c4 6 2

The maximum global tip deflection was calculated to be 10 ft (Calculation 4.1). This fails the global serviceability requirement; however, this does not account for the contribution of outriggers or exterior columns.

4.2.4 Reinforcement Requirements Given a representative core section of unit length, the percentage of steel needed for each bank was calculated using the maximum net tensile force at the extreme fiber. The yield stress of the steel reinforcement was assumed to be 60 ksi. The steel area for each bank was compared to the gross area of the representative section. Table 4.3 summarizes the core wall reinforcement requirements for preliminary calculations. The steel was assumed to be tension controlled.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN Table 4.3: Initial Core Wall Reinforcement Requirements Bank

1

2

3

4a

4b

Ag (ft )

11.5

8.5

6

4.5

3

σt (ksi)

-3.610

-2.989

-2.698

-1.463

-0.465

Ft (kip)

-5978

-3659

-2331

-948

-201

2

100

61

39

16

3

2

0.69

0.42

0.27

0.11

0.02

6.02%

4.98%

4.50%

2.44%

0.78%

2

As (in ) As (ft ) % Steel

Area of 1 ft concrete section Net tension stress at extreme fiber Ag*σt As = Ft / Fy

% Steel = As / Ag

4.2.5 Core Wall Lateral Resisting System The preliminary lateral design for the Chicago Spire core determined an initial core thickness and reinforcement requirements. The preliminary wall thicknesses were increased to account for core wall openings. The stresses at the bottom floor for each bank were used to design the core properties for the respective bank. Preliminary steel reinforcement was calculated assuming the steel would yield in tension before the concrete opposite it fails in compression. The serviceability requirements for wind and seismic loads were evaluated given the initial core stiffness. Architectural floor plans indicated roughly 40% of the circumference of the core is open space. The initial tube thickness was increased to maintain the core section properties. Table 4.4 summarizes the calculated core thickness and inner radius. The drawings of the core slab and link beam locations (Figure 3.6 and Figure 3.7) show the core wall openings.

Table 4.4: Initial Core Thickness by Bank

40

Bank

1

2

3

4a

4b

Inner Radius (ft)

34

34

32

25

25

Initial Thickness (ft)

8

6

4

3

2

Final Thickness (+40%)

11.5

8.5

6

4.5

3

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.3 Auxiliary Lateral Systems Tall building design is typically controlled by seismic or wind forces. Reinforced concrete core walls and columns cannot resist the overturning moment and base shear without an additional lateral system. Additional lateral systems were employed to create a cohesive, stiff structure to optimize design and meet serviceability requirements. Lateral systems require large beam members or truss systems with architectural constraints often controlling their location and design.

4.3.1 Need for Auxiliary System in the Chicago Spire The core thicknesses determined in the Section 4.2 calculations are excessive and unfeasible for construction. In order to reduce core wall thicknesses, outriggers will be constructed as large transfer girders on the mechanical floors of Banks 1-3. These will span two levels from the exterior columns to the concrete core wall.

Figure 4.4: Outriggers Spanning Two Mechanical Floors Preliminary calculations show that outriggers will increase the moment of inertia and stiffness of the structure. This decreases the net stresses at each bank. The concrete core wall thicknesses are reduced to optimize the compressive strength requirements. These final thicknesses are used as base points for the MIDAS Gen structural model. To determine the stiffness of the perimeter column system, it was necessary to first determine the effective moment of inertia of the circle of columns. There are two types of column groups in the spire: 21 columns in Banks 1 and 2, and 14 columns in Banks 3 and 4.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN The effective moment of inertia was determined by drawing a centerline through the middle of the building and calculating the distance of each individual column from that centerline. The moment of inertia for an object not centered on the centroid is: ICL = Iobject + Ad2 where Iobject = moment of inertia of column A = section area of column d = distance from centroid to center of object The moment of inertia of the columns, Iobject, is insignificant compared to Ad2 and can be neglected. ICL ≈ Ad2 The following assumptions were made for the core wall calculations utilizing outriggers and exterior columns.    

Steel and composite column section properties are from initial gravity design. Increase in concrete volume and area from columns considered negligible for stresses from gravity loads. Itotal = Icore + 0.7*Icolumns where 0.7 is an assumed factor provided that outriggers and belt trusses are not infinitely stiff. Calculations use smallest column size per section for a conservative approach.

Table 4.5 highlights the effective Modulus of Elasticity, moment of inertia and stiffness of each column section throughout the structure.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN Table 4.5: Summary of Column Properties for each Column Section Bank 4 4 4 4 3 3 3 2 2 2 1 1 1 1

Level 145 134 123 113 100 87 75 64 52 41 29 17 5 Lobby

# Columns 14 14 14 14 14 14 14 21 21 21 21 21 21 7

Column Radius (ft) 53.5 53.5 53.5 53.5 61 61 61 68.5 68.5 68.5 75.5 75.5 75.5 75.5

Ieff (ft4) 4050 4050 7905 12721 22613 29306 35457 197001 197001 197001 373939 373939 538473 538473

Eeff (ksi) 29000 29000 29000 29000 29000 29000 29000 8873 10953 12481 10458 11700 9390 9390

EI (kip-in2) 2.44E+12 2.44E+12 4.75E+12 7.65E+12 1.36E+13 1.76E+13 2.13E+13 3.62E+13 4.47E+13 5.10E+13 8.11E+13 9.07E+13 1.05E+14 1.05E+14

The moment of inertias from Table 4.5 were combined with the core wall moment of inertia to determine new compressive and tensile forces following a similar procedure described in Section 4.2.2. Table 4.6 summarizes the reduction in tensile and compressive forces at each bank. Despite minimal effects to the top of the Spire, outriggers make a significant contribution in Banks 1 and 2. Table 4.6: Stress Reduction in each Bank from Outriggers % Reduction in Each Bank: In Applied Compression In Applied Tension

1 17% 30%

2 10% 16%

3 3% 6%

4a 2% 5%

4b 1% 3%

The same loads and procedure described in Section 4.2.5 were used to calculate new core wall thicknesses that incorporate the outriggers. Table 4.7 summarizes the preliminary calculations for core wall thicknesses incorporating auxiliary lateral systems.

Table 4.7: Summary of Core Wall Thicknesses with Outriggers and Columns Bank

1

2

3

4.1

4.2

Inner Radius (ft)

34

34

32

25

25

Initial Thickness (ft)

6

5

4

3

2

Final Thickness (+40%)

8.5

7

6

4.5

3

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN The need for belt trusses and outriggers was assessed qualitatively and these members were not specifically designed. For the MIDAS Gen software model, the members will be W14x730 to increase structural stiffness.

4.3.2 Relative Stiffness of Structural Systems A basic analysis of the stiffness of the core and column systems was conducted to ensure uniform performance under applied loads. In order to perform as a cohesive system, the stiffness of the reinforced concrete core needs to be similar to that of the outrigger and column system. The stiffer system will take a proportionately larger amount of the stresses than the other system. Therefore, if the column and outrigger system is stiffer than the core, the full capacity of the core would not be used and columns could potentially be overstressed to the point of failure. The relative stiffness of the core and column system will be compared by using the product of the elastic modulus and the moment of inertia. Each bank has different section properties, so the core was analyzed in five different segments corresponding to Banks 1, 2, 3, 4.1, and 4.2. The values for each bank are tabulated in Table 4.8 below. Table 4.8: System Stiffness Summary

Bank 4.2 4.1 3 2 1

Core Stiffness, EI (kip-in2) 3.48E+13 3.48E+13 1.14E+14 1.95E+14 2.65E+14

Column Stiffness, EI (kip-in2) 2.44E+12 7.65E+12 2.13E+13 5.10E+13 1.05E+14

Sum (kip-in2) 3.72E+13 4.24E+13 1.35E+14 2.46E+14 3.70E+14

Sum-to-Core % Increase 7.00% 21.99% 18.73% 26.15% 39.58%

0.7-Reduced Sum (kip-in2) 3.65E+13 4.01E+13 1.29E+14 2.31E+14 3.38E+14

0.7-Reduced Sum-to-Core % Increase 4.90% 15.40% 13.11% 18.30% 27.71%

The two systems, although separate, will be connected via outriggers spanning from the core to the columns on the mechanical levels. To determine the effect of the combined systems, each system can be idealized as a spring with a stiffness equivalent to that of the actual system. The two “springs” will be connected in parallel by the outriggers, and by simple elastic behavior theory, the system will have an effective stiffness of the sum of the two springs’ individual stiffness. However, this value assumes a perfectly rigid connection by the outriggers between the core and the columns. This is unrealistic in practice, and as such, a reduction factor of 0.7 is applied to the column stiffness.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.4 Finite Element Model A detailed structural analysis of the Chicago Spire was conducted using MIDAS Gen. All material properties and baseline element shapes were taken from initial lateral and gravity design. Vertical members, outriggers and belt trusses, and core wall thicknesses were resized throughout the iterative modeling process based on element forces and moments, and serviceability requirements.

4.4.1 Initial Modeling Process A three-dimensional model of the Chicago Spire was created in MIDAS Gen to model the behavior of the building in response to dynamic and static forces. The following modeling procedures and assumptions were made for the initial model.    

The model spans from the lobby at ground elevation to the top of level 144. The tuned mass damper and hypothetical mechanical floors at the Spire’s peak are not considered. All below-grade elements are not modeled. The mega-columns and core wall at the ground elevation are fixed to the ground. Table 4.9 summarizes the initial elements properties modeled in MIDAS.

Table 4.9: Initial MIDAS Model Element Properties Structural Member

Element Type

Material Property

Core Wall

Plate, thick with drilling DOF

RC, C14000

Column B1 B2 B3

General Beam

SRC, C14000, A992

Column B4

General Beam

S, A992

Transferring Column

General Beam

S, A992

Radial Beam

General Beam

SRC, C4000, A992

Column Beam

General Beam

SRC, C4000, A992

Link Beam

General Beam

RC, C4000

Outrigger and Belt Truss

Truss

SRC, C4000, A992

(S)RC: (Steel) Reinforced Concrete CXXXX: Concrete and f’c (psi)



MIDAS Gen limits reinforced concrete materials to a f’c = 10,000 psi, thus the modulus of elasticity was calculated and inputted for a compressive strength of 14,000 psi for vertical elements. The modulus of elasticity is ( ) based on ACI-318-08 √ Section 8.5.1.



The density ratio, Ds/Dc=3.059, and modulus of elasticity ratio, Es/Ec=3.829, are also selfdefined in the section properties for the vertical composite columns.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN   



Core walls are modeled as thick plate element with drilling DOF, since out-of-plane shear is not considered negligible. Core walls contain openings as shown in structural and architectural drawings. Composite beams were simplified to W-Shape Steel Reinforced Concrete (SRC) in cross section properties. The widths chosen in these SRC beams are based on the effective widths of the composite beam from the gravity design. All structural elements have been applied fixed-fixed end-releases. Cantilevers and angled floor girders outside of the exterior column grid were not considered.

4.4.2 Loading and Load Combinations All design loads were applied as nodal point forces. The column load takedown from Section 3.6.1 and provided wind tunnel information were used to calculate gravity and lateral forces. The following procedures summarize the applied loads for design and serviceability criteria.       

The wind forces from the wind tunnel testing are used directly for strength design. The wind forces and torsional moments from Appendix 9.2 were applied to each level along the z-axis. The wind tunnel recommended combinations from Appendix 9.2 were used as a sub level of load combinations. A reduction factor of 0.83 (1/1.2) was applied to the RWDI wind loads to reduce the 100 year MRI loads to a 50 year MRI loads for serviceability design. Unfactored dead loads and live loads from the column load takedown were applied to nodes at column ends. Superimposed dead load and dead load combined for total dead load. Appendix 9.10 summarizes the nodal gravity forces used in MIDAS Gen. The total unfactored dead load and live load for the core was split equally into nodal forces to the nodes connecting the radial girders to the core walls or link beams. Appendix 9.10 summarizes the nodal gravity forces used in MIDAS Gen MIDAS Gen calculates material self-weight in the analysis, thus no self-weight is considered in applied dead loads. The load combinations from Section 2.6 are used for both strength and serviceability.

4.4.3 Iteration and Element Redesign Column Validation Original MIDAS Gen sizes for vertical columns, transfer columns, and mega-columns were from the initial gravity design. The MIDAS Gen model was analyzed for all the load combinations and the force and moment combinations for each column were used in a composite column interaction diagram to resize the columns for both gravity and lateral design. The interaction diagram checked for both strong and weak axis bending. Figure 4.5 shows the strain diagram for a composite column bending in the weak axis.

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Figure 4.5: Compression Block and Steel Strain from Weak Axis Bending The forces and moments for all load combinations were plotted on the interaction diagram. Steel shapes, concrete dimensions, and reinforcement specifications were adjusted to optimize the column design. This process was repeated several times with new column sizes recycled into MIDAS Gen model and new forces and moments plotted on the interaction diagrams. Appendix 9.11 shows the composite and steel column sizes after several iterations of column validation.

Exterior Steel Stiffness The new column sizes showed severe discontinuity under gravity forces due to the core and outriggers being significantly stiffer than the columns. The columns were showing tension forces as seen in Figure 4.6. Several sensitivity analyses were used to troubleshoot the model and reduce the load shedding shown in Figure 4.6 and the excessive deflection. The analyses are summarized in Appendix 9.11.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

Figure 4.6: Initial Discontinuity Check under Gravity Loads

Final Design The final design of the MIDAS Gen model saw several improvements from the original model. The improvements resulted in acceptable drift under serviceability loads and reasonable load shedding under gravity loads. The following changes helped reach these goals. Table 4.10 shows the final model element properties.   

Increased steel area in exterior column grid. Reduced thickness of core walls. Reduced size of belt truss members. Table 4.10: Final MIDAS Model Element Properties Core Wall Thickness by Bank (ft) 1 2 3 4 7

4

3

2

Vertical Column Size by Bank Belt Truss

Outrigger

1

2

3

4

W14x53

W14x730

BU1

BU1

BU2

BU2

While it is not economic or practical to restrict the structure to two built-up column shapes, these sizes were expected to change during energy optimization. Figure 4.7 shows the section views of these prefabricated steel shapes.

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Figure 4.7: a) BU1 and b) BU2

The final MIDAS Gen model included the built-ups in Figure 4.7 encased in concrete. However, the concrete was ultimately deemed unnecessary negligible in composite action given the high steel area. The final design will consist of solely, steel exterior columns.

4.4.4 Results Comparison The final design was a significant improvement from the original MIDAS Gen design based on gravity design and preliminary lateral studies. Although Figure 4.8 shows an increase in ultimate compressive forces, the load shedding at the mechanical floors follows the industry standard of ≈20%. Tension members no longer exist and the overall shape of the compression graph follows the expected graph of a single column line extending up a building. Table 4.11 shows a sample comparison of MIDAS results.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

Figure 4.8: Discontinuity Test Comparison between Original and Final Design

Table 4.11: Initial and Final MIDAS Results Allowable (

Initial

Final

27,500

49,000

N/A

Base Shear

kips

Global Deflection

ft

6.71

4.48

5.0

Maximum Inter-story Drift

in

0.88

0.56

0.40

h ) 400

The objective of the MIDAS Gen analysis was to meet the ultimate global deflection of h/400. It is nearly impossible for inter-story drift to meet serviceability requirements if the criterion is the same as the global deflection. The vertical columns can be resized using energy optimization for more stringent deflection requirements, thus hopefully meeting the inter-story drift limit of 0.40 in. The final deformed shape from the MIDAS Gen can be seen in Figure 4.9. The figure shows the exaggerated deflection of 4.48 in. 50

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN The troubleshooting and iteration of the MIDAS model proved to be the most tedious and time consuming aspect of the Chicago Spire structural design. Ultimately the model produced acceptable global deflection and forces for connection, foundation, and core wall design.

Figure 4.9: Deformed Shape for 50 year MRI Wind Loads (NTS)

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.5 Core Wall Reinforcement Design Core walls were designed using the final MIDAS Gen model thicknesses as reinforced concrete shear walls. The shear and flexural reinforcement was designed using loads, shears and moments pulled from the MIDAS Gen model. Reinforcement was designed separately for the North-South and East-West core walls on Bank 1, Bank 2 and Bank 3, and for the sole coupled core wall of Bank 4. The horizontal shear capacity was calculated using MIDAS Gen section areas and loads, and spacing and reinforcement were selected based on the required steel ratio. These values were subsequently applied to the core’s actual shape. Minimal vertical shear exists, thus the vertical reinforcing was designed based on required steel ratio. For the first three banks, the North-South (NS) and East-West (EW) cores worked together to resist flexural moment, and the moment capacity of the coupled cores was calculated using the vertical reinforcement. For Bank 4, the cores worked together to resist moment along their weak axis, but resisted moment individually across their strong axis. For this latter moment, the moment-axial force pairs were plotted on a column interaction diagram produced using vertical reinforcing steel. For all banks, the vertical reinforcing was sufficient to resist moment. The following assumptions were used to design of the core reinforcement.      

MIDAS Gen core section areas were sufficiently similar in size and shear capacity to actual core size and shear capacity. Core walls were designed for critical loads at the base of each bank. Reinforcement details could be designed based on a sub-area of a concrete gross area, and then applied to a different area of concrete, as long as steel ratios are kept constant. The link beams allow the core walls in a given bank to act as a single beam. Ties will be sufficient for any given reinforcement configuration. Core wall section areas are conservative to simplify design procedure. If there is sufficient area outside of these approximations so as to exceed the spacing of the reinforcement, reinforcement will be extended into that area.

Appendix 9.13 summarizes the reinforcement spacing and sizes for each bank. Calculation 4.5 shows the reinforcement design calculations.

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4.6 Energy Optimization The vertical system for the final MIDAS Gen model consisted of a column schedule of two steel builtups, BU1 and BU2. An energy optimization of the tower’s lateral load resistance system was performed to resize vertical elements. This analysis was not performed using the displacement optimal design feature of MIDAS Gen, but rather through an energy method design tool. MIDAS results were needed for component forces, and grouping by element type and location. The energy method used is outlined in “Energy-Based Design of Lateral Systems” (Baker, 1992), and was based on establishing equal energy density on all members. Once complete, each member contributes to the lateral resistance with equal efficiency, ultimately optimizing the design. The scope of the energy method analysis included members in which large axial forces were induced during lateral loading: namely all columns and outrigger trusses. Each bank of columns was broken down into three sub-sections, for the purpose of reducing column sizes with building height, as axial forces decrease. Belt trusses and induced moments were secondary concerns and thus were not included in this analysis. An optimization design tool details the procedure (Calculation 4.6). The tool requires both “real” and “virtual” axial forces generated from lateral loads only. “Real” forces used in the analysis corresponded to the 0.7 wind load combination at 50 year MRI, as prescribed by ASCE 7-10. “Virtual” or “notional” axial forces were obtained by applying a unit dummy load to the tip of the building, revealing the virtual work of each member. The following equation was used to calculate the required areas.

( Ai )req 

1  req E

150

 (ni Fi )0.5  L j [n j Fj ]0.5 j 1

where Areq = minimum required area Δreq = target drift E = modulus of elasticity, 29,000 for steel n = virtual axial force F = real axial force L = member length With global lateral drift as the objective function, the energy method tool minimized cross-sectional area, and ultimately the steel volume required for structural components.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN Because of the tower’s symmetry and the fact that wind loads can occur in any direction, the critical required area for each sub-section was applied to all members in that sub-section. Initial MIDAS Gen modeling targeted a global drift requirement of h/400. The first objective for the energy optimization was a target drift of 4 ft (h/500). Steel built-up columns were used at the lower levels and W-sections were used at the higher levels where applicable. The new members are summarized and compared to baseline values in Table 4.12. Table 4.12: Optimization Results for Δ = h/500

Type Bank 1 Mega-columns Vertical Vertical Vertical Transfer Outrigger Bank 2 Vertical Vertical Vertical Transfer Outrigger Bank 3 Vertical Vertical Vertical Transfer Outrigger Bank 4 Slanted Slanted Slanted

Floors

Baseline Area in2

Optimized Area Area Provided in2 in2

Proposed Section

1-4 5-16 17-28 29-37 38-39 38-39

848 848 848 848 848 215

903 800 748 678 587 175

920 800 768 688 608 178

BU1 BU2 BU3 BU4 BU5 W14x605

40-52 56-63 64-71 72-73 72-73

848 848 848 848 215

571 509 500 602 151

576 512 512 608 162

BU6 BU7 BU7 BU8 W14x550

74-87 88-99 100-108 109-110 109-110

688 688 688 688 215

468 335 244 159 48

480 347 250 162 52

BU9 BU10 BU11 W14x550 W14x176

111-122 123-133 134-144

688 688 688

153 135 96

162 134 101

W14x550 W14x455 W14x342

Using the optimized cross sections, baseline sizes were significantly reduced and structural material optimally distributed over the height of the tower. Only the mega-columns required larger cross-sections. It is worth noting that any reduced cross-sections must be rechecked for adequacy with respect to strength and inter-story drift requirements. Material savings for this optimization analysis is shown in Table 4.13.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN Table 4.13: Material Savings for Δ = h/500 Volume reduction in steel (ft3) Weight reduction in steel (tons) % reduction

66800 16700 36

This same optimization method was similarly used to create an understanding of what additional materials would be required to increase the Chicago Spire’s performance. The steel, shown in tons, needed for decreases in global drift (by 5%, 10%, 15%) are included in Figure 4.10.

Figure 4.10: Optimization Material Use versus % Reduction of Drift

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN

4.7 Eigenvalue Analysis A subspace iteration eigenvalue analysis was performed using the final model in MIDAS Gen. The first 15 mode shapes were found. Table 4.14 summarizes the natural frequency and period of the first fifteen mode shapes. The expected period for mode one of a tall building is n/10, where n = the number of floors. The eigenvalue analysis results show periods similar to the expected of 15 sec. Table 4.14: Natural Frequency and Period of first 15 mode shapes Mode No.

Frequency

Frequency

Period

(rad/sec)

(cycle/sec)

(sec)

1

0.4098

0.0652

15.33

2

0.4313

0.0686

14.57

3

0.6378

0.1015

9.85

4

1.3013

0.2071

4.83

5

1.4131

0.2249

4.45

6

1.7807

0.2834

3.53

7

2.4401

0.3884

2.57

8

2.9056

0.4624

2.16

9

3.1205

0.4966

2.01

10

3.4213

0.5445

1.84

11

3.9564

0.6297

1.59

12

4.2083

0.6698

1.49

13

5.9338

0.9444

1.06

14

6.4212

1.0220

0.98

15

7.0179

1.1169

0.90

The number of mode shapes to account for was based on the modal mass participation. According to ASCE 7-10, 12.9.1, the sum of the effective modal masses included in an analysis should be greater than 90% of the total mass (Table 4.15). This will ensure that the critical modes that affect the Chicago Spire are included in the design.

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4.0 LATERAL LOAD RESISTING SYSTEM DESIGN Table 4.15: Modal Mass Participation

Mode No.

Translation in X

Translation in Y

Rotation about Z

MASS(%)

SUM(%)

MASS(%)

SUM(%)

1

0

0

63.05

63.05

0

0

2

62.35

62.35

0

63.05

0

0

3

0

62.35

0

63.06

60.87

60.88

4

0

62.35

17.52

80.58

0

60.88

5

18.37

80.72

0

80.58

0

60.88

6

0

80.72

0

80.58

18.45

79.33

7

0

80.72

5.67

86.24

0

79.33

8

6.58

87.30

0

86.24

0

79.33

9

0

87.30

0

86.24

4.27

83.59

10

0

87.30

3.50

89.74

0

83.59

11

0

87.30

0

89.74

6.01

89.60

12

2.49

89.79

0

89.74

0

89.60

13

0

89.79

1.98

91.72

0

89.60

14

0

89.79

0

91.72

1.70

91.31

15

2.24

92.02

0

91.72

0

91.31

ASPIRE

MASS(%) SUM(%)

57

4.0 LATERAL LOAD RESISTING SYSTEM DESIGN The first two modes of the building are translation modes in orthogonal directions. The third mode is a torsional mode which primarily acts on the Bank 4. Figure 4.11 shows all three modes from the MIDAS Gen model. The periods for the first three mode shapes are: 15.33 seconds, 14.57 seconds, and 9.85 seconds respectively. The corresponding modal participations are: 63.05%, 62.35%, and 60.87%. This indicates that the first three modes are low frequency and the majority of the mass will be affected at those frequencies. The next three modes show the second mode shape for the different directions of translation. The sum of the modal participation of the first 15 modes in xtranslation, y-translation, and torsion are all over 90%.

Figure 4.11: From Left to Right: a) Mode Shape 1; b) Mode Shape 2; c) Mode Shape 3

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5.0 STEEL AND CONCRETE DETAILING

5.0 Steel and Concrete Detailing Thousands of connections exist over the height of the building ranging from simple framing connections to complicated mega-column terminations. ASPIRE identified typical connections that are prevalent throughout the tower and several classifications of complex connections. A full structural design would look at all the iterations of each connection to fully understand how each area load and each bank changes the connection. One occurrence of each connection has been identified for a full structural design. The same process and design tools can be applied to other, similar instances. Element geometry had a significant impact of the type of connections that could be used. All columns have been finalized as steel members, minimizing the prevalence of composite connections. The most common composite connection is between radial floor girders and the concrete core. The use of W-shapes versus built-up sections also affected decisions between bolted and welded connections. Ultimately all of the columns were built-up from 4 in thick steel plates which limited column connections to welds. Connections were standardized for the built-up columns to ensure that despite column section changes, similar connections can be used. Various failures were checked per AISC requirements depending on the type of connection.

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5.1 Typical Connections Five typical steel to steel connections and one typical composite connection will be used in the Chicago Spire. Radial girders and cantilevers will be connected to the outer ring columns with moment resisting connections; circumferential girders will be connected to the outer ring column with single plate connections; the joists will be connected to girders using single angle shear connections; the HSS beams running along the outside of the building will be connected to the cantilevers with angles bolted to the cantilever and welded to the HSS section; and column splices will connect each column with welded plates. The following typical connection design calculations follow AISC Steel Design Guide and can be found in Calculation 5.1.

5.1.1 Welded Column Splice All typical exterior columns are built-up steel shapes and will be spliced using steel plates. The column splices were designed by welding plates to connect each face of the connecting columns (Figure 5.1). This was the most economical design because of the similar column sizes throughout the structure. This type of splice minimizes the footprint of the columns, allowing them to meet architectural constraints. Column splices were designed against all load combinations to resist tension, moment, torsion and shear forces.

Figure 5.1: a) Elevation and b) Plan of Typical Welded Column Splice

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5.1.2 Floor Joist to Girder The floor joists are connected to the radial girders with single angle, shear connections. At each connection, two joists connect to opposite sides of the radial girder web. The girder web is not thick enough to weld at each side, therefore bolts were used (Figure 5.2). This greatly decreases the amount of field welds required during construction. The initial trial bolt number was calculated to withstand shear and bearing. Then all failure modes were checked, including bearing and tear out, shear yielding and rupture, and block shear of the angles and both webs. Weld

Figure 5.2: Elevation of Floor Joist to Girder Connection

5.1.3 Cantilever to HSS Section The connection between the cantilever beams and HSS Sections is similar to the single angle shear connection except the angle leg adjacent to the HSS section is welded instead of bolted (Figure 5.3). Also, an additional weld connects the top flange to the HSS beam to add rigidity to the connection. Weld

Figure 5.3: Elevation of HSS Beam to Cantilever Connection ASPIRE

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5.1.4 Cantilever and Radial Girder to Column Moment connections to the columns are required for both the radial girders and cantilevers. For the beam flanges, two angles will be welded along all edges to the column flange above and below the incoming beam and then bolted to the flange of the beam. For the beam, web, two rectangular plates will be welded perpendicularly to the column, sandwiching the web of the incoming beam. Bolts will be connected through predrilled holes in both the plates and the web. Figure 5.4 shows the elevation detail of the moment connections. Initial plate dimensions and bolt configurations were chosen based on member geometry and adjusted throughout the design process. Bolt sizes were determined from the required moment capacity of the connection. All applicable failure modes were checked including plate yielding in flexure, shear, and bearing; bolt yielding in tension and shear; and web yielding, crippling, and buckling.

Figure 5.4: Elevation of Built-up Column to Radial Girder and Cantilever Connection

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5.1.5 Circumferential Girder to Column The circumferential girders were designed as pinned-pinned and thus could be designed with a bolted connection. One plate is welded perpendicular to the built-up exterior column using a fillet weld. The circumferential girder is then placed with its web adjacent to the plate with its flanges above and below the plate. The plate and column girder are then bolted together. The size and number of bolts used were determined based on the shear and bearing capacity of the bolts. The weld of the plate to the column web was also checked. Column web yielding, crippling and buckling were checked along with block shear, bearing and tear out, shear yielding and shear rupture of the girder web and plate. Figure 5.5 shows the typical circumferential girder to column connection.

Weld

Figure 5.5: Elevation of Circumferential Girder to Column Plate Connection

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5.1.6 Radial Girder to Core Radial girders are connected to the core by a single, shear single plate connection and headed anchor bolts. Headed anchor bolts are welded to a steel anchor plate and cast into the exterior of the concrete core. A single steel plate is welded perpendicular to the base plate using a fillet weld. The radial girder is then bolted with its web adjacent to the plate, with its flanges above and below the plate. Figure 5.6 details the composite connection between the radial girder and the core wall. The single plate bolt details were determined based on the shear and bearing capacity of the bolts. Plate geometries are based on bolt spacing and beam dimensions. Maximum plate thickness is determined such that the plate moment strength does not exceed the moment strength of the bolt group in shear. The capacity of the connection is calculated as the minimum capacity for the limit states of shear yielding, shear rupture, block shear rupture, shear buckling, and flexural yielding of the plate and girder weld as well as bearing strength at bolt holes, bolt group shear strength, and weld capacity. Weld

Figure 5.6: a) Elevation and b) Section of Radial Girder to Core Wall Connection The headed anchor bolts details were determined based on the tensile and shear capacity of the steel anchor bolts and the concrete. The capacity of the connection is determined by an interaction of the design tension strength and design shear strength of the connection. Design tension strength is calculated as the minimum capacity for the limit states of steel strength of anchors in tension, concrete breakout strength of anchors in tension, and pullout strength for anchors in tension. Design shear strength is calculated as the minimum capacity for the limit states of steel strength of anchors in shear, concrete breakout strength of anchors in shear, and concrete pryout strength of anchors in shear.

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5.2 Complex Connections Several configurations of complex connections are found throughout the Chicago Spire, particularly at mechanical floors and at the tower’s base. These connections combined simple welds and bolts with gusset plates, encased steel, and prefabricated nodes to resist forces and moments produced by the MIDAS Gen model.

5.2.1 Mega-Column Base to Foundation This connection is located at the bottom of the mega-columns and is responsible for transferring the loads from the superstructure to the foundation. The foundation consists of two 10ft diameter caissons embedded six inches from the bottom of a caisson cap, much like a pile cap. The connection to the foundation presented a challenge due to the geometry of the mega-columns. The mega-columns are three slanted columns connecting to a single point, creating a large shear force at the base as well as a large concentrated compressive forced. A typical base plate design was initially considered to transfer the load however, because of the high loads, the base plate became infeasible and another option had to be considered. Aspire had thought of using an embedded steel shape to be able to connect the three mega-columns coming down as well as the embedded shape into the shaft of the caissons to properly transfer loads to the caissons. A built-up steel beam was used to connect the three columns, while a shaft column was used to transfer the tension to the caisson (Figure 5.7). The three node column will resist the compressive force coming from the super structure through bearing and will use shear studs to resist the shear. The three column beam was checked for failures such as bearing, local web crippling, and local web yielding. Together this connection is able to adequately transfer the load to the caissons while being the most economical solution. While the steel shapes embedded into the caisson cap will resists the axial and shear loads, the caisson cap will resist the bending moments by reinforcing steel bars. The caisson cap was designed considering bending moments about the X and Y direction using principals of reinforced concrete slab design. Calculation 5.2 summarizes the mega-column to foundation design.

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5.0 STEEL AND CONCRETE DETAILING

Mega-column

Built-up Steel Beam Embedded Steel

Pile Cap

Caisson

Figure 5.7: 3D Rendering of Base of Mega-Column to Caisson Connection

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5.2.2 Base of Outrigger Across the height of the structure, the exterior columns angle inwards as the diameter of the building decreases. The intersection of angled and vertical columns will be prefabricated, and the incoming and outgoing columns will be spliced to the prefabricated section above and below the connection node. Moment connections will be needed between the prefabricated column section and the bottom of the outrigger, the radial girder, and the cantilever. The flanges of the outrigger and column are too thick to punch through; thus welds will be used for the connection. Two plates will be used in the connection to improve the constructability of the connection. The first plate will be welded to the face of the column, and the second plate will be welded to the incoming outrigger and radial girder. Both flanges and the web of the outrigger will be welded to the end plate. Next, two angles and two rectangular plates will be welded to the plate and subsequently bolted to the radial girder (Figure 5.8). For the incoming outrigger, in addition to checking the strength of the welds, several failure modes were checked including plate yielding in shear and bearing; rupture of beam flange to plate welds; and beam web shear yielding (Calculation 5.3.1).

Vertical Columns

Outrigger

Girder

Figure 5.8: Bottom of Outrigger Connection

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5.0 STEEL AND CONCRETE DETAILING

5.2.3 Outrigger to Core Connection At each mechanical floor of the tower, outriggers primarily stiffen the connection between the steel frame and concrete core. These outriggers mainly help reduce the overall structural system’s lateral deflection. Therefore, to ensure that the outriggers perform in such a way, the outrigger connection with the concrete core was given major attention. The outrigger connection consists of two gusset plates that sandwich the flanges of the outrigger member and radial girder above the mechanical floor (Figure 5.9). Most girders in the building; however, were oriented with vertical webs and horizontal flanges. The gusset plate connection required rotating the floor girders by 90 degrees so that the gusset plates can be bolted to the flanges of both outrigger and girder. Gusset plate bolts were sized and design according to AISC Section J and accounted for failure modes such as block shear and plate yield (Calculation 5.3.2).

Embedded Steel Frame Concrete Core

Rotated Radial Girder

Outrigger

Figure 5.9: Elevation of Outrigger and Radial Girder Connection to Concrete Core The exact connection between the gusset plate and concrete core went through a few design iterations. Initially, the gusset plates were fillet welded to steel plates bolted to the concrete core, similar to the typical radial girder connection (Section 5.1.6). However, the high outrigger loads required around 500 bolts for such a connection. Eventually, an alternative design was developed that fillet welded gusset plates to a four story steel frame embedded in the concrete core. To design the embedded steel cage, MIDAS Gen was used to design a steel frame on the mechanical floor between Bank 3 and 4. The frame extends two stories above and below the points where the outrigger joins the steel frame (Figure 5.10).

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The following assumptions were made for the model.   

All members were assumed to be fully braced, simulating the frame’s embedment in concrete. All beams and columns are connected by moment connections. Connections details would be designed as per Section 5.1.1. The top and bottom nodes of the frame are assumed to be fixed in all directions and rotations.

Diagonal braces are added to the frame as compression only truss members (Figure 5.10). These fictitious members simulate how the concrete struts when the steel frame reacts to load. The brace sizes are relatively similar to the steel frame members, with steel frame having a greater stiffness to ensure that a majority of the load is absorbed by steel instead of concrete. For the final model, all loads from outriggers are applied axially to the nodes at which outrigger members connect with the frame. Axial loads are based on from critical load combinations from the final tower MIDAS model (Figure 5.10).

Figure 5.10: a) Model of Embedded Steel Frame and b) Model with Cross Bracing and Point Loads Through iterative design of steel sections, W33x152 members were selected for columns and W14x665 members for beams. The outriggers and radial girders at the mechanical floor between Bank 3 and 4 were both W14x730. The W33x152 section when oriented along its weak axis, would provide adequate space in the web for the outrigger spacing, gusset plates, and welds. With final beams and columns sized, shear studs and spacing were specified to ensure that the concrete could sufficiently brace the frame.

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5.2.4 Top of Mega-Column The top of the mega-column connection consists of two different connection configurations. Figure 5.11 shows the two scenarios: an interior column angled in one orientation and two exterior columns angled in two orientations. All of the mega-columns are steel built-up columns. In addition to the mega-columns, the connection also consists of a vertical built-up terminating at the top of each mega-column. Although both columns identical steel sections, lower column will be referred to as the mega-column, and the upper column as the vertical column. The mega-column and vertical column connection is a prefabricated node. The node is constructed with shop welded plates extending from the node faces to improve the constructability of the field column splice. The column splice will ultimately consist of four plates welded onto the columns to transfer tension, torsion, and shear. Half of the welds will be done in the shop, and half will be done in the field. The prefabricated design improves constructability and connection strength. The node also allows for standard splices that do not have to transfer massive forces and moments over an angled connection. The radial and circumferential girders will be designed as per Sections 5.1.1 and 5.1.5.

Figure 5.11: 3D Rendering of Mega-Column Connection

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5.2.5 Transfer Column Transfer columns exist at the mechanical levels where the exterior column radius decreases. Between Banks 2 and 3 some transfer columns are also designed for the reduction in total exterior columns. The transfer column connection consists of two different configurations, with typical top and bottom welded column splices. The mechanical space between Bank 2 and Bank 3 contains both of the typical transfer column connections found in the Chicago Spire. The column grid reduces from 21 columns in Bank 2 to 14 columns in Bank 3. Seven of the columns in Bank 2 are designed for the first configuration in Figure 5.12. Fourteen of the columns in Bank 2 are designed for the second configuration in Figure 5.13. In the first configuration, two field welded column splices occur at the top of the Bank 2 column and at the bottom of the Bank 3 column. The connecting member is a prefabricated connection node that is built to resist compression, tension, shear, moment, and torsion. In the second configuration, forces from the Bank 3 column are transferred to two Bank 2 columns below. Figure 5.13 shows the required angled transfer column. With this configuration there are three typical field welded column splices that occur at the top of the Bank 2 column and at the bottom of the Bank 3 column. The node between Bank 3 and the angled transfer column split will be prefabricated, along with the transfer column between the bottom of the node and the welded column splice at the top of the Bank 2 column.

Figure 5.12: Singular Transfer Column Connection Front and Side Elevation

Figure 5.13: Split Transfer Column Connection Front and Side Elevation

The welded column connections are comprised of four plates surrounding the members. For each splice, two plates will be shop welded to the connection node, and two plates will be shop welded to the columns. Welded column calculations are shown in Calculation 5.1.1.

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6.0 FOUNDATION DESIGN AND DETAILING

6.0 Foundation Design and Detailing The Chicago Spire foundation includes a deep foundation system to support the 150 floor tower and the seven floor parking garage. Rock-socketed caissons, driven piles under a mat foundation, concentric top of rock slurry wall rings, and a mat foundation on hardpan were all options to support the tower. As stated in the provided Geotechnical Report, the latter two options were considered costly, risky and time consuming. Therefore rock-socketed caisson will be used to support the tower. The project received city permits to have an allowable net bearing pressure for the rock of 300 tons per square foot. The seven floor parking garage will have a retaining wall structure around the perimeter, which will be internally braced by the floor slabs. The garage will be supported with belled caissons bearing on hardpan.

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6.1 Soil Properties Information on soil conditions came from eleven test borings and 34 borings to obtain bedrock cores (Geotechnical Report). The soil profile is 100 to 115 feet of primarily clay overburden on dolomite bedrock. The site grades range in elevation from +10 to +7 Chicago City Datum (CCD). The water table is five feet above the CCD. A one foot hardpan layer exists at -71 CCD. A detailed soil profile is shown in Figure 6.1. Soil properties were used to calculate apparent earth pressures and pore water pressures for the foundation design.

Figure 6.1: Provided Soil Profile for Foundation Design

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6.2 Retaining Wall Design The perimeter of the foundation is supported by a 30 in thick, reinforced concrete retaining wall. The wall was designed to withstand failure against the earth pressures and pore water pressure. The thick wall has a high self-weight which helps to resist the lateral forces from the soil profile. The self-weight also reduces the chances of bearing failure by distributing the vertical force to a larger area of soil.

A MASTAN analysis of the retaining wall was performed, modeling the wall as a one way slab assuming the bottom six floor slabs from the parking garage brace the retaining wall. As a conservative approach, the top two slabs are not considered as bracing for the retaining wall; which leaves a cantilever span at the top end of the retaining wall. The retaining wall was checked for overturning, lateral sliding and bearing failure (Figure 6.2).

LATERAL SLIDING

The Geotechnical Report includes a soil profile which consists of sand and clays. The soil stiffness increases with depth. The critical soil density is assumed to be 70 pcf to obtain the worst-case effective pressure producing maximum horizontal loads on the retaining wall. The buoyant force on soil due to the ground water table reduces the effective vertical pressure.

OVERTURNING

BRACING

HARD CLAY

BEARING FAILURE

The retaining wall is built through a top-down construction Figure 6.2: Failure Modes for process. The foundation soil is excavated with ring beams Retaining Wall Design constructed simultaneously at adequate unbraced lengths as designed by the geotechnical engineer. Ring beams are then removed from the bottom up as slabs and retaining walls are poured. The soil layers become stiffer further below the ground surface. At a depth of 85 ft, there is a very hard clay of undrained shear strength of 15 ksf. The retaining wall sits on this layer and the high bearing capacity prevents bearing failure. Construction joints are provided at every 20 ft to reduce the longitudinal settlement and tilt. Calculation 6.1 shows the design for the retaining wall structure.

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6.3 Parking Garage Slab Design The reinforced concrete slab for the parking garage was designed as a two-way slab using the equivalent frame method, as per ACI 318-08. An expansion joint is built between the two slab sections to reduce cracking. The following assumptions were made while designing the parking garage slab.         

All slab design assumes rectangular slab sections designed to the maximum span calculated from column locations in provided floor plans. Outside of the building footprint, columns are spaced in an orthogonal grid. Inside the building footprint, columns offset from an assumed orthogonal gridline by 6 ft or less are considered on that gridline. Core and foundation caissons bear the slab load. Slabs are designed as cantilevers to the retaining walls. Deformed Welded Wire Reinforcement (WWR) is used for flexural reinforcing design, Fy = 80 ksi. Light weight concrete is used with a density, ρc = 110 pcf and a 28-day compressive strength, f’c = 4000 psi. Diameter of circular columns is 32 in. The slab was designed without interior beams or edge beams.

The parking slab design utilized MASTAN to model the moment frame connections between the caissons and parking slabs for all seven floors. Design loads Section 2.4 were used to find the maximum positive and negative moments along the slab. Per ACI 318-08, 13.2.1 and 13.6.4.1, the critical moments are proportionally distributed to the column and middle strips of the slab width. Drop panels were designed at the top of each column to reduce negative moment reinforcement. The ultimate slab design was 12 in thick. The design does not call for interior or edge beams because of the high strength WWR used for flexural reinforcement. WWR can be costly; however, for large projects the steel savings outweigh the material cost The design process and calculations are summarized in Calculation 6.2.1.

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6.4 Bell Caisson Design Belled Caissons are used to support the parking garage slab. Caissons were designed following Chapter I: Design of Composite Members in the AISC Steel Construction Manual. Circular reinforced concrete columns were used in the parking garage, extending below the bottom slab into belled caissons, which rest on the hardpan at an elevation of 92 ft below the top slab of the parking garage. The bell shape was needed to lower the applied pressure on the soil. The bell design minimized the bearing pressure to be within the allowable pressure of 45 ksf. The columns unbraced lengths were based on support from the parking garage slabs. The columns were designed as reinforced concrete columns with steel reinforcing or W-shapes depending on the column load. Calculation 6.2.3 follows the AISC procedure for bell caisson design. Figure 6.3 shows an elevation of the foundation and belled caissons.

Figure 6.3: Elevation of Bell Caissons

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6.5 Rock-Socketed Caisson 6.5.1 Column Design Caissons of 10 ft diameter using 14 ksi concrete were designed to carry the load from the core and mega-columns to the bed rock. Each mega-column is supported by two caissons, whereas the core is supported by 20 caissons. The caissons are socketed into the bed rock; limiting the settlement of the caissons. Figure 6.4 shows an elevation view of the core and mega-column caissons.

Mega-Column Caisson

Mega-Column Caisson

Core Caissons

Bedrock Figure 6.4: Elevation of Rock-Socketed Caissons Each caisson is a steel cylinder filled with concrete (Figure 6.5). The steel cylinder prevents any soil-concrete interaction and provides a higher strength to the caisson due to composite action. There is no uplift friction on the caisson by soil, as the steel provides a smooth surface with negligible vertical friction. Stresses induced in the caisson due to the loads from super structure are well within the allowable limits.

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Figure 6.5: Detail of Caisson Settlement is the controlling criteria in the design of caissons, as a higher differential settlement may lead to severe structural damages. A stiffer base material provides greater resistance to the settlement in the caisson. The loads carried by the caissons are obtained from the MIDAS-GEN model and the Geotechnical Report. Three limit states, shown in Figure 6.6 were checked for the caisson design (Calculation 6.3).

Figure 6.6: Limit states for Caisson Design from Left to Right: a) Stress, b) Settlement and c) Uplift

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6.5.2 Ring Beam A reinforced concrete ring beam was designed to connect the core walls to the rock-socketed caissons. This will ensure a uniform distribution of the axial load to the 20 caissons. The ring beam will also dissipate the shear force. The shear force is resisted by the passive earth pressure of the ring pushing against the soil, by the friction between the soil and the slab, and by the bottom of the ring beam. Figure 6.7 shows an elevation of the ring beam and its relation to the slab, core wall, and rock-socketed caisson. Figure 6.8 shows the ring beam’s resistance to the horizontal soil pressure.

Figure 6.7: Elevation of Ring Beam

Soil Pressure

Figure 6.8: Plan View of Ring Beam Resistance to Soil Pressure

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6.5.3 Finite Element Model An ABAQUS model was developed to perform a finite element analysis and monitor the stresses in the rock-socketed caisson. Each mega-column is supported by two circular caissons. These megacolumns are inclined, which exerts a compressive pressure and a horizontal shear on the caissons below it. The loads carried by the caissons were obtained from the MIDAS Gen model. Since the caissons are encased in a steel cylinder, the vertical soil friction is negligible, and is not considered. The following material properties are used in the ABAQUS model.    

Young`s modulus of bedrock, Er = 3500 ksi Poisson`s ratio of the bedrock, ν = 0.28 Friction coefficient for bed rock and caisson interaction = 0.3 Directionality of the friction is isotopic.

For the caisson and bedrock socket, interaction property is modeled as contact, and the contact property is modeled as tangential. The bedrock and caisson are constrained as ties, where the caisson is the master surface and the bedrock is the slave surface. After performing iterations to obtain an optimum mesh configuration, the caisson and bedrock were meshed as triangular elements. The following stresses are obtained from the finite element analysis.

Caisson

Bedrock

Figure 6.9: a) Compression and b) Tension Stresses in Rock-Socketed Caisson under Mega-Columns

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6.0 FOUNDATION DESIGN AND DETAILING It can be seen in Figure 6.9 that the maximum stresses occur at the top surface of the caisson. The stresses decrease as we move down towards the middle portion of the caisson and at the interaction of caisson and bedrock, higher stresses are encountered. Table 6.1: Critical Von Mises Stresses from ABAQUS Model Von Mises Stress

Top Face

Bottom Face

Maximum Compression stress (ksi)

6.3

3.7

Maximum Tension stress (ksi)

4.9

1.9

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7.0 LONG-TERM DEFLECTION EFFECTS

7.0 Long-Term Deflection Effects The aim of the creep and shrinkage calculations for the core and the columns is to determine the deflection in each and the differential between the two. It can be predicted that the steel columns will have minimal shrinkage as compared to the core, so this should be accounted for during construction. Things to consider in this calculation will include the construction schedule, curing conditions, loads, geometry, and strength of the concrete and steel. When a load is applied on the structure, there is an initial elastic strain, which occurs when the load is placed on the column. In addition to this, there is a creep strain, which starts when a load is applied, and a shrinkage strain, which begins as the concrete begins to dry. Both of these increase over time and approach the ultimate strain value. The ultimate creep coefficient and shrinkage strain are both determined by the curing conditions, the concrete mixture, and the construction schedule. All of the calculated values for deflection will need to be considered in the final construction to meet serviceability requirements, particularly the difference between the deformation in the core and the columns.

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7.1 Conceptual Summary The aim of this chapter is to determine the creep and shrinkage of concrete in the core, as well as elastic deformations in both the core and columns. It is very important to evaluate the differential deformation between the core and columns to alleviate unexpected stresses and deformations. It can be predicted that the steel columns will have minimal deformation as compared to the core, so this will need to be accounted for during construction. Variables to consider in the deformation calculations will include the construction schedule, curing conditions, loads, geometry, and strength of the concrete and steel. When a load is applied on a steel column or the concrete core, there is an initial elastic strain, which occurs when the load is added. In addition to the immediate elastic strain, in the concrete core there is a long-term creep strain, which starts when a load is applied, and a long-term shrinkage strain, which begins as the concrete begins to dry. Both of these long-term strains increase over time and approach the ultimate strain value. The ultimate creep coefficient and shrinkage strain are both affected by the curing conditions, the concrete mixture, and the construction schedule. All of the calculated values will need to be considered in the final construction to meet serviceability requirements, particularly the differential deformation between the core and the columns.

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7.2 Creep and Shrinkage Analysis Several simplifying assumptions about the core composition and geometry were made in the analysis. The 28-day strength of the concrete is 14,000 psi as specified earlier in the project. Per ACI 209R, the GL2000 method assumes the concrete’s elastic modulus is a function of the strength, and specifies a time-dependent function to calculate the actual strength at any given point in time, as indicated in Figure 7.1 and Figure 7.2.

Figure 7.1: Concrete Strength Gain with Time

Figure 7.2: Concrete Elastic Modulus Gain with Time 84

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7.0 LONG-TERM DEFLECTION EFFECTS The core was assumed to be a cylindrical tube of concrete, with constant radius and thickness throughout each bank. The amount of steel reinforcement within the core was calculated previously, so the values from that calculation were used in this analysis. Appendix 9.14, Table 9.15 outlines core properties and dimensions used in the analysis. In addition, per the recommendation of a professional engineer, the core will be analyzed using the same model and methods as a typical column. The construction schedule of the spire was extremely important to the creep and shrinkage calculations. Aspire assumed a 4-day cycle for floor construction, meaning a new floor would be added every 4 days. Although this seemed like a very fast-paced schedule, it is important to note that the Burj Khalifa was constructed successfully using a 3-day cycle (Abdelrazaq, 2008). In addition, three simplifying assumptions for analysis were made:   

Curing time: 4 days Loading age: 4 days Construction loads occupy the top 4 floors at any given point during construction.

It is important to note that these assumptions may not be entirely realistic, but will give conservative values for strain. The construction loads are assumed to be mainly composed of heavy machinery and lifting equipment, which will move up the spire as new floors are constructed. Once the construction period has ended these loads will no longer exist. The exact sequence of construction was not considered. After consulting professional engineers, ASPIRE concluded that the main focus of this analysis should be the long-term deformations of the Spire, which will not be significantly affected by the order of construction. Due to the increased loading near the base of the tower compared to the top, the Spire was split up into 13 vertical segments. The middle floor of each of these segments was considered to be representative of the average deformation of the floors in the segment, and was analyzed. The floor deformation for that middle floor was then multiplied by the number of floors in the segment, giving a total deformation for the segment. The sum of the segment deformations results in the total building deformation. During the analysis, it was observed that the long-term creep and shrinkage rates had tapered off around 20 years, so the analysis was completed for a 20 year span from the start of construction. This is consistent with ultimate creep values being calculated after 20 years of loading.

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7.2.1 Columns All the vertical columns in the spire were designed as built-up steel members, so they will not be affected by any noticeable creep or shrinkage. As such, they were only analyzed for the elastic deformation due to loading. The elastic deformation was calculated by:

The elastic strain analysis resulted in an overall deflection of 6.77 inches expected in the steel columns over the 150-story building. See Appendix 9.14, Table 9.16 for the tabulated results for each floor segment and Appendix 9.14.1 for a representative calculation of the strains. Calculation 7.1 summarizes the steel column deformation.

7.2.2 Core The core analysis required that creep and shrinkage were considered, though they were negligible or nonexistent in the steel columns. The effects of creep and shrinkage were calculated using the GL2000 model. See Appendix 9.14.3 for a step-by-step qualitative approach to using the GL2000 model, and Appendix 9.14.1 for an example calculation. Calculation 7.2 summarizes the concrete core deformation. In the GL2000 model, several variables need to be chosen by the designer. The only variable related to the concrete mix design is the cement type. The GL2000 can be used with Type I, II, or III cements, which the designer must choose between. A sensitivity analysis revealed that Type III cement will result in the lowest creep and shrinkage values, most likely due to its rapid initial strength gain.

Table 7.1: Cement Type Deformation Sensitivity Analysis Cement Type Type I Type II Type III

Ultimate Deformation 24.79 24.91 23.95

However, as seen in Figure 7.3, there are also problems associated with Type III cement because the rapid strength gain results in lower final strength due to weaker bonds formed in the hydration process. The rapid strength gain also results in large amounts of heat of hydration during the chemical reaction, which can be problematic especially for our core due to its enormous mass. Type I cement was used for the Chicago Spire because of its higher eventual strength, which will be very necessary to attain the specified compressive strength of 14,000 psi.

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7.0 LONG-TERM DEFLECTION EFFECTS

Figure 7.3: Initial Strength Gain of Concrete for Various Cement Types The GL2000 model also requires input data on the humidity that is expected for the concrete’s environment. Using data from the National Climactic Data Center, the average humidity for Chicago was determined to be 71.4%. The average over a full year is used because the core is expected to be somewhat exposed to the environment for at least the first two years of construction, which is also the period of the greatest creep and shrinkage strains. See Appendix 9.14, Table 9.17 for a summary of the humidity data. The steel reinforcement in concrete has a restraining effect on the creep strains. Since steel does not experience the long-term deflections as significantly as concrete, more steel in a given amount of concrete will result in less overall deformation in that section of the core. The banks have steel percentages ranging from 0.2% in Bank 4 to 5.4% in Bank 2, as seen in Appendix 9.14, Table 9.18. In the analysis, both the amount of deformation in an unreinforced concrete “column” and our reinforced “column” were calculated. The ratio of the reinforced to unreinforced strains was used to modify the elastic, creep, and shrinkage results. It was observed that the reinforced concrete would strain only about 10-15% of the unreinforced concrete. The results of the analysis indicated that the creep strain would dominate the deformation, followed by elastic strain and only a minimal effect from shrinkage strain due to the large volumeto-surface ratios of the massive concrete core. Figure 7.4 shows the breakdown of strains for a typical floor in the spire. The end of construction, and thus of further loading, is clearly indicated by the elbow in both the elastic and creep strain curves. The shrinkage strain constantly increases, but at a very low rate.

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7.0 LONG-TERM DEFLECTION EFFECTS

Figure 7.4: Typical Strain Values for a Single Floor

The analysis of the creep and shrinkage for concrete resulted in an overall expected deformation of 24.8 inches in the core. As can be seen in Table 7.2, approximately 75% of the ultimate deflection occurs in the first two years, but there is still substantial movement out to 20 years, resulting in the ultimate deformation of 24.8 in.

Table 7.2: Core Total Deformations Time (yr) 0 2 3 10 20

Deformation (in) 0 18.8 20.0 23.0 24.8

Percentage of Deformation 0% 76% 81% 93% 100%

Figure 7.5 breaks down the core deformations by floor. It is clearly seen that a majority of the strains occur in Bank 4, with barely any strain evident in Bank 2. This large differential is due to the difference in amounts of steel in each bank, as can be seen in Appendix 9.14, Table 9.18. When altering the floor-to-floor heights to account for differential deformations between the core and columns, the small amount of deformation in Bank 2, along with the large amount of deformation in Bank 4, will need to be taken into account.

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7.0 LONG-TERM DEFLECTION EFFECTS

Figure 7.5: Core Deformations per Floor

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7.0 LONG-TERM DEFLECTION EFFECTS

7.3 Conclusion and Recommendations The creep and shrinkage strain analysis resulted in very different deformations between the core and the surrounding steel columns. As displayed in Table 7.3, the 24.8-inch deformation in the core is greater than the 6.77-inch deformation in the steel by 18.0 inches. This differential deformation can be very dangerous in tall buildings. Not only could aesthetically displeasing cracks form, but serious structural issues could result as well. If this deformation is not designed for, as the core deforms more than the columns, the floors will become slanted and connections will become overstressed. Table 7.3: 20-Year Deformation Comparisons Core Deformation: Steel Deformation: Core-Column Difference: Compensation / floor required:

24.8 in 6.77 in 18.0 in 0.12 in

To compensate for the differential settlement, the core should be built approximately 18 in higher than the original design calls for. Since the creep and shrinkage model is inherently inaccurate up to 20 -30%, additional height should be added in addition to the 18 in. For comparison, the Burj Khalifa designers estimated a 12 in deformation in their core, but increased the design height of the core by 22 in (Baker et al., 2007). Aspire recommends approximately a 30 in increase in the core height based on this preliminary analysis to account for uncertainties. As can be seen in Figure 7.6, the majority of the strains in the core will take place during the construction period. This fact means that by the time the building needs to be serviceable, most of its deformation will have occurred and need not be designed for. Also, the additional height that was added for each floor-to-floor height will not be as noticeable throughout the life of the structure. Rather, the floors will appear level and as designed for the tenants.

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Figure 7.6: Total Core Displacement over Time ASPIRE recommends further creep and shrinkage analysis in order to better understand the behavior of the building. Creep and shrinkage laboratory tests are highly recommended as soon as the concrete mix is decided upon. The data obtained from those tests can further improve the accuracy of the GL2000 model. For instance, the ultimate shrinkage value in the GL2000 model is approximated from a formula proportional to the square root of the mean compressive strength of the concrete. Alternatively, this value can be determined from the laboratory test and inputted directly into the analysis. In addition, the creep coefficient can be determined from the tests and used instead of a very complicated formula approximation. Especially considering the unique nature of a 14,000 psi concrete, it is highly advisable to further examine the creep and shrinkage behaviors.

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8.0 REFERENCES

8.0 References Abdelrazaq, A., Kim, K. J. & Kim, J. H. (2008). “Brief on the Construction Planning of the Burj Dubai Project, Dubai, UAE. Proceedings of the CTBUH 8th World Congress, 3rd-5th March 2008. Dubai, UAE.” Published by the Council on Tall Buildings and Urban Habitat, Chicago. pp. 386-394. American Concrete Institute. “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08).” ACI Manual of Concrete Practice, Part 1, 2010. American Concrete Institute. ACI 318-08 Building Code and Commentary. 2008. American Institute of Steel Construction. “Floor Vibrations Due to Human Activity.” American Institute of Steel Construction, Steel Design Guide Series 11. 2003. American Institute of Steel Construction. Steel Construction Manuel Thirteenth Edition, 2008. American Institute of Steel Construction. Engineering for Steel Construction: A Source Book on Connections, 1984. American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures. 2006. Reston, Virginia: American Society of Civil Engineers, 2006. American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures. 2010. Reston, Virginia: American Society of Civil Engineers, 2010. Baker, William F. “Energy-Based Design of Lateral Systems.” Structural Engineering International. Vol 2. No 2. 1 May 1992. p 99-102. Baker et al. “Creep and Shrinkage and the Design of Supertall Buildings – A Case Study: The Burj Dubai Tower.” American Concrete Institute. Special Publication, volume 246, pp. 133-148. 1 Sept 2007. Binder, Georges. One Hundred and One of the World's Tallest Buildings. Australia: The Images Publishing Group Pty Ltd, 2006. Google Books. Blodgett, Omer W. Design of Welded Structures. Cleveland, OH: Lincoln, 1972. 8.2-2. Print. "Chicago Spire." SkyScraperPage. Skyscraper Source Media, 2011. Web. 14 Sep 2011. . International Code Council, International Building Code, 2009. Salmon, Charles G. and John E. Johnson. Steel Structures: Design and Behavior. Fourth Edition. Prentice Hall: Upper Saddle River, NJ. 1996

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8.0 REFERENCES Smith, S.E. “What Is a Mechanical Floor?” 29 July 2011. wiseGEEK.com. 15 Sep. 2011 . Taranath, Bungale S. Steel, Concrete, & Composite Design of Tall Buildings. New York City: McGrawHill Book Company, 1998. Taranath, Bungale S. Structural Analysis & Design of Tall Buildings. New York City: McGraw-Hill Book Company, 1988. Print. Wight, J. and James MacGregor. Reinforced Concrete Mechanics & Design, Fifth Edition. Upper Saddle River, NJ: Pearson Prentice Hall. 2009 Vulcraft. VULCRAFT Steel Roof & Floor Deck, 2008.

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9.0 APPENDIX

9.0 Appendix Appendix consists of supplementary information and summary tables. Following the appendix are sample calculation and the complete structural drawing set. Note that a “--“ indicates that the size, length, dimension, percentage, etc. is not applicable for the given cell.

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9.0 APPENDIX

9.1 Gravity Design Loads Dead Load (psf)

Typical Floor Lobby Decking and Slab1 Assembly Areas (lobbies) Acoustical fiber board MEP Duct Allowance Ceramic or quarry tile (1 1/2 in) on 1 in. mortar bed2 Total Residential Decking and Slab1 Private rooms and corridors serving them Partition Walls Acoustical fiber board Ceramic or quarry tile (3/4 in) on 1 in. mortar bed MEP Duct Allowance Total Mechanical Decking and Slab1 Catwalks Machine Space MEP Duct Allowance

Superimposed Dead Load (psf)

Live Load (psf)

32 100

32

1 10 46 57

100

33 40 15

33

1 23 10 34

55

39 40 200 Total

Parking Slab (150 pcf @ 12 in.)3 Garages (passenger vehicles only) MEP Duct Allowance Cement finish (1-in.) on stone-concrete fill

39

10 10

240

150 40

Total

150

Total

55 55

Core Slab (110 pcf @ 6 in.) 3

10 32 42

40

1

Decking and Slab DL from Appendix 9.7 Ceramic floor twice as thick in lobby floors 3 Slab thickness determined by gravity design 2

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9.0 APPENDIX

9.2 RWDI Recommended Wind Load Table 9.1: RWDI Wind Load Combinations

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9.0 APPENDIX Table 9.2: RWDI Provided Wind Forces and Torsional Moments Floor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Fx (kips) 27 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 54 54 54 54 54 54 54 55 55 55 55 55 56 56 56 56 57 57 57

Fy (kips) 20 40 40 40 40 40 40 41 41 41 41 41 41 41 42 42 42 42 43 43 43 44 44 44 45 45 45 46 46 46 47 47 48 48 48 49 49 49

Torsional Moment, Mz (kip-ft) 44 96 102 109 144 195 212 233 239 240 252 264 275 287 298 306 314 324 335 345 354 364 372 381 392 399 411 418 427 433 443 451 458 467 474 484 491 479

ASPIRE

Critical Overturning Moment (kip-ft x 106) 9.41 9.28 9.16 9.04 8.92 8.80 8.68 8.56 8.45 8.33 8.21 8.10 7.98 7.87 7.76 7.64 7.53 7.42 7.31 7.20 7.09 6.98 6.88 6.77 6.66 6.56 6.45 6.35 6.25 6.14 6.04 5.94 5.84 5.74 5.64 5.55 5.45 5.35

Critical Force (kips) 27.4 54.6 54.4 54.4 54.5 54.4 54.3 54.4 54.3 54.2 54.1 54.2 54.4 54.4 54.5 54.7 54.7 54.9 54.9 55.1 55.2 55.4 55.6 55.8 56.0 56.1 56.3 56.5 56.7 56.9 57.2 57.4 57.6 57.8 58.1 58.5 58.7 58.7

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9.0 APPENDIX

Floor 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 98

Fx (kips) 57 57 56 56 56 57 57 57 57 58 58 58 58 59 59 59 59 60 60 60 61 61 61 62 62 63 63 63 63 64 64 64 64 64 64 64 61 61 61

Fy (kips) 49 49 49 49 49 50 50 51 51 51 52 52 53 53 54 54 55 55 56 56 56 57 57 58 58 59 60 60 60 61 61 62 62 62 62 62 59 59 59

Torsional Moment, Mz (kip-ft) 470 470 437 442 447 453 457 465 467 473 477 480 484 487 490 492 498 502 503 506 509 514 513 515 518 539 544 546 529 534 535 538 538 520 520 520 399 402 400 ASPIRE

Critical Overturning Moment (kip-ft x 106) 5.26 5.16 5.07 4.98 4.88 4.79 4.70 4.61 4.52 4.43 4.35 4.26 4.17 4.09 4.00 3.92 3.84 3.75 3.67 3.59 3.51 3.43 3.36 3.28 3.20 3.13 3.05 2.98 2.91 2.83 2.76 2.69 2.62 2.56 2.49 2.42 2.35 2.29 2.23

Critical Force (kips) 58.7 58.7 57.7 58.0 58.1 58.4 58.5 58.9 59.2 59.5 59.9 60.1 60.4 60.7 61.0 61.2 61.6 62.0 62.3 62.6 63.0 63.3 63.5 63.9 64.1 65.2 65.5 65.9 65.5 66.1 66.4 66.7 66.8 66.8 66.8 66.8 63.4 63.6 63.7

9.0 APPENDIX

Floor 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

Fx (kips) 62 62 62 62 63 63 63 63 64 64 64 65 65 65 66 66 66 66 67 67 68 68 68 69 69 70 70 71 71 72 72 70 70 70 69 70 70 69 69

Fy (kips) 60 60 60 60 61 61 62 62 62 63 63 64 64 64 65 65 65 66 66 66 67 67 68 68 68 69 69 69 69 69 69 69 69 69 67 67 68 67 67

Torsional Moment, Mz (kip-ft) 403 406 400 399 399 399 402 398 401 403 400 401 396 398 401 399 394 389 388 368 387 385 384 386 382 384 383 382 383 382 380 381 381 381 337 333 330 322 317

ASPIRE

Critical Overturning Moment (kip-ft x 106) 2.16 2.10 1.99 1.98 1.92 1.86 1.80 1.74 1.69 1.63 1.58 1.52 1.47 1.42 1.36 1.31 1.27 1.22 1.17 1.12 1.08 1.03 0.99 0.95 0.90 0.86 0.82 0.78 0.74 0.71 0.67 0.64 0.60 0.57 0.54 0.51 0.47 0.45 0.42

Critical Force (kips) 64.0 64.6 64.6 64.7 65.1 65.4 65.9 66.0 66.5 66.9 67.1 67.6 67.6 68.2 68.6 68.9 69.0 69.3 69.6 69.9 70.4 70.6 71.2 71.8 72.0 72.8 73.2 73.7 74.1 74.6 74.9 73.0 73.0 73.0 72.1 72.4 72.7 72.0 72.1

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9.0 APPENDIX

Floor 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

100

Fx (kips) 70 71 71 71 72 78 70 66 67 67 66 67 67 68 69 69 68 68 68 67 67 66 65 62 59 76 71 55 59 59

Fy (kips) 68 68 69 69 69 76 68 63 64 64 64 64 64 64 65 65 64 64 64 63 62 62 60 58 55 71 67 51 55 55

Torsional Moment, Mz (kip-ft) 315 312 310 307 304 314 260 266 264 258 251 248 242 237 233 225 217 211 202 193 185 176 165 148 129 115 104 92 92 92

ASPIRE

Critical Overturning Moment (kip-ft x 106) 0.39 0.36 0.34 0.31 0.29 0.27 0.24 0.22 0.20 0.19 0.17 0.15 0.13 0.12 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.00 0.00

Critical Force (kips) 72.9 73.4 73.9 74.0 74.6 80.9 73.0 68.4 69.2 69.2 68.8 69.2 69.7 70.6 71.2 71.2 70.9 70.8 70.2 69.6 69.2 68.3 67.1 64.5 61.7 78.8 73.8 56.6 60.8 60.8

9.0 APPENDIX

9.3 Seismic Load Summary Floor Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Floor Type1 L L L L L R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M

Lateral Force, Fx

Story Shear , Vx

Moment (Mx)

(kips) 0.01 0.05 0.11 0.19 0.3 0.43 0.58 0.76 0.96 1.18 1.43 1.7 2 2.32 2.66 3.03 3.42 3.83 4.27 4.73 5.22 5.73 6.26 6.81 7.39 8 8.62 9.28 9.95 10.65 11.37 12.11 12.88 13.68 14.49 15.33 16.2 25.17

(kips) 6,563 6,563 6,563 6,563 6,563 6,562 6,562 6,561 6,560 6,560 6,558 6,557 6,555 6,553 6,551 6,548 6,545 6,542 6,538 6,534 6,529 6,524 6,518 6,512 6,505 6,498 6,490 6,481 6,472 6,462 6,451 6,440 6,428 6,415 6,401 6,387 6,371 6,355

(kip-ft x 106) 8.82 8.74 8.65 8.56 8.48 8.39 8.30 8.22 8.13 8.04 7.96 7.87 7.79 7.70 7.61 7.53 7.44 7.35 7.27 7.18 7.10 7.01 6.92 6.84 6.75 6.67 6.58 6.50 6.41 6.33 6.24 6.16 6.07 5.99 5.90 5.82 5.74 5.65

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9.0 APPENDIX

Floor Level 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 102

Floor Type1 M L R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M M L R R R R

Lateral Force, Fx

Story Shear , Vx

Moment (Mx)

(kips) 26.51 15.46 15.69 16.46 17.26 18.07 18.9 19.75 20.62 21.5 22.41 23.33 24.27 25.24 26.22 27.21 28.23 29.27 30.32 31.4 32.49 33.6 34.73 35.88 37.04 38.23 39.43 40.65 41.89 43.15 44.43 45.73 47.05 77.4 79.57 39.19 38.42 39.45 40.49 41.55

(kips) 6,330 6,303 6,288 6,272 6,256 6,238 6,220 6,201 6,182 6,161 6,140 6,117 6,094 6,070 6,044 6,018 5,991 5,963 5,933 5,903 5,872 5,839 5,806 5,771 5,735 5,698 5,660 5,620 5,580 5,538 5,495 5,450 5,404 5,357 5,280 5,200 5,161 5,123 5,083 5,043

(kip-ft x 106) 5.57 5.49 5.40 5.32 5.24 5.16 5.07 4.99 4.91 4.83 4.75 4.67 4.59 4.51 4.43 4.35 4.27 4.19 4.11 4.04 3.96 3.88 3.80 3.73 3.65 3.58 3.50 3.43 3.36 3.28 3.21 3.14 3.07 3.00 2.93 2.86 2.79 2.72 2.66 2.59

ASPIRE

9.0 APPENDIX

Floor Level 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118

Floor Type1 R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M M L R R R R R R R

Lateral Force, Fx

Story Shear , Vx

Moment (Mx)

(kips) 42.62 43.71 44.81 45.92 47.05 48.19 49.34 50.51 51.69 52.89 54.1 55.32 56.55 57.8 59.07 60.34 61.64 62.94 64.26 65.59 66.94 68.29 69.67 71.05 72.45 73.87 75.29 76.74 78.19 79.66 147.66 150.38 56.76 53.67 54.63 55.6 56.58 57.57 58.57 59.58

(kips) 5,001 4,959 4,915 4,870 4,824 4,777 4,729 4,680 4,629 4,577 4,525 4,471 4,415 4,359 4,301 4,242 4,181 4,120 4,057 3,993 3,927 3,860 3,792 3,722 3,651 3,579 3,505 3,429 3,353 3,275 3,195 3,047 2,897 2,840 2,786 2,732 2,676 2,620 2,562 2,503

(kip-ft x 106) 2.53 2.46 2.40 2.33 2.27 2.20 2.14 2.08 2.02 1.96 1.90 1.84 1.78 1.73 1.67 1.61 1.56 1.50 1.45 1.40 1.35 1.30 1.25 1.20 1.15 1.10 1.06 1.01 0.97 0.92 0.88 0.84 0.80 0.76 0.73 0.69 0.66 0.62 0.59 0.56

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9.0 APPENDIX

Floor Level

Floor Type1

Lateral Force, Fx

(kips) 119 R 60.59 120 R 61.61 121 R 62.64 122 R 63.68 123 R 64.73 124 R 65.79 125 R 66.85 126 R 67.93 127 R 69.01 128 R 70.1 129 R 71.2 130 R 72.31 131 R 73.42 132 R 74.55 133 R 75.68 134 R 76.83 135 R 77.98 136 R 79.14 137 R 80.3 138 R 81.48 139 R 82.67 140 R 83.86 141 R 85.06 142 R 86.27 143 R 87.49 144 R 88.72 145 R 89.96 146 M 210.54 147 M 213.43 1 L: Lobby; R: Residential; M: Mechanical

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Story Shear , Vx

Moment (Mx)

(kips) 2,444 2,383 2,322 2,259 2,195 2,131 2,065 1,998 1,930 1,861 1,791 1,720 1,647 1,574 1,499 1,424 1,347 1,269 1,190 1,109 1,028 945 861 776 690 603 514 424 213

(kip-ft x 106) 0.52 0.49 0.46 0.43 0.40 0.37 0.35 0.32 0.30 0.27 0.25 0.23 0.20 0.18 0.16 0.14 0.13 0.11 0.09 0.08 0.07 0.05 0.04 0.03 0.02 0.02 0.01 0.00 0.00

9.0 APPENDIX

9.4 Core Slab Design Summary All core slabs are 6 in. thick, 110 pcf lightweight concrete.

Bank 1

Span (ft) Residential / Lobby: 1 10.16 2 8.25 3 14.70 4 8.40 Mechanical: 1 10.2 2 8.3 3 14.7 4 8.4 Bank 3 Residential / Lobby: 1 10.16 2 6.06 3 6.06 4 7.8 Mechanical: 1 10.16 2 6.06 3 6.06 4 7.8

Rebar in Both Rebar Directions Dist. # (in, o.c.) 4 4 4 4

14 18 6 18

5 5 5 5

12 18 6 18

Span (ft) Residential / Lobby: 1 10.16 2 8.25 3 14.7 4 8.4 Mechanical: 1 10.16 2 8.25 3 14.7 4 8.4

4 4 4 4

14 18 18 18

Bank 4.1 / 4.2 Residential / Lobby: 1 10.16 2 6.06 3 6.06 4 10.18

4 4 4 4

8 18 18 16

ASPIRE

Bank 2

Rebar in Both Directions Rebar Dist. # (in, o.c.) 4 4 4 4

14 18 6 18

5 5 5 5

12 18 6 18

4 4 4 4

14 18 18 14

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9.0 APPENDIX

9.5 Link Beam Summary Table 9.3: Link Beam Dimensions Length

Tributary Area

Bank 1 (ft) (ft2) 1 31.0 120 2 9.34 84.0 3 32.2 484 4 18.3 110 5 40.6 97.9 Bank 2 1 31.0 120 2 9.34 84.0 3 32.2 484 4 18.3 110 5 40.6 97.9 Bank 3 1 11.2 75.6 2 9.34 70.9 3 13.2 122 4 14.0 65.2 5 40.6 97.9 Bank 4.1 1 9.65 65.2 2 9.65 120 3 12.9 92.3 4 9.68 40.3 5 40.6 97.9 1 Bank 4.2 2 9.65 97.9 4 9.68 27.9 5 40.6 97.9 1 Bank 4.2 does not contain Link Beam Type 1 and 3

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Curvature, α

Radius, r

(deg) --42.0 ---

(ft) --40.0 ---

--42.0 ---

--40.0 ---

--43.0 ---

--15.4 ---

------

------

----

----

9.0 APPENDIX Table 9.4: Residential and Lobby Link Beam Summary b

h

1 2 3 4 5

(in) 16 6 48 10 20

(in) 16 10 16 16 16

1 2 3 4 5

16 6 48 10 20

16 10 16 16 16

sstirrup

nbar

stirrup #

9 9 9 9 9

6 2 20 3 6

3 3 4 4 4

(in) 7.2 4.2 7.1 7.1 7.1

9 9 9 9 9

6 2 20 3 6

3 3 4 4 4

7.2 4.2 7.1 7.1 7.1

1 6 12 9 2 6 10 9 3 28 16 9 4 10 10 9 5 20 16 9 Bank 4.1 1 8 8 9 2 8 10 9 3 30 16 9 4 8 6 9 5 20 16 9 1 Bank 4.2 2 8 10 9 4 8 6 9 5 20 16 9 1 Bank 4.2 does not contain Link Beam Type 1 and 3

2 2 11 2 6

3 3 3 3 4

5.2 4.2 7.2 4.2 7.1

2 2 10 2 6

3 3 4 3 3

3.2 4.2 7.1 2.2 7.2

2 2 6

3 3 3

4.2 2.2 7.2

Bank 1

bar #

Bank 2

Bank 3

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9.0 APPENDIX Table 9.5: Mechanical Floor Link Beam Summary b

h

1 2 3 4 5

(in) 22 8 72 12 24

(in) 16 10 16 16 16

1 2 3 4 5

22 8 72 12 24

16 10 16 16 16

sstirrup

nbar

stirrup #

9 9 9 9 9

6 2 20 3 6

3 3 4 4 4

(in) 7.2 4.2 7.1 7.1 7.1

9 9 9 9 9

6 2 20 3 6

3 3 4 4 4

7.2 4.2 7.1 7.1 7.1

1 10 10 9 2 2 8 10 9 2 3 48 16 9 11 4 10 10 9 2 5 24 16 9 6 Bank 4.1 1 10 8 9 2 2 10 10 9 2 3 12 10 9 10 4 8 8 9 2 5 24 16 9 6 1 Bank 4.2 2 8 10 9 2 4 6 8 9 2 5 24 16 9 6 1 Bank 4.2 does not contain Link Beam Type 1 and 3

3 3 3 3 4

4.2 4.2 7.2 4.2 7.1

3 3 3 3 3

3.2 4.2 4.2 3.2 7.2

3 3 3

4.2 3.2 7.2

Bank 1

bar #

Bank 2

Bank 3

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9.0 APPENDIX

9.6 Beam Spans and Tributary Areas Bank 1 Lobby and Mechanical Length ft

Joist 1 15.3

Joist 2 17.7

Joist 3 20.1

Circumferential Girder 22.5

Angled Girder 27.9

Radial Girder 37.0

Long Cantilever 21.2

Short Cantilever 9.1

Tributary Area Residential Length

ft2

122.9

150.3

174.9

223.4

285.9

--

--

--

ft

15.7

19.1

--

22.5

27.9

37.0

21.2

9.1

Tributary Area

2

173.3

236.5

--

258.6

285.9

--

--

--

Angled Girder 25.3

Radial Girder 31.2

Long Cantilever 19.2

Short Cantilever 8.7

ft

Bank 2 Lobby and Mechanical Length ft

Joist 1 14.3

Joist 2 16.3

Joist 3 18.3

Circumferential Girder 20.4

Tributary Area Residential Length

ft2

100.5

117.6

131.7

185.7

259.4

--

--

--

ft

14.9

17.7

--

20.4

25.3

31.2

19.2

8.7

Tributary Area

2

144.1

172.6

--

210.5

259.3

--

--

--

Joist 1 18.9

Joist 2 21.7

Joist 3 24.4

Circumferential Girder 27.2

Angled Girder 33.7

Radial Girder 27.6

Long Cantilever 19.3

Short Cantilever 5.0

ft

Bank 3 Lobby and Mechanical Length ft Tributary Area Residential Length

ft2

113.1

137.4

154.7

237.5

344.9

--

--

--

ft

18.9

23.1

--

27.2

33.7

27.6

19.3

5.0

Tributary Area

2

158.5

225.0

--

281.2

344.9

--

--

--

ft

Joist 1 18.9

Joist 2 21.7

Joist 3 24.4

Circumferential Girder 27.2

Angled Girder 33.7

Radial Girder 27.6

Long Cantilever 19.3

Short Cantilever 5.0

Tributary Area Residential Length

ft2

113.1

137.4

154.7

237.5

344.9

--

--

--

ft

19.6

23.1

--

26.7

33.0

27.6

16.5

5.0

Tributary Area

2

152.5

193.0

--

258.9

338.6

--

--

ft

Bank 4 Lobby Length

ft

ASPIRE

109

9.0 APPENDIX

9.7 Slab and Decking Summary Table 9.6: Decking and Slab Thickness Summary for Composite Beam System Lobby Properties Type t Rib Height Rib Spacing

1.5VL22 2.5 1.5 6

Residential 1-3 4 1.5VL22 1.5VL19 2.5 2.5 1.5 1.5 6 6

1 2VLI16 2.5 2 12

Mechanical 2 3 2VLI19 2VLI20 2.5 2.5 2 2 12 12

All decking uses 6x6 - W1.4xW1.4 shrinkage mesh

Table 9.7: Unfactored Dead Load for Composite Beam System Floor Type Lobby Residential Mechanical

DL 32 33 39

Includes weight of concrete and decking

110

ASPIRE

psf psf psf

4 2VLI16 2.5 2 12

9.0 APPENDIX

9.8 Composite Beam Summary Table 9.8: Composite Beam Summary Bank 1 Lobby Residential Mechanical

Joist 1

Joist 2

Joist 3

W12x14 (30) W12x14 (16) W14x22 (15)

W12x26 (70) W12x22 (19) W14x30 (17)

W12x35 (80)

W12x19 (56) W12x16 (29) W12x19 (14)

W12x14 (32) W12x16 (35) W12x22 (32)

W12x19 (36)

W12X16 (37) W12X22 (74) W14x22 (36)

W12X35 (86) W12X35 (92) W14x30 (42)

W12X40 (96)

W12X16 (37) W12 x 22 (39)

W12X35 (86) W12 x 30 (92)

W12X40 (96)

W12x22 (39)

W12x30 (92)

-W16x36 (20)

Angled Girder W14x82 (110) W14x53 (110) W18x76 (81)

Circumferential Girder W16x31 (45) W14x34 (90) W16x50 (44)

W14x61 (50) W14x43 (50) W16x67 (75)

W12x45 (80) W14x26 (80) W12x45 (40)

W14X120 (134) W14x82 (134) W21x111 (66)

W12X65 (108) W14x43 (108) W21x55 (81)

W14X120 (134) W14 x 74 (132)

W12X65 (108) W14 x38 (106)

W18x60 (66)

W14 x38 (106)

Radial Girder W21x73 (75) W14x61 (80)

Long Cantilever W24x306 (32) W21x182 (32) W27x539 (32)

Short Cantilever W14x193 (19) W21x101 (14) W24x176 (14)

W24x250 (29) W21x166 (29) W27x539 (29)

W18x175 (14) W21x101 (14) W24x250 (14)

W24x192 (29) W21x201 (29) W36x442 (29)

W18x106 (8) W18x46 (8) W21x166 (8)

W18x55 (67) W16x36 (24)

W24x370 (29) W24x176 (25)

W18x106 (8) W18x50 (8)

W16x36 (24)

W24x176 (25)

W18x50 (8)

W14x730

1

Bank 2 Lobby Residential Mechanical

-W12x26 (36)

W21x50 (63) W16x36 (27) W14x730

1

Bank 3 Lobby Residential Mechanical

-W14x38 (48)

W18x55 (83) W16x40 (24) W14x730

1

Bank 4.1 Lobby Residential

--

Bank 4.2 Residential 1

--

W14x730 are rotated girders at the mechanical floors

ASPIRE

111

9.0 APPENDIX

9.9 Initial Gravity Design Column Comparison Table 9.9: Initial Composite and Steel Column Comparison

Steel

Steel

2

Column 3a/3b1 Composite2 Concrete Shape (in) ---------------

Shape W4X13 W8X35 W14X90 W14X193 W14X342 W14X500 W14X550

Concrete2(in) 10X12 14X22 22X26 24X28 24X28 24X28 30X32

Shape --------

W14X730

30X32

W14x455

W14x132

30X30

52 41

W14X730 W14X730

38X40 48X48

W14x500 W14x730

30X30 30X30

1

29

Sq. Pl. 28x6

W14X730

56X58

W14x730

40X40

1

17

Sq. Pl. 32x6

W14X730

64X64

W14x730

50X50

1 1

5 Lobby

Sq. Pl. 36x6 --

W27X539 W14X730

68X70 72X74

W14x605 W14x730 Sq. Pl. 24x5 Sq. Pl. 26x6 Sq. Pl. 28x6 --

W14x665 W14x665

60X60 60X62

Level 145 134 123 113 100 87 75

2

64

2 2

2

Column 1 / 21 Composite2

Shape W14x99 W14x99 W14x193 W14x311 W14x426 W14x550 W14x665 Sq. Pl. 24x4.25 Sq. Pl. 24x5.25 Sq. Pl. 26x6

Bank 4 4 4 4 3 3 3

1

2

Column 2 only applies to Bank 3 & 4. Column 3a/3b only applies to Bank 1 & 2. Columns were sized for both steel and composite configurations and then the optimal design was chosen. The grey text shows the shapes and dimensions not chosen.

112

ASPIRE

9.0 APPENDIX

9.10 MIDAS Gen Gravity Loads Table 9.10: MIDAS Gen Unfactored Gravity Loads (kips / node)

Floor

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Type1

L L L L L R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R

Column 1 SDL + DL 0.0 5.4 5.4 5.4 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2 96.2

LL 0.0 0.0 0.0 0.0 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3

Column 2 SDL + DL LL

ASPIRE

Column 3a/b SDL + DL LL 0.0 0.0 5.4 0.0 5.4 0.0 5.4 0.0 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3 96.2 35.3

Core (Total Load for all core walls divided by # radial girders) SDL + DL

LL

36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4 36.4

32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 113

9.0 APPENDIX

Floor

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 114

Type1

R R M M L R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M M

Column 1 SDL + DL 96.2 96.2 56.3 5.4 75.8 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 74.6 43.8 4.6

LL 35.3 35.3 249.0 0.0 80.0 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 192.0 0.0

Column 2 SDL + DL LL

ASPIRE

Column 3a/b SDL + DL LL 96.2 35.3 96.2 35.3 56.3 249.0 5.4 0.0 75.8 80.0 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 74.6 27.2 43.8 192.0 4.6 0.0

Core (Total Load for all core walls divided by # radial girders) SDL + DL 36.4 36.4 25.1 9.7 33.1 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 32.7 22.4 9.3

LL 32.1 32.1 92.3 16.6 47.8 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 85.2 21.0

9.0 APPENDIX

Floor

74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

Type1

L R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M M L

Column 1 SDL + DL 57.9 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 57.0 33.3 3.2 64.7

LL 61.5 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 147.6 0.0 66.9

Column 2 SDL + DL LL 2.2 0.0 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 57.0 20.9 33.3 147.6 3.2 0.0 64.7 66.9

ASPIRE

Column 3a/b SDL + DL LL 57.9 61.5

Core (Total Load for all core walls divided by # radial girders) SDL + DL 24.3 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 14.3 3.6 24.0

LL 33.2 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 66.6 14.4 36.6

115

9.0 APPENDIX

Floor

Type1

Column 1

SDL + DL LL 112 63.7 22.8 113 63.7 22.8 114 63.7 22.8 115 63.7 22.8 116 63.7 22.8 117 63.7 22.8 118 63.7 22.8 119 63.7 22.8 120 63.7 22.8 121 63.7 22.8 122 63.7 22.8 123 63.7 22.8 124 54.6 19.4 125 54.6 19.4 126 54.6 19.4 127 54.6 19.4 128 54.6 19.4 129 54.6 19.4 130 54.6 19.4 131 54.6 19.4 132 54.6 19.4 133 54.6 19.4 134 54.6 19.4 135 54.6 19.4 136 54.6 19.4 137 54.6 19.4 138 54.6 19.4 139 54.6 19.4 140 54.6 19.4 141 54.6 19.4 142 54.6 19.4 143 54.6 19.4 144 54.6 19.4 145 32.6 136.9 1 L: Lobby; R: Residential; M: Mechanical R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R

116

Column 2 SDL + DL LL 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 63.7 22.8 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 54.6 19.4 32.6 136.9

ASPIRE

Column 3a/b SDL + DL LL

Core (Total Load for all core walls divided by # radial girders) SDL + DL 23.7 23.7 23.7 23.7 23.7 23.7 23.7 23.7 23.7 23.7 23.7 23.7 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 25.3 17.8

LL 23.3 23.3 23.3 23.3 23.3 23.3 23.3 23.3 23.3 23.3 23.3 23.3 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 74.7

9.0 APPENDIX

9.11 Column Validation Summary Table 9.11: Composite and Steel Shapes for Lateral Design Column Validation

1

Bank

Level

4 4 4 3 3 3 2 2 2 1 1 1 1

134 123 113 100 87 75 64 52 41 29 17 5 Lobby

Column 1 / 21 Concrete Steel Shape (in.) W14x233 -W14x370 -W14x550 -W18x35 22x20 W18x50 22x22 W21x111 26x24 W24x146 30x26 W24x131 30x26 W24x162 30x28 W36x361 42x38 W36x330 42x34 W36x330 42x34 W40x324 46x38

Steel % ---2.3% 3.0% 5.2% 5.5% 4.9% 5.7% 6.6% 6.8% 6.8% 5.5%

Column 3a/3b Concrete Shape (in.) Steel % ------------------W24x162 30x26 6.1% W24x146 30x26 5.5% W24x162 30x28 5.7% W36x330 42x34 6.8% W36x330 42x34 6.8% W36x330 42x34 6.8% W40x324 46x38 5.5%

Column 2 only applies to Bank 3 & 4. Column 3a/3b only applies to Bank 1 & 2

ASPIRE

117

9.0 APPENDIX

9.12 MIDAS Sensitivity Analyses Steel built-ups shown in Table 9.12 were used in the MIDAS model for several sensitivity analyses to test the axial discontinuity and lateral deflection of the model. Table 9.12: Built-up Steel and Concrete Properties Column Nomenclature

As (in2)

Ag (in2)

Gross dimension (in)

BU1 BU2 BU3 BU4

768 640 476 364

1600 1296 1024 784

40x40 36x36 32x32 28x28

Three different sensitivity analyses were performed and are summarized in Table 9.13. The builtups in Banks 1-3 were changed and the larger built-up test resulted in less deflection. The discontinuity results for the test are shown in Figure 9.1. Core wall thickness in Bank 3 was also tested (Figure 9.2). The sensitivity analysis for the effects of belt trusses and outriggers kept the core wall sizes to a uniform one foot. While the results are relative to this unrealistic design, they show patterns in belt truss and outrigger functionality given sizing and general existence. Ultimately, the sensitivity analysis showed that the large belt truss and outrigger members were causing large load shedding from the exterior columns to the core. Additionally, the large, built-up steel shapes encased in concrete reduced drift and eliminated the tension forces from the original column design.

118

ASPIRE

9.0 APPENDIX Table 9.13: Sensitivity Analyses Element Properties Core Wall Thickness by Bank (ft)

Vertical Column Size by Bank

111-122

4 123-133

134-145

Δmax

1 2 3 Built Up 10 8 4 10 8 4

4

Belt Truss

3.3 3.3

W14x730 W14x730

W14x730 BU1 /BU2 BU3 BU4 W14x730 BU1 BU2 BU2

W14x550 W14x550

W14x370 W14x370

W14x233 W14x233

5.34 5.09

Core Size 10 8 6 10 8 4 10 8 2

2 2 2

W14x730 W14x730 W14x730

W14x730 W14x730 W14x730

BU1 BU1 BU1

BU2 BU2 BU2 BU2 BU2 BU2

W14x550 W14x550 W14x550

W14x370 W14x370 W14x370

W14x233 W14x233 W14x233

5.06 5.16 5.37

W14x730 None None

BU1 BU1 BU1

BU2 BU2 BU2 BU2 BU2 BU2

W14x550 W14x550 W14x550

W14x370 W14x370 W14x370

W14x233 W14x233 W14x233

8.1 8.34 9.0

Belt Truss and Outrigger 1 1 1 1 W14x730 1 1 1 1 W14x730 1 1 1 1 None

Outrigger

1

2

3

Figure 9.1: Built Up Column Sensitivity Results to Dead Load

ASPIRE

119

9.0 APPENDIX

Figure 9.2: Core Wall Thickness Sensitivity Results to Dead Load

Figure 9.3: Belt Truss and Outrigger Sensitivity

120

ASPIRE

9.0 APPENDIX

9.13 Core Wall Reinforcement Table 9.14: Core Wall Reinforcement Details Thickness (ft) Bank 1 NS EW Bank 2 NS EW Bank 3 NS EW Bank 4 4.1 4.2

Horizontal Shear Bar Size Spacing (in)

Vertical Shear Bar Size Spacing (in)

Flexural Bar Size Spacing (in)

7 7

18 18

6 6

10 10

12 12

10 10

12 12

4 4

18 18

8 9

18 18

9 10

18 18

9 10

3 3

14 14

10 9

8 7

16 12

8 7

16 12

2 2

18 8

7 17

6 6

14 14

6 6

14 14

ASPIRE

121

9.0 APPENDIX

9.14 Creep and Shrinkage 9.14.1 Hand Calculations

122

ASPIRE

9.0 APPENDIX

ASPIRE

123

9.0 APPENDIX

124

ASPIRE

9.0 APPENDIX

ASPIRE

125

9.0 APPENDIX

9.14.2 Supplementary Materials Table 9.15: Concrete Core Properties

Bank Radius

1

2

3

4

Ro

40

38

36

26

ft

t

8

6

4

3.33

ft

Vc

23886

17417 11280

6721

ft3

Wc

3822

2787

1805

1075

kips

At

1810 21

1319 21

855 14

509 14

ft2

As

2873

10187

715

123

in2

86 182

63 133

61 129

36 77

ft2

Thickness Total Volume / Floor Total Weight/Floor Total Area/Floor # of Columns Steel Area Area per core "column" Self-Weight per core "column"

Table 9.16: Steel Deflection Summary Floors

Lobby 5-16 17-28 29-39 40-51 52-63 64-73 74-86 87-99 100-110 111-122 123-133 134-145

126

Deflection per Floor

Deformation per Floor Segment

Sum of Floor Segment Deformations

(in) 0.979 0.077 0.067 0.057 0.049 0.041 0.034 0.054 0.042 0.031 0.021 0.012 0.004

(in) 0.979 0.921 0.805 0.631 0.590 0.492 0.335 0.702 0.546 0.340 0.251 0.131 0.045

(in) 0.98 1.90 2.71 3.34 3.93 4.42 4.75 5.46 6.00 6.34 6.59 6.72 6.77

ASPIRE

kips

9.0 APPENDIX Table 9.17: Humidity Data for Chicago National Climatic Data for Humidity in Chicago, IL (All Values in %) Morning Afternoon January

78

70

February

78

67

March

79

63

April

77

58

May

77

57

June

79

58

July

82

60

August

86

61

September

85

61

October

81

59

November

80

66

December

80

71

80.17

62.58

Average

Average Humidity Between Morning and Afternoon 71.4%

Table 9.18: Concrete Reinforcement Data

Bank

1

2

3

4

Core Radius

Ro

40

38

36

26

ft

Core Thickness

tc

8

6

4

3.33

ft

251 12 1 10

239 9 0.75 18

226 12 1 8

nb

251

318

226

140

Stee Area per Bar

Asb

1.27

4

0.79

0.44

in2

Steel Area per Row

Asr

319

1273

179

62

in2

Number of Rows of Bars

nr

9

8

4

2

Total Steel Area

As

2873

10187

715

123

Percent Steel

ρg

0.011

0.054

0.006

0.002

Core Circumference Rebar Spacing (in) Rebar Spacing (ft) Bar Size Number of Bars per Row

s

ASPIRE

163 ft 14 in 1.1667 ft 6

in2

127

9.0 APPENDIX Table 9.19: 20 Year Concrete Deflection Deformation per Floor (in) 0.371 0.088 0.078 0.068 0.005 0.004 0.004 0.220 0.175 0.133 0.715 0.419 0.145

Deformation per Floor Segment (in) 0.371 1.054 0.937 0.752 0.057 0.049 0.035 2.857 2.274 1.468 8.585 4.611 1.737

Sum of Floor Segment Deformations (in) 0.37 1.43 2.36 3.11 3.17 3.22 3.26 6.11 8.39 9.86 18.44 23.05 24.79

9.14.3 Analysis Procedure for Creep and Shrinkage Quantifying the amount of displacement in both the columns and core is essential for constructing a serviceable building. If there is a large difference between the displacement of the columns and the core that is not accounted for, floors will begin to slant over time and cause uncomfortable situations for occupants. The quantification of displacements depends on a multitude of factors, requiring an in-depth analysis. Step 1: Determine the expected loads on the concrete in question. The necessary loads are the DL, SDL, the sustained portion of LL on the building. These loads will need to be broken up by floor because the amount of creep is highly dependent on the amount of load and the sequence in which it is applied. Step 2: Create a construction schedule to determine when the concrete will be loaded with which amount of load. For our skyscraper, as each of the 150 floors is added vertically, an additional load will be placed on the floors below. The timing of when these additional loads are applied will greatly affect the amount of creep experienced by concrete below. Step 3: Determine the composition properties of the concrete mixture that will be used and its curing process. Factors such as cement type, temperature and humidity during curing, and length of time moist curing all affect the amount of ultimate creep and shrinkage that the concrete will experience. 128

ASPIRE

9.0 APPENDIX Step 4: Conduct laboratory tests to determine ultimate creep and shrinkage strains for the concrete mixture specified in Step 3. The data from these tests will be used as initial values for creep and shrinkage strains that will then be modified by calculated correction factors. Step 5: Evaluate the geometries of structural elements. Correction factors based on the geometries of the elements will be applied to the creep and shrinkage values calculated in order to obtain an accurate estimate. Important geometric considerations are the height of the element as well as its surface-to-volume ratio. Step 6: Calculate the expected creep and shrinkage coefficients for loading, construction timing, mixture composition properties, and geometries per GL2000 Method from ACI 209.2R-27. These coefficients are then used to factor the ultimate creep and shrinkage strain values obtained from laboratory tests to calculate the final expected displacements. Step 7: Compare the newly calculated strain values for the column and core concrete to determine the anticipated differential displacement. The differences will be used to modify the column and core heights to account for the eventual differential displacement in the concrete. Assumptions from GL2000 Method: The method is defined for concretes with mean compressive strengths less than 11,890 psi. The core compressive strength is 14,000 psi, but it is assumed that since mix details are not provided this method still provides the best estimate for creep and shrinkage strains. Type III cement was used to provide the highest initial strength gain, which led to the smallest ultimate deformation of the core. Per this type of cement, values for the s and k parameters were 0.13 and 1.15, respectively. In order to determine the correction term for humidity average data was taken from the National Climatic Data Center for Chicago, IL. The average relative humidity over the year was found to be 0.71. The time when curing stops and the time when subsequent loading is added were both taken to be four days. Because of this, the correction term for drying occurring before loading does not affect the creep coefficient.

ASPIRE

129

11.0 Calculation Book

2011 – 2012 ASPIRE Master of Engineering Structural Design Project

Cornell University Ithaca, NY May 2012

Table of Contents 1.0

General Notes ................................................................................................................ 1

1.1

List of Variables .......................................................................................................... 2

1.2

Color Key Explanation ................................................................................................ 7

2.0

Preliminary Load Analysis .............................................................................................. 8

2.1

Gravity Design Loads .................................................................................................. 9

2.2

Wind Load Calculations ............................................................................................ 10

2.2.1

ASCE 7 Wind Load Calculations......................................................................... 11

2.2.2

Wind Tunnel Data ............................................................................................. 19

2.3

Seismic Calculations ................................................................................................. 23

2.3.1

Seismic Weight Calculation ............................................................................... 24

2.3.2

Seismic Load Calculations ................................................................................. 29

3.0

Gravity Design .............................................................................................................. 32

3.1

Tributary Areas ......................................................................................................... 33

3.2

Core Area

3.2.1

Concrete Slab Design ........................................................................................ 39

3.2.2

Link Beam Design .............................................................................................. 45

3.3

Floor Area ................................................................................................................. 51

3.3.1

Composite Decking ........................................................................................... 52

3.3.2

Composite Beam Design ................................................................................... 64

3.3.3

Vibration Analysis ............................................................................................. 93

3.4

Columns .................................................................................................................... 99

3.4.1

Column Load Takedown ................................................................................. 100

3.4.2

Composite Column Design .............................................................................. 114

3.4.3

Steel Column Design ....................................................................................... 118

4.0

Lateral Design............................................................................................................. 120

4.1

Preliminary Deflection Calculations ....................................................................... 121

4.2

MIDAS Gen FEA Summary ...................................................................................... 124

4.3

Preliminary Core Wall Thickness Calculation – No Outriggers .............................. 125

4.4

Final Core Wall Thickness Calculation – Outriggers ............................................... 128

4.5

Core Rebar Design .................................................................................................. 131

4.5.1

Design of Core Rebar for Vertical and Horizontal Shear ................................ 132

4.5.2

Design of Core Rebar for Flexural Capacity .................................................... 134

4.5.3

Bank 4 Strong Axis Bending ............................................................................ 138

4.6

Energy Method Optimization ................................................................................. 156

4.6.1

Optimization Calculations ............................................................................... 158

4.6.2

Resizing of Built-up Members ......................................................................... 161

5.0

Connection Design ..................................................................................................... 162

5.1

Typical Connections

5.1.1

Welded Column Splice .................................................................................... 163

5.1.2

Floor Joist to Radial Girder Connection .......................................................... 168

5.1.3

Girder to Column Connections ....................................................................... 171

5.1.4

HSS to Cantilever Connection ......................................................................... 177

5.1.5

Radial Girder to Concrete Core ....................................................................... 180

5.2

Base of Mega-Column Connection......................................................................... 189

5.2.1

Mega-Column to Caisson Connection ............................................................ 190

5.2.2

Caisson Cap Moment Reinforcement ............................................................. 194

5.3

Outrigger Connections ........................................................................................... 196

5.3.1

Bottom of Outrigger to Column Connection .................................................. 197

5.3.2

Top of Outrigger to Core ................................................................................. 199

6.0

Foundation Design ..................................................................................................... 219

6.1

Retaining Wall ........................................................................................................ 220

6.1.1

Soil Profile ....................................................................................................... 221

6.1.2

Effective Pressure ........................................................................................... 222

6.1.3

Retaining Wall Design ..................................................................................... 224

6.1.4

Retaining Wall Mastan Analysis ...................................................................... 228

6.2

Parking Garage ....................................................................................................... 230

6.2.1

Two-Way Slab Using WWR ............................................................................ 231

6.2.2

Parking Garage Columns ................................................................................. 247

6.2.3

Belled Caisson Design .................................................................................... 248

6.3

Tower Foundation .................................................................................................. 250

6.3.1

Abaqus Analysis of Caissons ........................................................................... 251

6.3.2

Mega-Column Caisson Design......................................................................... 253

6.3.3

Ring Beam Design ........................................................................................... 255

6.3.4

Core Caisson Design ........................................................................................ 257

6.3.5

Caisson Rebar .................................................................................................. 259

7.0

Creep and Shrinkage .................................................................................................. 260

7.1

Steel Column Deformation..................................................................................... 261

7.1.1

Steel Column Properties and Loads ................................................................ 262

7.1.2

Steel Column Deformation Calculations ......................................................... 263

7.2

Concrete Core Deformation ................................................................................... 265

7.2.1

Concrete Core Properties and Loads .............................................................. 266

7.2.2

Concrete Core Deformation Calculations ....................................................... 267

8.0

References ................................................................................................................. 269

8.1

Energy-Based Design of Lateral Systems by William F. Baker ............................... 270

8.2

Geotechnical Report for the Chicago Spire ............................................................ 274

1.0 General Notes 1.1 List of Variables

2

1.2 Color Key Explanation

7

The calculation book is a compilation of all the calculations performed for the design of The Chicago Spire. The calculations shown are the final design calculations performed for each deliverable. Hand calculations and spreadsheets are included in the calculation book. The spreadsheets included are demonstrative of the many calculations performed (Ex: Spreadsheet containing the design of a single column is attached. However, the spreadsheet was used to design columns on multiple floors.)

1.0 General Notes C-1

1.1 List of Variables a a A ao/g ap/g Ase,V Av/s Ax b b B beff bf Bj bo C c c C' C1 Call Capp Cb Cc Ccol cgb cgN Cj Cw d d D deff distx Dj DL dm Ds Du dx e Ec EIeff Es F f’c fa fb

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Whitney Stress Block Theory depth of compression zone distance from support face to 1st bolts, in torque coefficient acceleration limit for vibrational analysis peak acceleration for vibrational analysis effective cross sectional area of single bolt, in 2 steel area/spacing ratio in 2/in area of ____________ (concrete, rebar, net area, etc), in 2 beam/column width, in eccentricity of curvature, in angular twist coefficient effective width of slab section, in flange width of a steel section, in effective panel width, in punching shear perimeter, in concrete compressive force, lbs concrete cover, in turbulence intensity factor instantaneous center of rotation at the centroid of the bolt group effective rigidity allowable compression, ksi applied compression, ksi beam bending coefficient centerline circumfrence, ft distance from concrete compression face to neutral axis vertical centroid of bolt group, in location of factored tensile force, in effective width factor warping constant, in 6 structural depth, in (Note: for steel sections, this is the member depth) depth below grade (ft) weld size, in effective concrete depth, in distance, in transformed joist moment of inertia, in 4/ft dead load moment arm, in transformed slab moment of inertia, in 4/ft pretension multiplier diameter of _____ (bolt, column, rebar, shear stud, etc), in eccentricity modulus of elasticity of concrete effective stiffness of composite section, kip-in2 modulus of elasticity of steel bolt head size, in specified compressive strength of concrete, ksi axial compression stress, ksi lateral compression stress, ksi

1.1 List of Variables

C-2

f'c,avg

= average compressive strength of concrete, ksi

f'c-comp = compressive stress in concrete, ksi fcomp Fcr FDL Fe FEXX Flim FLL FMs FMW fn fr fs Fs FS ft Fu Fw Fy Fyr g G h h heff hf Ic Ic Icomp Ieff Io Is Isr It Ix Iy

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

J K K K1 Ka kc kcp kh kp L L L' C-3

allowable compressive stress, ksi flexural buckling stress, ksi factored dead load elastic critical buckling stress, ksi electrode strength, ksi elastic buckling limit factored live load factored seismic moment factored wind moment natural frequency of the floor, Hz allowable tension stress, ksi stress in concrete reinforcing steel force in concrete reinforcing steel, kip factor of safety lateral tensile stress, ksi specified ultimate strength of steel, ksi nominal strength of weld, ksi specified minimum yield strength of steel section, ksi specified minimum yield stress of reinforcing bars, ksi acceleration due to gravity, in/sec 2 shear modulus, ksi beam/slab depth, in floor to floor height, ft effective embedment depth of anchor, in factor for fillers moment of inertia of core, in 4 moment of inertia of the concrete section, in 4 moment of inertia of the composite section, in 4 moment of inertia for post-composite deflection, in 4 moment of inertia of column, in 4 moment of inertia of steel shape, in 4 moment of inertia of reinforcing bars, in 4 transformed moment of inertia, in 4 moment of inertia of strong axis, in 4 moment of inertia of weak axis, in 4 polar moment of inertia, in 4 distance from flange to web weld, in effective length factor effective length factor in plane of bending earth pressure coefficient coefficient for basic concrete breakout strength in tension coefficient for pryout strength horizontal subgrade modulus Rankine's coefficient for passive earth pressure laterally unbraced length of the member, ft length of member, ft uncurved length of beam, in

1.1 List of Variables

lc l c edge l c int lcbtm ld Leh Lev Lex Ley Lgird LL Lo Log Lout Lp Lw lw Mg Mn Mpost Mpre Ms Mu Mw N n n n N Nn Nx P P Pcp Pe Pg Ph Pn Po Po Pp Ps Pu Qn r R Rflex Ri Rn Ro

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

clear distance btwn edge of hole and edge of adjacent hole, in clear distance, in dir. of force, between edge of hole and edge of material, in clear distance, in dir. of force, between edge of hole and edge adjacent hole, in clear distance btwn edge of hole and edge of material for bottom bolts, in embedment length, in horizontal edge distance, in vertical edge distance, in effective length on strong axis, ft effective length on weak axis, ft width at girder, in live load total open length in core, ft opening length in core, ft width at outrigger, in length of plate, in length of weld, in Whitmore Section width, in applied moment allowable moment post-composite moment, kip-ft pre-composite moment, kip-ft seismic moment, kip-ft maximum applied moment wind moment, kip-ft bearing length, in number of ______ (number of bolts, shear studs, etc) ratio between steel and concrete modulus of elasticity dynamic modular ratio tension force (from ACI318-08), kips nominal tension strength, kips nominal tension strength of a group of anchors/hooked bolt, lbs perimeter of column, in total load, kips outer perimeter of cross section, in Euler buckling load, kips applied axial load perimeter of torsion reinforcing, in allowable column axial load excitation for vibrational analysis, lbs nominal axial compressive strength without consideration of length effects, kips Rankine's passive earth pressure, kips percentage of solid wall compression load, kips nominal strength of one stud shear connector radius of curvature, in reaction, kips flexural resistance, psi inner radius, ft load capacity at connection, kips outer radius, ft

1.1 List of Variables

C-4

Ru rx rx ry s Sc Smin Ss Stens Sx Sy T T Tapp Tb tf Tn Tth Tu Tu tw tx U Ubs Ubs V V V’h V’h Vc Vc Vcpg Vn Vsa Vth Vu w W wa Wc wc wd wj wp wslf wt yb yt ӯ Z

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = C-5

load at connection, kips radius of _____ (column, bolt, etc), in radius of gyration (strong), in radius of gyration (weak), in spacing, in section modulus for compression, in 3 minimum required section modulus, in 3 section modulus of steel shape, in 3 section modulus for tension, in 3 section modulus (strong), in 3 section modulus (weak), in 3 clear space, in distance between weld centers, in applied tension, ksi min. fastener tension, kips thickness of flange of steel section, in nominal tensile capacity, kips threshold torsional moment, kip-ft maximum tension force, kips maximum applied torsional moment, kip-ft thickness of web of steel section, in thickness of _______ (concrete, plate, wall, etc), in shear lag factor block shear rupture reduction coefficient reduction coefficient shear force, kips basic wind speed, mph adjusted horizontal shear, kips partial composite action horizontal shear, kips allowable shear in concrete, kips concrete volume, ft3 Nominal pryout strength (group), kips total shear capacity, kips Nominal strength in shear, kips theoretical concrete volume, ft 3/ft2 maximum applied shear, kips distributed load, plf weight supported, lbf angle width, in core wall self-weight, kip weight of concrete per unit volume, pcf decking weight, psf effective panel weight, lbs plate width, in self-weight of an element weld throat thickness, in distance from neutral axis to the bottom of the section, in distance from neutral axis to the top of the section, in location of neutral axis, in reinforcing steel strain multiplier

1.1 List of Variables

α α β β1 Δ εcu εs εys θ λ µ ρactual ρbal π ρc ρclay ρg ρs ρsr ρsw σact σall σc σc σr σt Φ Φx ψx Ω

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

angle of curvature, radians angle of backfill above wall, radians modal damping ratio for vibrational analysis concrete stress block coefficient deflection, in concrete ultimate compressive strain strain in concrete reinforcing steel steel yield strain angle of twist, radians modification factor reflecting the reduced mechanical properties of lightweight concrete mean slip coefficient density of the steel in slab density of steel at which a balanced failure between concrete crushing and steel yielding in tension 3.141592654 density of concrete, pcf density of clay, psf steel ratio spiral reinforcement ratio reinforcement ration for continuous longitudinal reinforcing, A sr/Ag beam self weight density, lb/ft actual stress per caisson, ksi allowable stress, ksi net compression stress, ksi allowable stress in concrete, ksi allowable stress in rock, ksi net tensile stress, ksi strength reduction factor factored allowable strength (moment, axial, shear, bearing, etc.) modification factor for anchor bolts angle of friction for soil, radians

1.1 List of Variables

C-6

1.2 Color Key Explanation Color Key:

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

The yellow cell indicates a user input. The user should input values for the spreadsheet to calculate the results. The gray cell indicates a constant or a previous calculation. When it is a previous calculation, it is directly referencing the cell where the calculation was performed. Both constants and previous calculations are considered inactive cells. The white cell indicates a calculation or a value that is obtained via lookup. An example of a lookup would be the various section properties of a W-shape for a specific shape.

The green cell indicates that a check is being performed and the conditions are satisfied.

The red cell indicates that a check is being performed and the conditions are not satisfied.

C-7

1.2 Color Key Explanation

2.0 Preliminary Load Analysis 2.1 Gravity Design Loads

9

2.2 Wind Load Calculations

10

2.2.1 ASCE 7 Wind Load Calculations

11

2.2.2 Wind Tunnel Data

19

2.3 Seismic Calculations 2.3.1 Seismic Weight Calculation

24

2.3.2 Seismic Load Calculations

29

2.0 Preliminary Load Analysis C-8

2.1 Gravity Design Loads Loads taken from ASCE 7

Dead Load

Typical Floor

(psf)

Core

Parking

Mechanical

Residential

Lobby

Decking and Slab

C-9

Superimposed Dead Load (psf)

Live Load (psf)

32

Assembly Areas (lobbies) Acoustical fiber board MEP Duct Allowance Ceramic or quarry tile (1 1/2 in) on 1 in. mortar bed Total Decking and Slab Private rooms and corridors serving them Partition Walls Acoustical fiber board Ceramic or quarry tile (3/4 in) on 1 in. mortar bed MEP Duct Allowance Total Decking and Slab Catwalks Machine Space MEP Duct Allowance Total Slab (150 pcf @ 12 in.) Garages (passenger vehicles only) MEP Duct Allowance Cement finish (1-in.) on stone-concrete fill Total Slab (110 pcf @ 6 in.) Total

2.1 Gravity Design Loads

100

32 33

1 10 46 57

100 40 15

33 39

1 23 10 34

55 40 200

39 150

10 10

240 40

150 55 55

10 32 42

40

2.2 Wind Load Calculations 2.2.1 ASCE 7 Wind Load Calculations

11

2.2.2 Wind Tunnel Data

19

2.2 Wind Load Calculations C-10

2.2.1 ASCE 7 Wind Load Calculations

Created by: JLB,CJB,JAC,DBL

3/10/2012

Reference tool that calculates wind loads for strength according to ASCE 7-10 and then compares these values to wind tunnel data from RWDI tests. See associated macthcad file and RWDI file for input values.

Definition of Variables from ASCE 7 Chapter 26 Basic Wind Speed Wind Directionality Factor Exposure Category 3-Second Gust Speed Exponent Mean Hourly Wind Speed Power Law Exponent Mean Hourly Wind Speed Factor Turbulence Intensity Factor Integral Length Scale Factor Integral Length Scale Power Law Exponent Nominal Height of Atmosphere Boundary Layer

V Kd

Topographic Factor Rigidity Peak Factor for Background Response

Kzt

α α b c l ϵ zg

120 0.85 D 11.5 0.11 0.80 0.15 650 0.13 700

mph (26.5) (26.6) (26.7) (26.9-1) (26.9-1) (26.9-1) (26.9-1)

ft

(26.9-1) (26.9-1)

ft

(26.9-1) (26.8.2)

gQ

1.00 Flexible 3.40

Peak Factor for Resonant Response

gV

3.40

(26.9.5)

Peak Factor for Wind Response Number of Stories Period Building Natural Frequency Building Width Building Length Mean Roof Height Equivalent Height Damping Ratio Mean Hourly Wind Speed Integral Length Scale of Turbulence Reduced Frequency

gR

3.49 150 15.0 0.07 150 150 2,000 1,200 0.02 210 1,019 0.32

(26.9-11)

C-11

N T n1 B L h ẕ β Vz Lz N1

2.2.1 ASCE 7 Wind Load Calculations

(26.9.5)

sec Hz ft ft ft ft

(26.9.4)

mph (26.9-16) ft (26.9-9) Hz (26.9-14)

Definition of Variables from ASCE 7 Chapter 26 (cont) R Calculation Intermediate Values

Resonant Response Factor Intensity of Turbulence Background Response Factor Gust Effect Factor Enclosure classification Product of Internal Pressure Coefficient and Gust-Effect Factor

Rn

0.21

(26.9-13)

ηh

2.92

(26.9.5)

Rh

0.28

(26.9-15a)

ηB

0.22

(26.9.5)

RB

0.87

(26.9-15a)

ηL

0.73

(26.9.5)

RL

0.65 1.47 0.08 0.71 1.12 Enclosed 0.18 -0.18

R Iz Q Gf GCpi

2.2.1 ASCE 7 Wind Load Calculations

(26.9-15a) (26.9-12) (26.9-7) (26.9-8) (26.9.5)

(26.11-1)

C-12

Calculated Values from ASCE 7 Chapter 26 Basic Wind Speed Wind Directionality Factor Exposure Category Topographic Factor

V Kd Kzt

Gust Effect Factor Enclosure Classification Product of Internal Pressure Coefficient and GustEffect Factor 3-Second Gust Speed Exponent Nominal Height of Atmosphere Boundary Layer

120 0.85 D 1.00

mph (26.5) (26.6) (26.7) (26.8.2)

Gf

1.12 Enclosed 0.18 GCpi -0.18 α 11.5 zg 700

(26.9.5)

Fig (26.11-1) Fig (26.9-1) Fig (26.9-1)

Calculated Values from ASCE 7 Chapter 27 Wall Pressure Coefficients Plan Length to Width Ratio Windward Wall Pressure Coefficient

L/B Cp

1.00 0.80

Fig (27.4-1)

Leeward Wall Pressure Coefficient

Cp

-0.50

Fig (27.4-1)

Side Wall Pressure Coefficient

Cp qh

-0.70

Fig (27.4-1)

63.0

psf

Horizontal Dimension - Bank 1

Bx

189

ft

Horizontal Dimension - Bank 2

Bx

174

ft

Horizontal Dimension - Bank 3

Bx

153

ft

Horizontal Dimension - Bank 4

Bx

133

ft

Horizontal Dimension - Bank 4.2 Story Height

Bx h

120 13.2

ft ft

eR

0.0

ft

Iz

0.08

(26.9-7)

Peak Factor for Background Response

gQ

3.40

(26.9.5)

Peak Factor for Wind Response Background Response Factor Resonant Response Factor

gR

3.49 0.71 1.47

(26.9-11)

Leeward Velocity Pressure 1

Fig (27.4-1)

(27.4.1)

Building Dimensions

Eccentricity Calculation Values Shear Center and Center of Mass Eccentridity Intensity of Turbulence

C-13

Q R

2.2.1 ASCE 7 Wind Load Calculations

(27.4.6)

(26.9-8) (26.9-12)

Eccentricity Calculation per Bank Bank 1 eQ

Eccentricity for Rigid Structures

ex, ey

Flexible Building Eccentricity

28.3 21.1 -21.1

ft ft ft

(27.4-8)

26.1 19.5 -19.5

ft ft ft

(27.4-8)

23.0 17.1 -17.1

ft ft ft

(27.4-8)

(27.4.6)

Bank 2 eQ

Eccentricity for Rigid Structures

ex, ey

Flexible Building Eccentricity

(27.4.6)

Bank 3 eQ

Eccentricity for Rigid Structures

ex, ey

Flexible Building Eccentricity

(27.4.6)

Bank 4 eQ

Eccentricity for Rigid Structures

ex, ey

Flexible Building Eccentricity

20.0 14.9 -14.9

(27.4-8)

18.0 13.4 -13.4

(27.4-8)

(27.4.6)

Bank 4.2 Eccentricity for Rigid Structures Flexible Building Eccentricity

eQ ex, ey

(27.4.6)

Notes 1 Both qh and qi are taken conservatively to be the maximum qz value from windward pressure calculations. This maximum occurs at the 150th level 2 In all calculations, the negative value of GCpi is used to get larger values of wind pressure. See Section 27.4-2

2.2.1 ASCE 7 Wind Load Calculations

C-14

ASCE Ch 27 Wind Load Cases Floor (relative to ground)

Velocity Height Pressure (relative Width of Velocity Exposure to Buidling Pressure Coefficien ground) t

Windward Leeward Side Wall Windward Leeward Pressure Pressure Pressure Force Force

Side Wall Force

Design Wind Load Case 1

PWX PWY PLX PLY

#

z

w

Kz

qz

p

p

p

f

f

f

0 1 2 3 4 5 6 7 8 9 10 … 136 137 138 139 140 141 142 143 144 145

ft 0 13 26 40 53 66 79 92 105 119 132 … 1,791 1,804 1,817 1,830 1,843 1,857 1,870 1,883 1,896 1,909

ft 189 188 188 188 187 187 186 186 186 185 185 … 100 97 93 90 87 83 80 77 73 70

1 1 1 1 1 1 1 1 1 1 2 … 2 2 2 2 2 2 2 2 2 2

psf 32 32 36 38 40 42 43 44 45 46 47 … 63 63 63 63 63 63 63 63 63 63

psf 35 35 38 41 43 45 46 48 49 50 51 … 68 68 68 68 68 68 68 68 68 68

psf -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 … -24 -24 -24 -24 -24 -24 -24 -24 -24 -24

psf -38 -38 -38 -38 -38 -38 -38 -38 -38 -38 -38 … -38 -38 -38 -38 -38 -38 -38 -38 -38 -38

lb 86,397 86,234 94,919 101,663 106,677 110,685 114,034 116,910 119,426 121,665 123,677 … 89,377 86,398 83,420 80,441 77,462 74,483 71,504 68,525 65,546 62,563

lb -59,628 -59,515 -59,403 -59,290 -59,177 -59,065 -58,952 -58,840 -58,727 -58,615 -58,502 … -31,617 -30,563 -29,509 -28,455 -27,402 -26,348 -25,294 -24,240 -23,187 -22,131

lb -47,367 -94,734 -94,734 -94,734 -94,734 -94,734 -94,734 -94,734 -94,734 -94,734 -94,734 … -60,276 -60,276 -60,276 -60,276 -60,276 -60,276 -60,276 -60,276 -60,276 -60,276

C-15

psf 35 35 38 41 43 45 46 48 49 50 51 … 68 68 68 68 68 68 68 68 68 68

psf 35 35 38 41 43 45 46 48 49 50 51 … 68 68 68 68 68 68 68 68 68 68

2.2.1 ASCE 7 Wind Load Calculations

psf -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 … -24 -24 -24 -24 -24 -24 -24 -24 -24 -24

psf -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 … -24 -24 -24 -24 -24 -24 -24 -24 -24 -24

Design Wind Load Case 1

FWX

FWY

FLX

FLY

FX

FY

lb 86,397 86,234 94,919 101,663 106,677 110,685 114,034 116,910 119,426 121,665 123,677 … 89,377 86,398 83,420 80,441 77,462 74,483 71,504 68,525 65,546 62,563

lb 86,397 86,234 94,919 101,663 106,677 110,685 114,034 116,910 119,426 121,665 123,677 … 89,377 86,398 83,420 80,441 77,462 74,483 71,504 68,525 65,546 62,563

lb -59,628 -59,515 -59,403 -59,290 -59,177 -59,065 -58,952 -58,840 -58,727 -58,615 -58,502 … -31,617 -30,563 -29,509 -28,455 -27,402 -26,348 -25,294 -24,240 -23,187 -22,131

lb -59,628 -59,515 -59,403 -59,290 -59,177 -59,065 -58,952 -58,840 -58,727 -58,615 -58,502 … -31,617 -30,563 -29,509 -28,455 -27,402 -26,348 -25,294 -24,240 -23,187 -22,131

lb 146,025 145,749 154,321 160,953 165,854 169,750 172,986 175,749 178,153 180,279 182,179 … 120,994 116,961 112,929 108,896 104,863 100,831 96,798 92,765 88,733 84,694

lb 146,025 145,749 154,321 160,953 165,854 169,750 172,986 175,749 178,153 180,279 182,179 … 120,994 116,961 112,929 108,896 104,863 100,831 96,798 92,765 88,733 84,694

Line Load, X/Y kips/ft 11 11 12 12 13 13 13 13 14 14 14 … 9 9 9 8 8 8 7 7 7 6

ASCE Ch 27 Wind Load Cases Floor (relative to ground)

Design Wind Load Case 2

Design Wind Load Case 2

#

.75PWX

.75PWY

.75PLX

.75PLY

MT

0 1 2 3 4 5 6 7 8 9 10 … 136 137 138 139 140 141 142 143 144 145

psf 26 26 29 31 32 34 35 36 37 37 38 … 51 51 51 51 51 51 51 51 51 51

psf 26 26 29 31 32 34 35 36 37 37 38 … 51 51 51 51 51 51 51 51 51 51

psf -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 … -18 -18 -18 -18 -18 -18 -18 -18 -18 -18

psf -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 … -18 -18 -18 -18 -18 -18 -18 -18 -18 -18

k-ft/ft 32 32 43 51 58 63 67 71 74 77 80 … 92 92 83 83 83 83 83 83 83 131

Design Wind Load Case 3

.75FWX .75FWY .75FLX

.75FLY

MT

.75FX

.75FY

lb 64,798 64,675 71,189 76,247 80,008 83,014 85,526 87,682 89,569 91,248 92,758 … 67,033 64,799 62,565 60,331 58,096 55,862 53,628 51,394 49,160 46,922

lb -44,721 -44,636 -44,552 -44,468 -44,383 -44,299 -44,214 -44,130 -44,045 -43,961 -43,876 … -23,712 -22,922 -22,132 -21,342 -20,551 -19,761 -18,971 -18,180 -17,390 -16,598

k-ft 79,859 79,709 105,954 126,410 141,704 153,997 164,324 173,238 181,081 188,095 194,434 … 121,516 117,466 102,330 98,676 95,022 91,368 87,714 84,059 80,405 120,618

lb 109,519 109,312 115,741 120,715 124,391 127,312 129,740 131,812 133,615 135,209 136,634 … 90,745 87,721 84,697 81,672 78,648 75,623 72,599 69,574 66,550 63,521

lb 109,519 109,312 115,741 120,715 124,391 127,312 129,740 131,812 133,615 135,209 136,634 … 90,745 87,721 84,697 81,672 78,648 75,623 72,599 69,574 66,550 63,521

lb 64,798 64,675 71,189 76,247 80,008 83,014 85,526 87,682 89,569 91,248 92,758 … 67,033 64,799 62,565 60,331 58,096 55,862 53,628 51,394 49,160 46,922

lb -44,721 -44,636 -44,552 -44,468 -44,383 -44,299 -44,214 -44,130 -44,045 -43,961 -43,876 … -23,712 -22,922 -22,132 -21,342 -20,551 -19,761 -18,971 -18,180 -17,390 -16,598

2.2.1 ASCE 7 Wind Load Calculations

Design Wind Load Case 3

.75PWX .75PWY .75PLX .75PLY psf 26 26 29 31 32 34 35 36 37 37 38 … 51 51 51 51 51 51 51 51 51 51

psf 26 26 29 31 32 34 35 36 37 37 38 … 51 51 51 51 51 51 51 51 51 51

psf -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 … -18 -18 -18 -18 -18 -18 -18 -18 -18 -18

psf -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 -18 … -18 -18 -18 -18 -18 -18 -18 -18 -18 -18

.75FWX .75FWY .75FLX

.75FLY

.75FX

.75FY

lb 64,798 64,675 71,189 76,247 80,008 83,014 85,526 87,682 89,569 91,248 92,758 … 67,033 64,799 62,565 60,331 58,096 55,862 53,628 51,394 49,160 46,922

lb -44,721 -44,636 -44,552 -44,468 -44,383 -44,299 -44,214 -44,130 -44,045 -43,961 -43,876 … -23,712 -22,922 -22,132 -21,342 -20,551 -19,761 -18,971 -18,180 -17,390 -16,598

lb 109,519 109,312 115,741 120,715 124,391 127,312 129,740 131,812 133,615 135,209 136,634 … 90,745 87,721 84,697 81,672 78,648 75,623 72,599 69,574 66,550 63,521

lb 109,519 109,312 115,741 120,715 124,391 127,312 129,740 131,812 133,615 135,209 136,634 … 90,745 87,721 84,697 81,672 78,648 75,623 72,599 69,574 66,550 63,521

lb 64,798 64,675 71,189 76,247 80,008 83,014 85,526 87,682 89,569 91,248 92,758 … 67,033 64,799 62,565 60,331 58,096 55,862 53,628 51,394 49,160 46,922

lb -44,721 -44,636 -44,552 -44,468 -44,383 -44,299 -44,214 -44,130 -44,045 -43,961 -43,876 … -23,712 -22,922 -22,132 -21,342 -20,551 -19,761 -18,971 -18,180 -17,390 -16,598

C-16

ASCE Ch 27 Wind Load Cases Floor (relative to ground) #

0 1 2 3 4 5 6 7 8 9 10 … 136 137 138 139 140 141 142 143 144 145

C-17

Design Wind Load Case 4

.563PWX .563PWY .563PLX .563PLY psf 20 20 22 23 24 25 26 27 28 28 29 … 38 38 38 38 38 38 38 38 38 38

psf 20 20 22 23 24 25 26 27 28 28 29 … 38 38 38 38 38 38 38 38 38 38

psf -14 -14 -14 -14 -14 -14 -14 -14 -14 -14 -14 … -14 -14 -14 -14 -14 -14 -14 -14 -14 -14

psf -14 -14 -14 -14 -14 -14 -14 -14 -14 -14 -14 … -14 -14 -14 -14 -14 -14 -14 -14 -14 -14

Design Wind Load Case 4

MT k-ft/ft 48 48 64 77 86 94 101 106 111 116 120 … 139 139 139 125 125 125 125 125 125 125

.563FWX .563FWY .563FLX .563FLY lb 48,641 48,550 53,439 57,236 60,059 62,316 64,201 65,820 67,237 68,497 69,630 … 50,319 48,642 46,965 45,288 43,611 41,934 40,257 38,580 36,903 35,223

lb 48,641 48,550 53,439 57,236 60,059 62,316 64,201 65,820 67,237 68,497 69,630 … 50,319 48,642 46,965 45,288 43,611 41,934 40,257 38,580 36,903 35,223

lb -33,570 -33,507 -33,444 -33,380 -33,317 -33,254 -33,190 -33,127 -33,063 -33,000 -32,937 … -17,800 -17,207 -16,614 -16,020 -15,427 -14,834 -14,241 -13,647 -13,054 -12,460

lb -33,570 -33,507 -33,444 -33,380 -33,317 -33,254 -33,190 -33,127 -33,063 -33,000 -32,937 … -17,800 -17,207 -16,614 -16,020 -15,427 -14,834 -14,241 -13,647 -13,054 -12,460

MT

FX

FY

lb 119,896 119,669 159,073 189,783 212,744 231,200 246,705 260,088 271,863 282,393 291,911 … 182,436 176,356 170,275 148,146 142,660 137,173 131,687 126,201 120,715 115,221

lb 82,212 82,057 86,883 90,617 93,376 95,569 97,391 98,947 100,300 101,497 102,567 … 68,120 65,849 63,579 61,308 59,038 56,768 54,497 52,227 49,957 47,683

lb 82,212 82,057 86,883 90,617 93,376 95,569 97,391 98,947 100,300 101,497 102,567 … 68,120 65,849 63,579 61,308 59,038 56,768 54,497 52,227 49,957 47,683

2.2.1 ASCE 7 Wind Load Calculations

Wind Pressure vs. Height

2000

2000

1800

1800

1600

1600

1400

1400 Wind Pressure p [psf]

Velocity Pressure qz [psf]

Velocity Pressure vs. Height

1200 1000 800

1200 1000 800

600

600

400

400

200

200

0

0 0

35

70

0

55

Hieght z [ft]

110

Height z [ft]

Case 1 Loads (lb)

Case 2 Loads (lb)

352,449 70,490 77,736 83,418 87,698 91,167 94,104 96,662 98,932 100,980 102,848 104,566 106,161 107,649 109,045 55,181

352,449 70,490 77,736 83,418 87,698 91,167 94,104 96,662 98,932 100,980 102,848 104,566 106,161 107,649 109,045 55,181

-243,246 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -24,325

-243,246 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -48,649 -24,325

1,739,084

1,739,084

-948,660

-948,660

1,739 Kips

1,739 Kips

-949 Kips

-949 Kips

264,336 52,867 58,302 62,563 65,774 68,375 70,578 72,497 74,199 75,735 77,136 78,424 79,620 80,737 81,784 41,386

Case 3 Loads (lb) 264,336 52,867 58,302 62,563 65,774 68,375 70,578 72,497 74,199 75,735 77,136 78,424 79,620 80,737 81,784 41,386

-182,435 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -18,243

-182,435 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -18,243

325,780 65,156 86,774 103,723 116,493 126,841 135,605 143,235 150,006 156,116 161,688 166,814 171,572 176,012 180,176 92,052

1,304,313 1,304,313 -711,495 -711,495 2,358,042 1,304 1,304 -711 -711 2,358 Kips Kips Kips Kips Kips

2.2.1 ASCE 7 Wind Load Calculations

264,336 52,867 58,302 62,563 65,774 68,375 70,578 72,497 74,199 75,735 77,136 78,424 79,620 80,737 81,784 41,386

264,336 52,867 58,302 62,563 65,774 68,375 70,578 72,497 74,199 75,735 77,136 78,424 79,620 80,737 81,784 41,386

-182,435 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -18,243

-182,435 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -36,487 -18,243

1,304,313 1,304,313 -711,495 -711,495 1,304 1,304 -711 -711 Kips Kips Kips Kips

C-18

2.2.2 Wind Tunnel Data

Created by:

JLB,CJB,JAC,DBL

3/10/2012

Values obtined from RWDI wind tunnel test data file. Values represent 100 year return period.

Key Raw Data from RWDI Wind Tunnel Test Calculated Critical Moment and Critical Force from RWDI Load Combinations Adjusted values to remove spikes in Wind Tunnel Data E = 970,560 ksf

Load Combinations # X Forces Fx Y Forces Fy

1 90%

3 90%

5 -100%

7 -100%

9 30%

11 30%

13 -40%

15 -30%

17 30%

19 30%

20 30%

21 -70%

23 -70%

24 -70%

30%

-30%

30%

-30%

95%

-100%

95%

-100%

50%

-75%

-70%

50%

-75%

-70%

Wind Tunnel Forces Floor Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Base LV2 LV3 LV4 LV5 LV6 LV7 LV8 LV9 LV10 LV11 LV12 LV13 LV14 LV15 LV16 LV17 LV18 LV19 LV20 LV21 LV22 LV23 LV24

C-19

Moment of 4 Inertia (ft ) 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255

Height Above Level LV1 (ft) 0 13 26 40 53 66 79 92 105 119 132 145 158 171 184 198 211 224 237 250 263 277 290 303

Force Fx (lb) 26,700 53,300 53,100 53,100 53,200 53,100 52,900 53,000 52,900 52,800 52,700 52,800 53,000 53,000 53,000 53,200 53,200 53,400 53,400 53,600 53,600 53,800 54,000 54,200

Force Fy (lb) 19,800 39,700 39,600 39,700 40,100 40,000 40,200 40,600 40,500 40,500 40,700 40,800 41,200 41,300 41,700 41,900 42,200 42,300 42,700 43,100 43,400 43,600 43,900 44,300

Critical Torsion Mz Moment (kip(lb-ft) ft E+6) 44,000 96,000 102,000 109,000 144,000 195,000 212,000 233,000 239,000 240,000 252,000 264,000 275,000 287,000 298,000 306,000 314,000 324,000 335,000 345,000 354,000 364,000 372,000 381,000

9.41 9.28 9.16 9.04 8.92 8.80 8.68 8.56 8.45 8.33 8.21 8.10 7.98 7.87 7.76 7.64 7.53 7.42 7.31 7.20 7.09 6.98 6.88 6.77

2 2 F Resultant = √(Fx + Fy ) (kips) for each load case

Inter-Story Total Drift Critical Force Drift (in) (in) (kips) 0.00 0.01 0.02 0.03 0.04 0.05 0.05 0.06 0.07 0.08 0.09 0.10 0.10 0.11 0.12 0.13 0.13 0.14 0.15 0.15 0.16 0.16 0.17 0.17

0.00 0.01 0.02 0.05 0.08 0.13 0.18 0.25 0.32 0.40 0.49 0.59 0.69 0.80 0.92 1.05 1.18 1.32 1.47 1.62 1.78 1.94 2.11 2.28

27.4 54.6 54.4 54.4 54.5 54.4 54.3 54.4 54.3 54.2 54.1 54.2 54.4 54.4 54.5 54.7 54.7 54.9 54.9 55.1 55.2 55.4 55.6 55.8

2.2.2 Wind Tunnel Data

1 24.8 49.4 49.2 49.3 49.4 49.3 49.1 49.2 49.1 49.0 49.0 49.1 49.3 49.3 49.3 49.5 49.5 49.7 49.7 49.9 50.0 50.2 50.4 50.6

3 24.8 49.4 49.2 49.3 49.4 49.3 49.1 49.2 49.1 49.0 49.0 49.1 49.3 49.3 49.3 49.5 49.5 49.7 49.7 49.9 50.0 50.2 50.4 50.6

5 27.4 54.6 54.4 54.4 54.5 54.4 54.3 54.4 54.3 54.2 54.1 54.2 54.4 54.4 54.5 54.7 54.7 54.9 54.9 55.1 55.2 55.4 55.6 55.8

7 27.4 54.6 54.4 54.4 54.5 54.4 54.3 54.4 54.3 54.2 54.1 54.2 54.4 54.4 54.5 54.7 54.7 54.9 54.9 55.1 55.2 55.4 55.6 55.8

9 20.4 41.0 40.9 40.9 41.3 41.2 41.4 41.7 41.6 41.6 41.8 41.9 42.2 42.3 42.7 42.9 43.2 43.3 43.6 44.0 44.3 44.5 44.7 45.1

11 21.4 42.8 42.7 42.8 43.2 43.1 43.2 43.6 43.5 43.5 43.7 43.8 44.2 44.3 44.6 44.8 45.1 45.2 45.6 46.0 46.3 46.5 46.8 47.2

13 21.6 43.3 43.2 43.3 43.6 43.5 43.7 44.0 43.9 43.9 44.0 44.1 44.5 44.6 44.9 45.1 45.4 45.5 45.8 46.2 46.5 46.7 47.0 47.3

15 21.4 42.8 42.7 42.8 43.2 43.1 43.2 43.6 43.5 43.5 43.7 43.8 44.2 44.3 44.6 44.8 45.1 45.2 45.6 46.0 46.3 46.5 46.8 47.2

17 12.7 25.5 25.4 25.5 25.6 25.6 25.6 25.8 25.7 25.7 25.8 25.8 26.0 26.1 26.2 26.3 26.5 26.5 26.7 26.9 27.0 27.1 27.3 27.5

19 16.9 33.8 33.7 33.8 34.0 34.0 34.1 34.4 34.3 34.3 34.4 34.5 34.8 34.8 35.1 35.2 35.4 35.5 35.8 36.1 36.3 36.5 36.7 37.0

20 16.0 32.1 32.0 32.0 32.3 32.2 32.3 32.6 32.5 32.5 32.6 32.7 32.9 33.0 33.2 33.4 33.6 33.7 33.9 34.2 34.4 34.5 34.7 35.0

21 21.2 42.3 42.1 42.1 42.3 42.2 42.1 42.3 42.2 42.1 42.1 42.2 42.4 42.5 42.6 42.7 42.8 42.9 43.0 43.3 43.3 43.5 43.7 43.9

23 23.9 47.7 47.6 47.6 47.9 47.8 47.8 48.0 47.9 47.8 47.9 48.0 48.3 48.3 48.5 48.7 48.9 49.0 49.2 49.5 49.7 49.9 50.1 50.4

24 23.3 46.5 46.4 46.4 46.6 46.5 46.5 46.7 46.6 46.6 46.6 46.7 47.0 47.0 47.2 47.4 47.5 47.7 47.9 48.1 48.3 48.5 48.7 49.0

Floor Level 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 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

LV25 LV26 LV27 LV28 LV29 LV30 LV31 LV32 LV33 LV34 LV35 LV36 LV37 LV38 LV39 LV40 LV41 LV42 LV43 LV44 LV45 LV46 LV47 LV48 LV49 LV50 LV51 LV52 LV53 LV54 LV55 LV56 LV57 LV58 LV59 LV60 LV61 LV62 LV63 LV64 LV65 LV66

Moment of 4 Inertia (ft ) 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,895,255 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711

Height Above Level LV1 (ft) 316 329 342 356 369 382 395 408 421 435 448 461 474 487 500 514 527 540 553 566 579 593 606 619 632 645 658 672 685 698 711 724 737 751 764 777 790 803 816 830 843 856

Force Fx (lb) 54,400 54,400 54,600 54,800 55,000 55,200 55,400 55,600 55,800 56,000 56,300 56,600 56,800 56,800 56,800 56,800 55,800 56,100 56,200 56,500 56,600 56,900 57,200 57,500 57,800 58,000 58,300 58,600 58,800 59,000 59,400 59,800 60,000 60,300 60,700 61,000 61,100 61,500 61,700 62,700 63,000 63,400

Force Fy (lb) 44,700 45,000 45,400 45,700 46,100 46,400 46,800 47,100 47,700 48,000 48,300 48,700 49,000 49,000 49,000 49,000 48,600 49,100 49,300 49,700 49,900 50,500 50,800 51,300 51,800 52,200 52,600 53,100 53,600 54,000 54,500 54,900 55,500 55,900 56,300 56,900 57,200 57,800 58,100 59,400 59,800 60,400

Critical Torsion Mz Moment (kip(lb-ft) ft E+6) 392,000 399,000 411,000 418,000 427,000 433,000 443,000 451,000 458,000 467,000 474,000 484,000 491,000 479,000 470,000 470,000 437,000 442,000 447,000 453,000 457,000 465,000 467,000 473,000 477,000 480,000 484,000 487,000 490,000 492,000 498,000 502,000 503,000 506,000 509,000 514,000 513,000 515,000 518,000 539,000 544,000 546,000

6.66 6.56 6.45 6.35 6.25 6.14 6.04 5.94 5.84 5.74 5.64 5.55 5.45 5.35 5.26 5.16 5.07 4.98 4.88 4.79 4.70 4.61 4.52 4.43 4.35 4.26 4.17 4.09 4.00 3.92 3.84 3.75 3.67 3.59 3.51 3.43 3.36 3.28 3.20 3.13 3.05 2.98

2 2 F Resultant = √(Fx + Fy ) (kips) for each load case

Inter-Story Total Drift Critical Force Drift (in) (in) (kips) 0.18 0.18 0.19 0.19 0.20 0.20 0.20 0.21 0.21 0.21 0.22 0.22 0.22 0.22 0.22 0.23 0.31 0.31 0.31 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.31 0.31 0.31 0.31 0.31 0.30 0.30 0.30

2.46 2.64 2.83 3.02 3.22 3.42 3.62 3.83 4.04 4.25 4.47 4.68 4.91 5.13 5.35 5.58 5.89 6.20 6.52 6.84 7.15 7.47 7.79 8.11 8.43 8.75 9.07 9.39 9.71 10.03 10.35 10.67 10.99 11.30 11.62 11.93 12.24 12.55 12.86 13.16 13.46 13.76

56.0 56.1 56.3 56.5 56.7 56.9 57.2 57.4 57.6 57.8 58.1 58.5 58.7 58.7 58.7 58.7 57.7 58.0 58.1 58.4 58.5 58.9 59.2 59.5 59.9 60.1 60.4 60.7 61.0 61.2 61.6 62.0 62.3 62.6 63.0 63.3 63.5 63.9 64.1 65.2 65.5 65.9

2.2.2 Wind Tunnel Data

1 50.8 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.7 53.0 53.2 53.2 53.2 53.2 52.3 52.6 52.7 53.0 53.1 53.4 53.7 54.0 54.3 54.5 54.8 55.1 55.3 55.5 55.9 56.3 56.5 56.8 57.2 57.5 57.6 58.0 58.2 59.2 59.5 59.9

3 50.8 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.7 53.0 53.2 53.2 53.2 53.2 52.3 52.6 52.7 53.0 53.1 53.4 53.7 54.0 54.3 54.5 54.8 55.1 55.3 55.5 55.9 56.3 56.5 56.8 57.2 57.5 57.6 58.0 58.2 59.2 59.5 59.9

5 56.0 56.1 56.3 56.5 56.7 56.9 57.2 57.4 57.6 57.8 58.1 58.5 58.7 58.7 58.7 58.7 57.7 58.0 58.1 58.4 58.5 58.9 59.2 59.5 59.9 60.1 60.4 60.7 61.0 61.2 61.6 62.0 62.3 62.6 63.0 63.3 63.5 63.9 64.1 65.2 65.5 65.9

7 56.0 56.1 56.3 56.5 56.7 56.9 57.2 57.4 57.6 57.8 58.1 58.5 58.7 58.7 58.7 58.7 57.7 58.0 58.1 58.4 58.5 58.9 59.2 59.5 59.9 60.1 60.4 60.7 61.0 61.2 61.6 62.0 62.3 62.6 63.0 63.3 63.5 63.9 64.1 65.2 65.5 65.9

9 45.5 45.8 46.1 46.4 46.8 47.1 47.5 47.8 48.3 48.6 48.9 49.3 49.6 49.6 49.6 49.6 49.1 49.6 49.8 50.2 50.4 50.9 51.2 51.7 52.2 52.6 52.9 53.4 53.9 54.3 54.8 55.2 55.7 56.1 56.5 57.1 57.3 57.9 58.2 59.5 59.9 60.5

11 47.6 47.9 48.3 48.6 49.0 49.3 49.7 50.0 50.6 50.9 51.2 51.6 51.9 51.9 51.9 51.9 51.4 51.9 52.1 52.5 52.7 53.3 53.6 54.1 54.6 55.0 55.4 55.9 56.4 56.8 57.3 57.8 58.3 58.8 59.2 59.8 60.1 60.7 61.0 62.3 62.7 63.3

13 47.7 48.0 48.3 48.6 49.0 49.3 49.7 50.0 50.5 50.8 51.1 51.5 51.8 51.8 51.8 51.8 51.3 51.8 52.0 52.3 52.5 53.1 53.4 53.9 54.4 54.7 55.1 55.6 56.1 56.5 57.0 57.4 57.9 58.3 58.7 59.3 59.6 60.2 60.5 61.8 62.1 62.7

15 47.6 47.9 48.3 48.6 49.0 49.3 49.7 50.0 50.6 50.9 51.2 51.6 51.9 51.9 51.9 51.9 51.4 51.9 52.1 52.5 52.7 53.3 53.6 54.1 54.6 55.0 55.4 55.9 56.4 56.8 57.3 57.8 58.3 58.8 59.2 59.8 60.1 60.7 61.0 62.3 62.7 63.3

17 27.7 27.8 28.0 28.1 28.3 28.5 28.7 28.9 29.1 29.3 29.5 29.7 29.8 29.8 29.8 29.8 29.5 29.8 29.9 30.1 30.2 30.5 30.7 30.9 31.2 31.4 31.6 31.8 32.1 32.3 32.6 32.8 33.1 33.3 33.5 33.8 34.0 34.3 34.4 35.2 35.4 35.7

19 37.3 37.5 37.8 38.0 38.3 38.5 38.8 39.1 39.5 39.7 40.0 40.3 40.5 40.5 40.5 40.5 40.1 40.5 40.6 40.9 41.1 41.5 41.8 42.2 42.5 42.8 43.2 43.5 43.9 44.2 44.6 44.9 45.4 45.7 46.0 46.4 46.7 47.1 47.3 48.4 48.7 49.1

20 35.3 35.5 35.8 36.0 36.2 36.5 36.7 36.9 37.4 37.6 37.8 38.1 38.3 38.3 38.3 38.3 37.9 38.3 38.4 38.7 38.8 39.3 39.5 39.8 40.2 40.5 40.8 41.1 41.5 41.7 42.1 42.4 42.8 43.1 43.4 43.8 44.0 44.5 44.7 45.6 45.9 46.4

21 44.2 44.2 44.5 44.6 44.9 45.1 45.3 45.5 45.8 46.0 46.2 46.5 46.7 46.7 46.7 46.7 46.0 46.3 46.4 46.7 46.8 47.2 47.4 47.7 48.0 48.3 48.6 48.9 49.1 49.3 49.7 50.1 50.3 50.6 51.0 51.3 51.5 51.9 52.1 53.0 53.3 53.7

23 50.7 50.9 51.2 51.4 51.7 52.0 52.3 52.6 53.0 53.2 53.5 53.9 54.1 54.1 54.1 54.1 53.4 53.8 54.0 54.3 54.5 55.0 55.3 55.7 56.1 56.4 56.8 57.2 57.5 57.8 58.3 58.7 59.1 59.5 59.9 60.4 60.6 61.1 61.4 62.5 62.9 63.4

24 49.3 49.4 49.7 49.9 50.2 50.5 50.8 51.0 51.4 51.6 51.9 52.3 52.5 52.5 52.5 52.5 51.8 52.2 52.3 52.7 52.8 53.3 53.6 53.9 54.3 54.6 55.0 55.4 55.7 56.0 56.4 56.8 57.2 57.6 58.0 58.4 58.6 59.1 59.3 60.5 60.8 61.3

C-20

Floor Level 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

LV67 LV68 LV69 LV70 LV71 LV72 LV73 LV74 LV75 LV76 LV77 LV78 LV79 LV80 LV81 LV82 LV83 LV84 LV85 LV86 LV87 LV88 LV89 LV90 LV91 LV92 LV93 LV94 LV95 LV96 LV97 LV98 LV99 LV100 LV101 LV102 LV103 LV104 LV105 LV106 LV107

108 LV108

C-21

Moment of 4 Inertia (ft )

Height Above Level LV1 (ft)

Force Fx (lb)

Force Fy (lb)

Critical Torsion Mz Moment (kip(lb-ft) ft E+6)

2 2 F Resultant = √(Fx + Fy ) (kips) for each load case

Inter-Story Total Drift Critical Force Drift (in) (in) (kips)

1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 1,393,711 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008 815,008

869 882 895 909 922 935 948 961 974 988 1,001 1,014 1,027 1,050 1,053 1,067 1,080 1,093 1,106 1,119 1,132 1,146 1,159 1,172 1,185 1,198 1,211 1,225 1,238 1,251 1,264 1,277 1,290 1,304 1,317 1,330 1,343 1,356 1,369 1,383 1,396

63,000 63,500 63,800 64,100 64,200 64,200 64,200 64,200 60,900 61,100 61,200 61,500 62,000 62,000 62,100 62,500 62,800 63,200 63,300 63,800 64,200 64,400 64,800 64,800 65,400 65,800 66,100 66,200 66,400 66,700 67,000 67,500 67,700 68,200 68,800 69,000 69,800 70,200 70,700 71,200 71,600

60,100 60,700 61,200 61,600 61,900 62,000 62,000 62,000 58,600 58,900 59,200 59,600 60,200 60,200 60,400 60,900 61,200 61,700 61,800 62,400 62,900 63,200 63,600 63,600 64,200 64,700 65,100 65,300 65,600 66,000 66,400 66,900 67,300 67,600 68,000 68,100 68,500 68,600 68,800 69,000 69,300

529,000 534,000 535,000 538,000 538,000 520,000 520,000 520,000 399,000 402,000 400,000 403,000 406,000 400,000 399,000 399,000 399,000 402,000 398,000 401,000 403,000 400,000 401,000 396,000 398,000 401,000 399,000 394,000 389,000 388,000 368,000 387,000 385,000 384,000 386,000 382,000 384,000 383,000 382,000 383,000 382,000

2.91 2.83 2.76 2.69 2.62 2.56 2.49 2.42 2.35 2.29 2.23 2.16 2.10 1.99 1.98 1.92 1.86 1.80 1.74 1.69 1.63 1.58 1.52 1.47 1.42 1.36 1.31 1.27 1.22 1.17 1.12 1.08 1.03 0.99 0.95 0.90 0.86 0.82 0.78 0.74 0.71

0.30 0.29 0.29 0.29 0.28 0.28 0.28 0.27 0.46 0.46 0.45 0.44 0.43 0.75 0.10 0.41 0.40 0.40 0.39 0.38 0.37 0.36 0.36 0.35 0.34 0.33 0.32 0.31 0.31 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.24 0.23 0.22 0.21 0.20

14.06 14.35 14.64 14.93 15.22 15.50 15.77 16.05 16.51 16.96 17.41 17.85 18.29 19.03 19.13 19.55 19.95 20.35 20.74 21.12 21.49 21.85 22.21 22.56 22.90 23.23 23.55 23.87 24.17 24.47 24.75 25.03 25.30 25.57 25.82 26.06 26.30 26.53 26.74 26.95 27.16

65.5 66.1 66.4 66.7 66.8 66.8 66.8 66.8 63.4 63.6 63.7 64.0 64.6 64.6 64.7 65.1 65.4 65.9 66.0 66.5 66.9 67.1 67.6 67.6 68.2 68.6 68.9 69.0 69.3 69.6 69.9 70.4 70.6 71.2 71.8 72.0 72.8 73.2 73.7 74.1 74.6

1 59.5 60.0 60.3 60.6 60.7 60.7 60.7 60.7 57.6 57.8 57.9 58.2 58.6 58.6 58.8 59.1 59.4 59.8 59.9 60.4 60.8 61.0 61.4 61.4 61.9 62.3 62.6 62.7 62.9 63.2 63.5 64.0 64.2 64.6 65.2 65.4 66.1 66.4 66.9 67.3 67.7

815,008

1,409

71,900

69,400

380,000

0.67

0.19

27.35

74.9

68.0

2.2.2 Wind Tunnel Data

3 59.5 60.0 60.3 60.6 60.7 60.7 60.7 60.7 57.6 57.8 57.9 58.2 58.6 58.6 58.8 59.1 59.4 59.8 59.9 60.4 60.8 61.0 61.4 61.4 61.9 62.3 62.6 62.7 62.9 63.2 63.5 64.0 64.2 64.6 65.2 65.4 66.1 66.4 66.9 67.3 67.7

5 65.5 66.1 66.4 66.7 66.8 66.8 66.8 66.8 63.4 63.6 63.7 64.0 64.6 64.6 64.7 65.1 65.4 65.9 66.0 66.5 66.9 67.1 67.6 67.6 68.2 68.6 68.9 69.0 69.3 69.6 69.9 70.4 70.6 71.2 71.8 72.0 72.8 73.2 73.7 74.1 74.6

7 65.5 66.1 66.4 66.7 66.8 66.8 66.8 66.8 63.4 63.6 63.7 64.0 64.6 64.6 64.7 65.1 65.4 65.9 66.0 66.5 66.9 67.1 67.6 67.6 68.2 68.6 68.9 69.0 69.3 69.6 69.9 70.4 70.6 71.2 71.8 72.0 72.8 73.2 73.7 74.1 74.6

9 60.1 60.7 61.2 61.6 61.9 62.0 62.0 62.0 58.6 58.9 59.2 59.6 60.1 60.1 60.3 60.8 61.1 61.6 61.7 62.3 62.8 63.1 63.5 63.5 64.1 64.6 64.9 65.1 65.4 65.8 66.2 66.7 67.1 67.4 67.8 67.9 68.4 68.5 68.7 68.9 69.3

11 63.0 63.6 64.1 64.5 64.8 64.9 64.9 64.9 61.4 61.7 62.0 62.4 63.0 63.0 63.2 63.7 64.0 64.5 64.7 65.3 65.8 66.1 66.5 66.5 67.1 67.6 68.1 68.3 68.6 69.0 69.4 69.9 70.3 70.6 71.1 71.2 71.6 71.8 72.0 72.2 72.6

13 62.4 63.0 63.5 63.9 64.2 64.3 64.3 64.3 60.8 61.1 61.3 61.7 62.3 62.3 62.5 63.0 63.3 63.8 63.9 64.5 65.0 65.3 65.7 65.7 66.4 66.9 67.3 67.5 67.7 68.1 68.5 69.1 69.4 69.8 70.2 70.3 70.8 71.0 71.2 71.5 71.8

15 63.0 63.6 64.1 64.5 64.8 64.9 64.9 64.9 61.4 61.7 62.0 62.4 63.0 63.0 63.2 63.7 64.0 64.5 64.7 65.3 65.8 66.1 66.5 66.5 67.1 67.6 68.1 68.3 68.6 69.0 69.4 69.9 70.3 70.6 71.1 71.2 71.6 71.8 72.0 72.2 72.6

17 35.5 35.8 36.1 36.3 36.5 36.5 36.5 36.5 34.5 34.7 34.8 35.0 35.4 35.4 35.5 35.8 35.9 36.2 36.3 36.6 36.9 37.0 37.3 37.3 37.6 37.9 38.1 38.2 38.4 38.6 38.8 39.1 39.3 39.5 39.8 39.8 40.1 40.2 40.4 40.6 40.8

19 48.9 49.4 49.7 50.0 50.3 50.3 50.3 50.3 47.6 47.8 48.0 48.4 48.8 48.8 49.0 49.4 49.6 50.0 50.1 50.6 51.0 51.2 51.5 51.5 52.0 52.4 52.7 52.8 53.1 53.4 53.7 54.1 54.4 54.7 55.0 55.1 55.5 55.6 55.8 56.0 56.2

20 46.1 46.6 46.9 47.2 47.4 47.5 47.5 47.5 44.9 45.1 45.3 45.6 46.1 46.1 46.2 46.6 46.8 47.2 47.2 47.7 48.1 48.3 48.6 48.6 49.0 49.4 49.7 49.8 50.1 50.3 50.6 51.0 51.3 51.6 51.9 52.0 52.3 52.4 52.6 52.8 53.1

21 53.4 53.8 54.1 54.4 54.6 54.6 54.6 54.6 51.7 51.9 52.1 52.4 52.8 52.8 52.9 53.3 53.6 53.9 54.0 54.5 54.9 55.1 55.4 55.4 55.9 56.3 56.6 56.7 56.9 57.2 57.5 57.9 58.1 58.5 59.0 59.1 59.7 59.9 60.3 60.6 60.9

23 63.1 63.6 64.0 64.4 64.6 64.7 64.7 64.7 61.2 61.5 61.7 62.1 62.6 62.6 62.8 63.2 63.6 64.0 64.1 64.7 65.2 65.4 65.8 65.8 66.4 66.9 67.3 67.4 67.7 68.0 68.4 68.9 69.2 69.6 70.1 70.3 70.9 71.1 71.5 71.8 72.2

24 60.9 61.5 61.9 62.2 62.4 62.5 62.5 62.5 59.2 59.4 59.6 59.9 60.5 60.5 60.6 61.1 61.4 61.8 61.9 62.5 62.9 63.2 63.6 63.6 64.2 64.6 64.9 65.1 65.3 65.7 66.0 66.5 66.8 67.2 67.7 67.9 68.5 68.7 69.1 69.4 69.8

68.0

74.9

74.9

69.4

72.7

71.9

72.7

40.9

56.3

53.2

61.1

72.4

70.0

Floor Level 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

LV109 LV110 LV111 LV112 LV113 LV114 LV115 LV116 LV117 LV118 LV119 LV120 LV121 LV122 LV123 LV124 LV125 LV126 LV127 LV128 LV129 LV130 LV131 LV132 LV133 LV134 LV135 LV136 LV137 LV138 LV139 LV140 LV141 LV142 LV143 LV144 LV145 LV146 Total

Moment of 4 Inertia (ft ) 815,008 815,008 815,008 815,008 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843 248,843

Height Above Level LV1 (ft) 1,422 1,435 1,448 1,462 1,475 1,488 1,501 1,514 1,527 1,541 1,554 1,567 1,580 1,593 1,606 1,620 1,633 1,646 1,659 1,672 1,685 1,699 1,712 1,725 1,738 1,751 1,764 1,778 1,791 1,804 1,817 1,830 1,843 1,857 1,870 1,883 1,896 1,909

Force Fx (lb) 70,000 70,000 70,000 69,300 69,500 69,800 69,100 69,200 70,000 70,500 71,000 71,100 71,600 77,700 70,100 65,700 66,500 66,500 66,100 66,500 67,000 67,900 68,500 68,500 68,200 68,100 67,600 67,000 66,600 65,800 64,600 62,100 59,400 75,800 71,000 54,500 58,500 58,500 8,996,000

Force Fy (lb) 69,000 69,000 69,000 66,900 67,200 67,600 67,000 67,000 67,800 68,300 68,700 68,800 69,300 75,500 67,700 63,100 63,900 63,900 63,500 63,900 64,000 64,400 64,800 64,600 64,300 64,100 63,500 62,900 62,400 61,600 60,400 58,000 55,400 71,400 66,600 50,700 54,700 54,700 8,267,200

Critical Torsion Mz Moment (kip(lb-ft) ft E+6) 381,000 381,000 381,000 337,000 333,000 330,000 322,000 317,000 315,000 312,000 310,000 307,000 304,000 314,000 260,000 266,000 264,000 258,000 251,000 248,000 242,000 237,000 233,000 225,000 217,000 211,000 202,000 193,000 185,000 176,000 165,000 148,000 129,000 115,000 104,000 92,000 92,000 92,000 52,856,000

0.64 0.60 0.57 0.54 0.51 0.47 0.45 0.42 0.39 0.36 0.34 0.31 0.29 0.27 0.24 0.22 0.20 0.19 0.17 0.15 0.13 0.12 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.00 0.00

F Resultant = √(Fx2 + Fy2) (kips) for each load case

Inter-Story Total Drift Critical Force Drift (in) (in) (kips) 0.18 0.18 0.17 0.16 0.50 0.47 0.45 0.43 0.40 0.38 0.35 0.33 0.31 0.29 0.27 0.25 0.23 0.21 0.19 0.17 0.16 0.14 0.12 0.11 0.10 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.00

27.53 27.71 27.88 28.04 28.54 29.02 29.47 29.89 30.29 30.67 31.02 31.35 31.66 31.95 32.22 32.47 32.69 32.90 33.09 33.26 33.42 33.56 33.68 33.79 33.89 33.97 34.05 34.11 34.16 34.20 34.23 34.25 34.27 34.28 34.29 34.29 34.30 34.30

73.0 73.0 73.0 72.1 72.4 72.7 72.0 72.1 72.9 73.4 73.9 74.0 74.6 80.9 73.0 68.4 69.2 69.2 68.8 69.2 69.7 70.6 71.2 71.2 70.9 70.8 70.2 69.6 69.2 68.3 67.1 64.5 61.7 78.8 73.8 56.6 60.8 60.8

2.2.2 Wind Tunnel Data

1 66.3 66.3 66.3 65.5 65.7 66.0 65.4 65.4 66.2 66.7 67.1 67.2 67.7 73.5 66.3 62.1 62.8 62.8 62.5 62.8 63.3 64.1 64.6 64.6 64.3 64.2 63.8 63.2 62.8 62.0 60.9 58.5 56.0 71.5 67.0 51.4 55.1 55.1

3 66.3 66.3 66.3 65.5 65.7 66.0 65.4 65.4 66.2 66.7 67.1 67.2 67.7 73.5 66.3 62.1 62.8 62.8 62.5 62.8 63.3 64.1 64.6 64.6 64.3 64.2 63.8 63.2 62.8 62.0 60.9 58.5 56.0 71.5 67.0 51.4 55.1 55.1

5 73.0 73.0 73.0 72.1 72.4 72.7 72.0 72.1 72.9 73.4 73.9 74.0 74.6 80.9 73.0 68.4 69.2 69.2 68.8 69.2 69.7 70.6 71.2 71.2 70.9 70.8 70.2 69.6 69.2 68.3 67.1 64.5 61.7 78.8 73.8 56.6 60.8 60.8

7 73.0 73.0 73.0 72.1 72.4 72.7 72.0 72.1 72.9 73.4 73.9 74.0 74.6 80.9 73.0 68.4 69.2 69.2 68.8 69.2 69.7 70.6 71.2 71.2 70.9 70.8 70.2 69.6 69.2 68.3 67.1 64.5 61.7 78.8 73.8 56.6 60.8 60.8

9 68.8 68.8 68.8 66.9 67.2 67.5 66.9 66.9 67.7 68.2 68.7 68.8 69.3 75.4 67.7 63.1 63.9 63.9 63.5 63.9 64.0 64.5 64.9 64.7 64.4 64.2 63.6 63.0 62.6 61.8 60.6 58.2 55.6 71.5 66.8 50.9 54.8 54.8

11 72.1 72.1 72.1 70.1 70.4 70.8 70.1 70.1 71.0 71.5 71.9 72.0 72.6 79.0 70.9 66.1 66.9 66.9 66.5 66.9 67.1 67.5 68.0 67.8 67.5 67.3 66.7 66.0 65.5 64.7 63.4 60.9 58.2 74.9 69.9 53.3 57.4 57.4

13 71.3 71.3 71.3 69.3 69.6 70.0 69.4 69.4 70.2 70.7 71.2 71.3 71.8 78.2 70.2 65.5 66.3 66.3 65.9 66.3 66.4 66.9 67.4 67.2 66.9 66.7 66.1 65.5 65.0 64.2 62.9 60.4 57.7 74.3 69.4 52.9 57.0 57.0

15 72.1 72.1 72.1 70.1 70.4 70.8 70.1 70.1 71.0 71.5 71.9 72.0 72.6 79.0 70.9 66.1 66.9 66.9 66.5 66.9 67.1 67.5 68.0 67.8 67.5 67.3 66.7 66.0 65.5 64.7 63.4 60.9 58.2 74.9 69.9 53.3 57.4 57.4

17 40.4 40.4 40.4 39.4 39.5 39.8 39.4 39.4 39.9 40.2 40.4 40.5 40.8 44.4 39.9 37.2 37.7 37.7 37.4 37.7 37.8 38.1 38.4 38.3 38.1 38.0 37.7 37.3 37.0 36.6 35.9 34.5 32.9 42.3 39.5 30.2 32.5 32.5

19 55.8 55.8 55.8 54.3 54.5 54.9 54.4 54.4 55.0 55.4 55.8 55.8 56.2 61.2 55.0 51.3 51.9 51.9 51.6 51.9 52.0 52.4 52.8 52.6 52.4 52.2 51.8 51.3 50.9 50.2 49.3 47.3 45.2 58.2 54.3 41.4 44.6 44.6

20 52.7 52.7 52.7 51.2 51.5 51.7 51.3 51.3 51.9 52.3 52.6 52.7 53.1 57.8 51.8 48.4 49.0 49.0 48.7 49.0 49.1 49.5 49.8 49.7 49.4 49.3 48.9 48.4 48.0 47.4 46.5 44.7 42.7 54.9 51.3 39.1 42.1 42.1

21 59.9 59.9 59.9 58.9 59.1 59.4 58.8 58.9 59.6 60.0 60.4 60.5 60.9 66.2 59.6 55.8 56.5 56.5 56.1 56.5 56.8 57.4 57.9 57.8 57.6 57.4 57.0 56.5 56.1 55.4 54.4 52.3 50.0 64.0 59.8 45.8 49.2 49.2

23 71.3 71.3 71.3 69.8 70.0 70.4 69.7 69.8 70.6 71.1 71.6 71.7 72.2 78.5 70.6 66.0 66.8 66.8 66.4 66.8 67.1 67.8 68.3 68.2 67.9 67.7 67.1 66.5 66.1 65.2 64.0 61.5 58.8 75.4 70.5 53.9 58.0 58.0

24 68.8 68.8 68.8 67.4 67.7 68.0 67.4 67.4 68.2 68.7 69.2 69.3 69.8 75.8 68.2 63.8 64.6 64.6 64.2 64.6 64.9 65.5 66.0 65.9 65.6 65.5 64.9 64.3 63.9 63.1 61.9 59.5 56.9 72.9 68.1 52.1 56.1 56.1

C-22

2.3 Seismic Calculations 2.3.1 Seismic Weight Calculation

24

2.3.2 Seismic Load Calculation

29

Story Shear, Vx 7,000

Story Shear (kips)

6,000 5,000 4,000 3,000 2,000 1,000 0 0

20

40

60

80

100

120

140

160

140

160

Floor Number

Seismic Force vs. Floor Number Seismic Force (kips) acting on each floor

250.00

200.00

150.00

100.00

50.00

0.00 0

20

40

60

80

100

Floor Number

2.3 Seismic Load Calculations C-23

120

C-24

fc := 14ksi

0   34    r :=  34  ft  32     25 

I ( b) :=

4

π

4

⋅ ( Rb) − ( rb)

2

A ( b) := π ⋅ ( Rb) − ( rb)



4



2

Let "b" be equal to the bank number

0   43    R :=  41  ft  37     28 

8

fc ⋅ psi = 9.712 × 10 psf

2.3.1 Seismic Weight Calculation

Econc := 57000 ⋅

Core Inner and Outer Dimensions:

ρc := 160pcf

Concrete Proper es

Es mates the seismic weight of the building using preliminary core sizes.

2.3.1 Seismic Weight Calcula on

C-25

DL R := 32.5psf

LLR := 55psf

2

d

SDLR := 34psf

SDLL := 57psf

SDLM := 10psf

)

3

WL := DL L + SDLL ⋅ Afloor = 1.236 × 10 kip

2.3.1 Seismic Weight Calculation

3 ( ) 3 WR := ( LLpartition + DL R + SDLR) ⋅ Afloor = 1.063 × 10 kip

WM := LLM + DL M + SDLM ⋅ Afloor = 4.015 × 10 kip

(

WM (mechanical), WL (lobby), and WR (residen al) are the weights of individual floors, not including column, cladding, or core weights.

Total Weights per floor:

Afloor := π ⋅ = 1.389 × 10 ft 4

d := 133ft

hfloor := 13.17ft

Floor Dimensions:

4 2

DL L := 32psf

LLL := 100psf

LLpartition := 10psf

DL M := 39psf

LLM := 240psf

Floor Loads:

C-26

nRB2 := 31

nL := 8

nRB4 := 33

nRB3 := 34

2.3.1 Seismic Weight Calculation

C 3 := 82plf ⋅ hfloor ⋅ 14 + 30in ⋅ 30in ⋅ hfloor ⋅ ρc ⋅ 14 = 199.499 kip

( ) C 4 := 99plf ⋅ hfloor ⋅ 14 + ( 18in ⋅ 18in ⋅ hfloor ⋅ ρc) ⋅ 14 = 84.63 kip

C 2 := 426plf ⋅ hfloor ⋅ 21 + [ ( 30in ⋅ 30in ) ⋅ 7 + ( 24in ⋅ 24in ) ⋅ 14] ⋅ hfloor ⋅ ρc = 328.012 kip

C 1 := 311plf ⋅ hfloor ⋅ 21 + [ ( 42in ⋅ 42in ) ⋅ 7 + ( 36in ⋅ 36in ) ⋅ 14] ⋅ hfloor ⋅ ρc = 532.213 kip

Column Weights per floor by bank (see Table 5 in Gravity System Report):

CW4 := ρc ⋅ hfloor ⋅ A ( 4) = 1.053 × 10 kip

3

CW3 := ρc ⋅ hfloor ⋅ A ( 3) = 2.284 × 10 kip

3

CW2 := ρc ⋅ hfloor ⋅ A ( 2) = 3.475 × 10 kip

3

CW1 := ρc ⋅ hfloor ⋅ A ( 1) = 4.588 × 10 kip

3

Core Wall Weights per floor by bank:

nfloors := nR + nL + nM = 147

nR := nRB1 + nRB2 + nRB3 + nRB4 = 131

nRB1 := 33

nM := 8

Floor numbers:

C-27

)

(

) 4

)

(

)

4

)

(

)

(

)

(

)

(

)

5

2.3.1 Seismic Weight Calculation

WRTot := nR ⋅ WR + WClad + nRB1 ⋅ CW1 + C 1 + nRB2 ⋅ CW2 + C 2 + nRB3 ⋅ CW3 + C 3 + nRB4 ⋅ CW4 + C 4 = 5.553 × 10 kip

(

WLTot := 4 ⋅ WL + nL ⋅ WClad + 5 ⋅ CW1 + C 1 + 1 ⋅ CW2 + CW3 + CW4 + C 2 + C 3 + C 4 = 3.841 × 10 kip

(

WMTot := nM ⋅ WM + WClad + 2 ⋅ CW1 + CW2 + CW3 + CW4 + C 1 + C 2 + C 3 + C 4 = 5.765 × 10 kip

(

Total Weights by floor type:

WClad := 10psf ⋅ hfloor ⋅ d ⋅ π = 55.028 kip

Cladding Weights per floor:

C-28

5

)(

)(

)(

)(

(

(

(

)

(

(

)

)

 0   W1    W :=  W2  W   3  W4   

2.3.1 Seismic Weight Calculation

5

(nRB4 ⋅ WR + 2 ⋅ WM + 1 ⋅ WL) = 6.006 × 104 kip

(nRB3 ⋅ WR + 2 ⋅ WM + 1 ⋅ WL) = 1.072 × 105 kip

WTOTcore := W1 + W2 + W3 + W4 = 5.147 × 10 kip

)

1 W3 := 1 + nRB3 + 2 ⋅ CW3 + 2 1 W4 := 1 + nRB4 + 2 ⋅ CW4 + 2

)

)

1 5 W1 := 5 + nRB1 + 2 ⋅ CW1 + ⋅ nRB1 ⋅ WR + 2 ⋅ WM + 5 ⋅ WL = 2.081 × 10 kip 2 1 5 W2 := 1 + nRB2 + 2 ⋅ CW2 + nRB2 ⋅ WR + 2 ⋅ WM + 1 ⋅ WL = 1.393 × 10 kip 2

(

Weight per bank ac ng on core. *assume columns and cladding do not load core *assume half of floor weight is carried by core.

WTOT := WMTot + WLTot + WRTot = 6.513 × 10 kip

Total Weight of Building:

C-29

Created by:

CJB

6.563E+05 kips

4588 3475 2284 1053

532 328 199 85

0.01 6563

55.03 55.03 55.03 55.03

(kips / floor)

Cladding Weight 6238 4921 3601 2256

(kips / floor)

Wresidential 9190 7873 6553 5208

(kips / floor)

Wmechanical

Yes No

kips

W floor type is weight of slab system, beams, and vertical elements per floor

6411 5094 3774 2429

(kips / floor)

Wlobby

Color Key:

5 1 1 1

nLobby

33 31 34 33

2 2 2 2 Total:

nResidential nMechanical

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

2.3.2 Seismic Load Calculations

Eqauations from ASCE 7-10 Chapters 11 and 12 used in Seismic Force Calculations

Total Design Base Shear

Cs

1 2 3 4

Column Weight

(kips / floor) (kips / floor)

Core Wall Bank Weight

Weights by floor type Mechanical 4015 kips / floor Lobby 1236 kips / floor Residential 1063 kips / floor

NOTE: SEISMIC WEIGHT IS DIFFERENT THAN ACTUAL WEIGHT

Total Building Weight, Wtot

Spreadsheet calculates the effective weight and base shear of the Chicago Spire. The weights by floor type are calculated using a Mathcad file combining the previously defined dead and live loads for each typical floor type.

Base Shear Calculations and Effective Seismic Weight

2.3.2 Seismic Load Calculations

2.563E+05 1.734E+05 1.393E+05 8.729E+04 6.563E+05

(kips / bank)

Total Bank Weight

4/27/2012

Σ [nfloor type * Wfloor type]

Seismic Load Calculations

Created by:

CJB

4/27/2012

Calculation based on ASCE 7-10 Chapters 11 and 12 for seismic loads.

Floor Level x 147 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131 130 129 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111 110 109

Floor Type Mechanical Mechanical Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Lobby Mechanical Mechanical

Weight

V = 6563, T = 5.68, k = 2 k wxhx Cvx Height

wx, kips 5.21E+03 5.21E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.26E+03 2.43E+03 6.55E+03 6.55E+03

hx, ft 1935.50 1922.33 1909.17 1896.00 1882.83 1869.67 1856.50 1843.33 1830.17 1817.00 1803.83 1790.67 1777.50 1764.33 1751.17 1738.00 1724.83 1711.67 1698.50 1685.33 1672.17 1659.00 1645.83 1632.67 1619.50 1606.33 1593.17 1580.00 1566.83 1553.67 1540.50 1527.33 1514.17 1501.00 1487.83 1474.67 1461.50 1448.33 1435.17

ft-kips 1.95E+10 1.92E+10 8.22E+09 8.11E+09 8.00E+09 7.89E+09 7.78E+09 7.67E+09 7.56E+09 7.45E+09 7.34E+09 7.23E+09 7.13E+09 7.02E+09 6.92E+09 6.81E+09 6.71E+09 6.61E+09 6.51E+09 6.41E+09 6.31E+09 6.21E+09 6.11E+09 6.01E+09 5.92E+09 5.82E+09 5.73E+09 5.63E+09 5.54E+09 5.45E+09 5.35E+09 5.26E+09 5.17E+09 5.08E+09 4.99E+09 4.91E+09 5.19E+09 1.37E+10 1.35E+10

0.03252 0.03208 0.01371 0.01352 0.01333 0.01315 0.01296 0.01278 0.01260 0.01242 0.01224 0.01206 0.01188 0.01171 0.01153 0.01136 0.01119 0.01102 0.01085 0.01068 0.01052 0.01035 0.01019 0.01002 0.00986 0.00970 0.00954 0.00939 0.00923 0.00908 0.00892 0.00877 0.00862 0.00847 0.00832 0.00818 0.00865 0.02291 0.02250

2.3.2 Seismic Load Calculations

Lateral Force Story Shear Fx, kips 213.43 210.54 89.96 88.72 87.49 86.27 85.06 83.86 82.67 81.48 80.30 79.14 77.98 76.83 75.68 74.55 73.42 72.31 71.20 70.10 69.01 67.93 66.85 65.79 64.73 63.68 62.64 61.61 60.59 59.58 58.57 57.57 56.58 55.60 54.63 53.67 56.76 150.38 147.66

Vx, kips 213 424 514 603 690 776 861 945 1,028 1,109 1,190 1,269 1,347 1,424 1,499 1,574 1,647 1,720 1,791 1,861 1,930 1,998 2,065 2,131 2,195 2,259 2,322 2,383 2,444 2,503 2,562 2,620 2,676 2,732 2,786 2,840 2,897 3,047 3,195

Moment k-ft 0 2,810 8,393 15,159 23,094 32,181 42,404 53,747 66,194 79,729 94,338 110,003 126,711 144,445 163,191 182,934 203,658 225,348 247,991 271,571 296,075 321,486 347,793 374,979 403,032 431,937 461,680 492,248 523,628 555,805 588,767 622,500 656,990 692,226 728,194 764,882 802,276 840,417 880,538 C-30

Floor Level x 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66

Floor Type Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Lobby Mechanical Mechanical Residential Residential Residential Residential Residential Residential

C-31

Weight

V = 6563, T = 5.68, k = 2 k wxhx Cvx Height

wx, kips 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.60E+03 3.77E+03 7.87E+03 7.87E+03 4.92E+03 4.92E+03 4.92E+03 4.92E+03 4.92E+03 4.92E+03

hx, ft 1422.00 1408.83 1395.67 1382.50 1369.33 1356.17 1343.00 1329.83 1316.67 1303.50 1290.33 1277.17 1264.00 1250.83 1237.67 1224.50 1211.33 1198.17 1185.00 1171.83 1158.67 1145.50 1132.33 1119.17 1106.00 1092.83 1079.67 1066.50 1053.33 1040.17 1027.00 1013.83 1000.67 987.50 974.33 961.17 948.00 934.83 921.67 908.50 895.33 882.17 869.00

ft-kips 7.28E+09 7.15E+09 7.01E+09 6.88E+09 6.75E+09 6.62E+09 6.49E+09 6.37E+09 6.24E+09 6.12E+09 6.00E+09 5.87E+09 5.75E+09 5.63E+09 5.52E+09 5.40E+09 5.28E+09 5.17E+09 5.06E+09 4.94E+09 4.83E+09 4.73E+09 4.62E+09 4.51E+09 4.40E+09 4.30E+09 4.20E+09 4.10E+09 4.00E+09 3.90E+09 3.80E+09 3.70E+09 3.61E+09 3.51E+09 3.58E+09 7.27E+09 7.08E+09 4.30E+09 4.18E+09 4.06E+09 3.94E+09 3.83E+09 3.72E+09

0.01214 0.01191 0.01169 0.01147 0.01126 0.01104 0.01083 0.01062 0.01041 0.01020 0.00999 0.00979 0.00959 0.00939 0.00919 0.00900 0.00881 0.00862 0.00843 0.00824 0.00806 0.00788 0.00770 0.00752 0.00734 0.00717 0.00700 0.00683 0.00666 0.00649 0.00633 0.00617 0.00601 0.00585 0.00597 0.01212 0.01179 0.00717 0.00697 0.00677 0.00658 0.00638 0.00619

2.3.2 Seismic Load Calculations

Lateral Force Story Shear Fx, kips 79.66 78.19 76.74 75.29 73.87 72.45 71.05 69.67 68.29 66.94 65.59 64.26 62.94 61.64 60.34 59.07 57.80 56.55 55.32 54.10 52.89 51.69 50.51 49.34 48.19 47.05 45.92 44.81 43.71 42.62 41.55 40.49 39.45 38.42 39.19 79.57 77.40 47.05 45.73 44.43 43.15 41.89 40.65

Vx, kips 3,275 3,353 3,429 3,505 3,579 3,651 3,722 3,792 3,860 3,927 3,993 4,057 4,120 4,181 4,242 4,301 4,359 4,415 4,471 4,525 4,577 4,629 4,680 4,729 4,777 4,824 4,870 4,915 4,959 5,001 5,043 5,083 5,123 5,161 5,200 5,280 5,357 5,404 5,450 5,495 5,538 5,580 5,620

Moment k-ft 922,604 965,718 1,009,862 1,055,016 1,101,161 1,148,279 1,196,351 1,245,359 1,295,284 1,346,108 1,397,813 1,450,382 1,503,797 1,558,041 1,613,096 1,668,946 1,725,574 1,782,962 1,841,096 1,899,957 1,959,531 2,019,801 2,080,752 2,142,368 2,204,634 2,267,534 2,331,053 2,395,177 2,459,891 2,525,181 2,591,032 2,657,430 2,724,361 2,791,811 2,859,767 2,928,239 2,997,759 3,068,298 3,139,457 3,211,217 3,283,563 3,356,477 3,429,943

3.0 Gravity Design 3.1 Tributary Areas

33

3.2 Core Area 3.2.1 Concrete Slab Design

39

3.2.2 Link Beam Design

45

3.3 Floor Area

51

3.3.1 Composite Decking 3.3.1.1

Composite Decking Design

52

3.3.1.2

Composite Decking Hand-Calc. and Mastan Analysis

56

3.3.2 Composite Beam Design 3.3.2.1

Joist Design Tool

64

3.3.2.2

Radial Girders

67

3.3.2.3

Rotated Radial Girder Beam Design

77

3.3.2.4

Circumferential Girder Design

80

3.3.2.5

Cantilevers

3.3.2.6

HSS Edge Beam Design

3.3.3 Vibration Analysis

3.4 Columns

83 88

93

99

3.4.1 Column Load Takedown

100

3.4.2 Composite Column Design 114 3.4.3 Steel Column Design

118

3.0 Gravity Design C-32

Tributary Areas Calculations

Chung Yu Wang 11/6/2011

Title: Tributary Area and Sizing of Flexural Elements under Uniformly Distributed Load for Bank 1, Residential (5th floor).

Figure 1: Typical Tributary Areas

Assumptions: 1) Except for elements in Bank 4, all elements in same bank have the same tributary area and geometry if they are located at the same location of each floor. 2) The tributary areas of the joists are technically trapezoidal in shape, but we assume the tributary area to be rectangular in shape with the width of the rectangle to be the base length of the trapezoid. 3) HSS are load bearing members. 4) Angled Girder takes ½ of the tributary area and load from the following area, and HSS 1 takes ¼ of the tributary and load from the same area.

C-33

Tributary Areas Calculations

Chung Yu Wang 11/6/2011

Figure 2: HSS-AG Tributary Area

5) To estimate the area of the HSS-AG tributary area, we use Revit and rotate the slab so point B meets point A. The corner of the slab is at the end of the cantilevering girder. Use straight sketch lines to draw a boundary that encloses the area and take length measurements to find the approximate, larger than actual, area. 6) The distances from columns to façade and from girder to façade are held constant throughout the building.

J1L  188in

pCJ1  103in

J2L  229in

pJ1J2  136in

b  w 

pCJ1  pJ1J2 2 J1L  J2L 2

 119.5in

 208.5in

Area  b  w  173.026ft

GL  270in

J2L  229in

pJ2G  137in b  w 

pJ1J2  136in

pJ1J2  pJ2G 2 J2L  GL 2

2

 136.5in

 249.5in

Area  b  w  236.505ft

2

C-34

Tributary Areas Calculations Girder, G of Floor G (Floor Plan Given) GL  245in SF  282in pJ2G  109in pCG  813in pGSF  

pCG

 GL

Area  



C-35

 SF  pCG  122.78in



SF  GL 2

 pJ2G  pGSF  212.062ft 2    2  

Chung Yu Wang 11/6/2011

Tributary Areas Calculations

Chung Yu Wang 11/6/2011

Girder, G of Floor 5 (Bank 1) GL  270in pGSF  122in pCG  896in pJ2G  137in SF  

GL 

  (pCG  pGSF)  306.763in

 pCG

Assume pGSF, distance from girder to exterior is held constant throughout the building

Area  

SF  GL pJ2G  pGSF 2  259.343ft  2 2  

C-36

Tributary Areas Calculations

Chung Yu Wang 11/6/2011

Angled Girder, AG of Floor 60 (Bank 2) A  295in B  144in C  291in D  142in E  212in AGL  303in 4 2

A1  B C  4.19 10 in A2  



D  C

4 2

  (A  B)  3.269 10 in 

2

Assume AG takes 1/2 of this total area A1  A2

Area AG 

 259.012ft

2

2

Angled Girder, AG of Floor 5 (Bank 1) GL  270in GL60  245in

Factor 

GL GL60

 1.102

2

Area AG60  37346in

Area AG  Factor  Area AG60  285.811ft AGL60  303in AGL5  Factor  AGL60  in

C-37

2

Tributary Areas Calculations

Chung Yu Wang 11/6/2011

HSS1 of Floor 5 HSS1Area 

Area AG 2

 142.906ft

2

HSS 1 is the perimeter element that is taking part of the tributary area. We assume that HSS1 has ¼ of the area or ½ that of the angled girder on the same floor.

HSS2 of Floor 5 pGSF  122in SF  307in Area  



pGSF 2

  SF  130.049ft 

2

C-38

C-39

Created by: ADV

11/30/2011

Mechanical

Residential / Lobby

Slab #

1 2 3 4

1 2 3 4

10.2 8.3 14.7 8.4

10.16 8.25 14.70 8.40

Span (ft)

Formulas Used Rxn = wl/2 Mmax = wl2/8

6 6 6 6

6 6 6 6

Slab Depth (in)

55.0 55.0 55.0 55.0

55.0 55.0 55.0 55.0

DL (psf)

10 10 10 10

57 57 57 57

SDL (psf)

5.65 3.63 12.20 3.78

3.62 2.33 7.82 2.42

Max Moment (kip-ft)

3.2.1 Concrete Slab Design

240 240 240 240

100 100 100 100

LL (psf)

Bank 1

2.34 1.88 3.44 1.91

1.50 1.20 2.20 1.20

End Reaction (kips/ft * width)

5 5 5 5

4 4 4 4

Rebar #

12 18 6 18

14 18 6 18

Rebar Dist. (in, o.c.)

This sheet displays the results from using the slab tool. All slabs were designed using the tool and the information from those results is tabulated below. The loads shown are unfactored. The moments and ends reactions are calculated using factored loads.

Designed Slab Information

3.2.1 Concrete Slab Design

C-40

Mechanical

Residential / Lobby

Slab #

Mechanical

Residential / Lobby

Slab #

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

10.16 6.06 6.06 7.80

10.16 6.06 6.06 7.80

Span (ft)

10.2 8.3 14.7 8.4

10.16 8.25 14.70 8.40

Span (ft)

6 6 6 6

6 6 6 6

Slab Depth (in)

6 6 6 6

6 6 6 6

Slab Depth (in)

55.0 55.0 55.0 55.0

55.0 55.0 55.0 55.0

DL (psf)

55.0 55.0 55.0 55.0

55.0 55.0 55.0 55.0

DL (psf)

10 10 10 10

57 57 57 57

SDL (psf)

10 10 10 10

57 57 57 57

SDL (psf)

5.65 1.87 1.87 3.22

3.62 1.20 1.20 2.07

Max Moment (kip-ft)

5.65 3.63 12.20 3.78

3.62 2.33 7.82 2.42

Max Moment (kip-ft)

3.2.1 Concrete Slab Design

240 240 240 240

100 100 100 100

LL (psf)

Bank 3

240 240 240 240

100 100 100 100

LL (psf)

Bank 2

2.34 1.35 1.35 1.77

1.50 0.86 0.86 1.13

End Reaction (kips/ft width)

2.34 1.88 3.44 1.91

1.50 1.20 2.20 1.23

End Reaction (kips/ft width)

4 4 4 4

4 4 4 4

Rebar #

5 5 5 5

4 4 4 4

Rebar #

8 18 18 16

14 18 18 18

Rebar Dist. (in, o.c.)

12 18 6 18

14 18 6 18

Rebar Dist. (in, o.c.)

C-41

Residential / Lobby

Slab #

Residential / Lobby

Slab #

1 2 3 4

1 2 3 4

10.16 --10.18

Span (ft)

10.16 6.06 6.06 10.18

Span (ft)

6 6 6 6

Slab Depth (in)

6 6 6 6

Slab Depth (in)

55.0 55.0 55.0 55.0

DL (psf)

55.0 55.0 55.0 55.0

DL (psf) 57 57 57 57

57 57 57 57

3.62 --3.64

Max Moment (kip-ft)

3.62 1.20 1.20 3.64

Max Moment (kip-ft)

3.2.1 Concrete Slab Design

100 100 100 100

Bank 4.2 LL SDL (psf) (psf)

100 100 100 100

Bank 4.1 LL SDL (psf) (psf)

1.50 --1.50

End Reaction (kips/ft width)

1.50 0.86 0.86 1.50

End Reaction (kips/ft width)

4 --4

Rebar #

4 4 4 4

Rebar #

14 --14

Rebar Dist. (in, o.c.)

14 18 18 14

Rebar Dist. (in, o.c.)

C-42

DL LL SDL

Loads

Bank Location Slab #

55.0 plf 100 plf 57 plf

3.7

Max Allowable Moment

Unfactored Loading

OK 3.43

Overall Slab Check Max Moment in Slab

1 1 1

3.43

Mmax (kip-ft)

3.2.1 Concrete Slab Design

Factored Loading (1.2DL + 1.6LL) DL 66 plf LL 160 plf SDL 68.4 plf

kip-ft

kip-ft

Color Key:

Yes No

4

14

Rebar o.c. (in)

Resultant End reaction (factored) Single end 1,422 lbs 1.4 kips

1.4

11/30/2011

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

Created by: ADV

Important Information End Rxn (kips) Rebar #

This sheet is a tool to design a simply supported reinforced concrete slab, given the necessary information.

Reinforced Concrete Slab Design

C-43

9.66 6 1 4,000 psi

ft in

0.17 0.130 YES

As As-min

Area of steel (per foot width)

Minimum required steel area Area of steel acceptable?

Allowable internal moment Load factor Factored Allowable Moment

Concrete cover Structural depth Ultimate tensile force Ultimate compression force Compression zone 1/2 of Compression zone Internal moment arm Allowable internal moment 4.10 0.9 3.69

Mn φ φMn

C a a/2 d-a/2 Mn

0.75 5.00 10,098 10,098 0.25 0.12 4.88 49,240

c d Tu

ACI 318, 9.3.2.1 per foot-width of slab

= Tu(d-a/2)

= C/(0.85*f'c*b) ; Whitney stress block

= Tu

= fy*As

= h-c-d/2

As > As-min?

= 0.0018*bh; ACI 318-08 7.12.2.1

= 12*Ab/s

ACI 318-08 7.6

Assumed Sand-Lightweight Concrete

= λ*wc1.5*33*f'c1/2; ACI 318-08 8.5, 8.6

3.2.1 Concrete Slab Design

kip-ft

kip-ft

in in lbs lbs in in in lb-in

Calculations for a Representative 1-ft Width of the Slab:

in

2

psi in2

60,000

fy

Steel Strength

s

14 in OK Es 29,000,000 psi

Ec 2,046,689 psi # 4 dbar 0.5 in 2 in Abar 0.20

f'c

L h

Area of bar Rebar spacing o.c. Rebar Spacing Check Steel Elastic Modulous

Concrete Modulus of Elasticity Rebar size Nominal bar diameter

Span length Slab depth Concrete type Concrete strength

Basic Slab Properties

C-44

Max Moment in slab Mu < φMn?

3.43 YES

0.28%

ρactual

Mu

2.85%

ρbal

Percent steel for balanced failure YES

0.00207

εys

Strain limit for steel

ρactual Tapplied

Reference: Blodgett, Omer W. Design of Welded Structures

3.2.2 Link Beam Design

C-50

3.3 Floor Area

51

3.3.1 Composite Decking 3.3.1.1

Composite Decking Design

52

3.3.1.2

Composite Decking Hand-Calc. and Mastan Analysis

3.3.2 Composite Beam Design 3.3.2.1

Joist Design Tool

64

3.3.2.2

Radial Girders

67

3.3.2.3

Rotated Radial Girder Beam Design

77

3.3.2.4

Circumferential Girder Design

80

3.3.2.5

Cantilevers

3.3.2.6

HSS Edge Beam Design

3.3.3 Vibration Analysis

83

93

3.3 Floor Area C-51

88

56

3.3.1.1 Composite Decking Design Summary of Composite Decking Selections This table presents a summary of decking thicknesses and deck type based on the type of floor and bank type.

Slab Depth (in) Load Case LL (psf) SDL (psf) Load (psf) Rise Average Framing Length (ft) Radial Length (ft) Spans Weight of Framing (lbs) Span Dist (ft) DECK TYPE Deck+Slab Weight (PSF)

4.0

Low

Residential Exterior 55 42 97 MidMidHigh Low High

4.5

Low

Amenities 100 57 157 MidMidLow High

High

Low

Mechanical 240 10 250 Mid- MidLow High

High

19.25

17

22.5

22.4

18.75

16.6

22

22.25

18.75

16.6

22

22.25

31.36

26.75

24.03

31.80

31.36

26.75

24.03

31.80

31.36

26.75

24.03

31.80

3

3

3

3

4

4

4

4

4

4

4

4

1155

1020

1350

1344

1500

1328

1760

1780

1500

1328

1760

1780

10.5 9 8.5 11 8 7 6.5 8 8 7 6.5 8 1.5VL22 1.5VL22 1.5VL22 1.5VL19 1.5VL22 1.5VL22 1.5VL22 1.5VL22 2VLI16 2VLI19 2VLI20 2VLI16

29.6

29.6

29.6

29.6

29.6

29.6

29.6

3.3.1.1 Composite Decking Design

29.6

35.6

34.6

34.3

35.6

C-52

Low Rise Amenities This is a sample calculation to check the decking and concrete thickness for the low rise amenities. Calculations for all other floor types was performed in the same manner. DATA concrete density f'c of concrete Ec of concrete slab thickness Number of spans Span length L/H interior spans Value OK? L/H exterior spans Value OK? Self wt of concrete slab sip DL unfactored DL factored DL(Unf*1,2) sip LL factored LL (Unf*1,6) dummy DL dummy LL

110 4 2408 4.5 4 8.0 21.3 YES 21.3 YES 41.25 57 98.25 117.9 100 160 100 100

lb/ft ksi ksi in

3

ft

plf plf plf plf plf plf plf plf

1) MOMENT CALCULATIONS

100 psf DL on All Spans 100 psf LL on Span 1 only 100 psf LL on Span 2 only 100 psf LL on Span 3 only 100 psf LL on Span 4 only

Adjust Dummy values for actual loads Actual DL on All Spans Peak skipped LL combination for above sketch Sum of LL moments from critical spans DL Moment x 1.2 LL Moment x 1.6 Total Design Moment Magnitude of Simple Span Factored Moment (1.2D + 1.6L)L2/8 (same for all locations) Total Design Moment / Simple Span M Factor Cm where Total Design Moment = Cm(wuI2)

A 0 0 0 0 0

Dummy Moments [Kips·ft/ft] AB B BC 0.7086 -1.063 0.3543 0.8371 -0.8057 -0.03143 0.09429 -0.6914 0.5971 0.2943 -0.2914 -0.002857 0.02371 -0.4057 0.1686

C -0.7086 -0.1371 -0.5943 -0.5943 -0.1371

A 0 0 0 0 0 -0.74

AB 0.70 1,3 1.13 0.84 1.81 2.65

Moments [Kips·ft/ft] B -1.04 1,2,4 -1.90 -1.25 -3.04 -4.3

BC 0.35 2,4 0.77 0.42 1.23 1.64

C -0.70 2,3 -1.19 -0.84 -1.90 -2.7

0

2.2

-2.2

2.2

-2.2

0 0

1.19 0.15

1.93 0.24

0.74 0.09

1.23 0.15

C-53

3.3.1.1 Composite Decking Design

2) REINFORCEMENT BAR CALCULATIONS A #3 0.11 0.375 0.75 3.56 13 13.5 YES

AB #4 0.2 0.5 0.75 3.50 13 13.5 YES

Reinforcement Bars B #6 0.44 0.75 0.75 3.38 13 13.5 YES

BC #4 0.2 0.5 0.75 3.50 13 13.5 YES

C #4 0.2 0.5 0.75 3.50 13 13.5 YES

A 1.5VL22 0.354 0.01475 0 4.49

0.10

0.18

0.41

0.18

0.18

0.35

0.35

0.35

Steel Area in 1-ft strip (in2)

Minimum steel area(in /ft)

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

Minimum steel area(in 2/ft)

Maximum steel area(in 2/ft) Area between the limits? fy of steel(ksi) Es of steel(ksi)

1.22 YES 60

1.20 YES 60

1.15 YES 60

1.20 YES 60

1.20 YES 60

1.54 YES 60

1.54 YES 60

1.54 YES 60

29,000

29,000

29,000

29,000

29,000

29,000

29,000

29,000

Maximum steel area(in 2/ft) Area between the limits? fy of steel(ksi) Es of steel(ksi)

A 21.2 21.2 0.26 4.36 7.7 0.9 -6.9

B 21.2 21.2 0.26 4.36 7.7 0.9 -6.9

C 21.2 21.2 0.26 4.36 7.7 0.9 -6.9

Reinforcing Bars size 2 Area of one bar (As/bar)(in ) Bar Diameter(in) Bar Cover(in) Structural Depth "d" (in) Spacing between bars (in) Maximum Spacing of bars (in) Spacing Requirement OK? Steel Area in 1-ft strip (in2) 2

Tension force (assuming Steel has yielded)(kips) Compression force=Tension force Centroid of comp.force (a/2)("Whitney Model")(in) Moment Arm between T &C force (in) Nominal Moment Capacity (Mn) (kips-ft) Strength Reduction factor (Ф) Usable Moment Capacity (Ф*Mn)(kips-ft) Moment based on skip loads and factored loads ,M u( kips-ft) Is Ф*Mn>Mu?

Force & Moment Calculations BC C 11.1 11.1 11.1 11.1 0.14 0.14 3.43 3.43 3.2 3.2 0.9 0.9 2.9 -2.9

C 1.5VL22 0.354 0.01475 0 4.49

AB 11.1 11.1 0.14 3.43 3.2 0.9 2.9

B 24.4 24.4 0.30 3.23 6.6 0.9 -5.9

-0.74

2.65

-4.3

1.64

-2.7

-0.74

-4.3

-2.7

YES

YES

YES

YES

YES

YES

YES

YES

Veryfing assumptions for calculations made AB B BC

Mesh Type 2 Mesh Area per foot (in ) .5*Thickness Cover(in) Structural Depth "d" (in)

YES

A 6.1 6.1 0.07 3.53 1.8 0.9 -1.6

A

*Assume section qualifies for Ф=0.9

C

Strain of the steel at yielding (ε y)

0.00207

0.00207

0.00207

0.00207

0.00207

Strain of the concrete(ε cu) β1 ρbal

0.003 0.85 0.0285

0.003 0.85 0.0285

0.003 0.85 0.0285

0.003 0.85 0.0285

0.003 0.85 0.0285

ρactual

0.00238

0.00440

0.01003

0.00440

0.00440

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

Is ρbal > ρactual? Is ρactual 25% ?

Total Shear Load Number of Ribs

22.91

in

26.22

Smin

in

22.91

Min. Req. Section Modulus

Shear connectors, partial composite action Ss Steel Section Modulus Stens Section Modulus for Tension # of Studs

# of Ribs studs / rib Stud capacity

Concrete Cover ≥ 1/2"

= 5*W*L4/(384*E*I)

= 5*W*L4/(384*E*I)

= Ix + (Ic - Ix )*(V'h/Vh)2

3.3.2.1 Joist Design Tool

Post Composite

Pre Composite

Service Loads (Unfactored)

Shear Stud Spacing ≤ 18"

= ΣQn = (studs/rib)*Vstud*nribs*m/l ; AISC I3-1c Slab Thickness ≥ 2"

= V'h

Stud Checks from AISC I3.2c.1: Nominal Rib height ≤ 3" Shear Stud Diamater ≤ 3/4" Shear Stud Length ≥ 1 1/2"

= Vh*(Smin - Ss / Savail - Ss)2 = N/A if 100% composite action

= MIN(i, ii)

= 0.85*f'c* Ac = As*Fy

Shear Stud Properties kips kips kips

Diameter Length Spacing

389 208 208

Option 1 Option 2 Horizontal Shear

(i) (ii) Vh

Horizontal Shear Vh

1265

433

Vstud

nribs

Created by:

plf plf

YES

YES

YES

YES YES YES

30

30 1 17.2

0.75 3.00 6

I3.2c.1.d

I3.2c.1.c

I3.2c.1.b

I3.2c.1.b

I3.2c.1.a I3.2c.1.b

in in in

CJB / ADV

= Qn per rib ; AISC Table 3-21

11/1/2011

C-67

Created by: CJB / ADV

0.39

7.53

98.3

890 55

tw

bf

Ss

Ix

Web Thickness

Flange Width

Steel Section Modulus

Moment of Inertia Weight

2111.25

137.21

314.52

Str

Sc

Section Modulus for Tension

Section Modulus for Comp.

6.71

yt

N.A. to top of beam

Icomp

15.39

yb

N.A. to bottom of beam

Composite Moment of Inertia

82.70 N/A 82.70

(a) (b) beff

Span/4 Beam Spacing Effective Flange Width

Composite Beam Properties

18.1 0.63

d tf

Overall Depth Flange Thickness

16.2

As

W 18 x 55

(67) 5 38%

Area of Steel

Section Type

Selected Shape's Properties

Shear Stud Shear Stud Spacing % Composite Action

3 Lobby Radial Girder Bank 3 W-Shape 18 x 55 Overall Check, Acceptable? YES

Bank: Type: Beam:

in

3

in3

in in4

in

in in in

plf

in4

in in3

in

in in

in2

= Ic / yt

= Ic / yb

= MIN(a,b)

Angled girder applies a point load at the midspan of the cantilever. The façade applies an additional point load at the end.

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

3.3.2.2a Radial Girder Design

SDL LL

DL LL

B Total Composite Depth

T

Decking Type Slab thickness Rib Height C P

Slab and Decking Properties

Postcomposite

Text from Summary Precomposite

Joist Reaction Loads for 1 Joist

Precomposite Postcomposite Total w/o Construction

Radial Girder Column Moments

Radial Girder Beam Span:

Input from Bank Information

3.87 9.05

Joist 1 2.35 1.81

27.57

in in in in 1.75 in 22.1 in

3.5 in

1.5VL22 2.5 1.5 36 6

4.70 10.9

Joist 2 3.09 2.20

98.1 kip-ft 277.3 kip-ft 336.4 kip-ft

ft

5.29 12.3

Joist 3 3.56 2.47

kips kips

kips kips

from Tower Geometry

Design tool to calculate the W-Shape and Shear stud configuration for radial girders in the lobby and mechanical floors. The predetermined decking material runs parallel to the girders. Loads are applied as point loads from the joists. A separate spreadsheet calculates pre- and post-composite deflection

Radial Girder Design Tool for Lobby and Mechanical Floors

3.3.2.2a Radial Girder Design 11/1/2011

C-68

3.09 2.20

3.09 2.20

21.3 15.2

21.3 15.2 Joist 2

4.70 10.90

4.70 10.90

32.4 75.1

32.4 75.1

0.73 0.57

3.97 3.05

6.1 4.7

18.2 14.0 Joist 1

1.21 2.83

6.53 15.27

10.0 23.4

30.0 70.2

4.18

98.1 88.5 277.3 253.1 336.4 122

Distance from Load to Core Distance from Load to Column Precomposite Column Reaction DL LL Core Reaction DL LL Column Moment DL LL Core Moment DL LL Postcomposite Column Reaction SDL LL Core Reaction SDL LL Column Moment SDL LL Core Moment SDL LL

Self Weight Moment (Core and Column)

Precomposite Column Moment Precomposite Core Moment Postcomposite Column Moment Postcomposite Core Moment Total Max Moment w/o Construction Smin

kip-ft kip-ft kip-ft kip-ft kip-ft in3

kip-ft

Joist 2 13.78 13.78 Joist 2

Joist 1 6.89 20.67 Joist 1

Factored Moment Calculation

3.3.2.2a Radial Girder Design

M / (0.66*Fy)

13.7 31.8

41.0 95.4

1.65 3.84

8.93 20.76

9.2 6.4 Joist 3

27.6 19.1

1.11 0.77

6.01 4.17

Joist 3 20.67 6.89 Joist 3

kip-ft kip-ft

kip-ft kip-ft

kips kips

kips kips

kip-ft kip-ft

kip-ft kip-ft

kips kips

kips kips

ft ft

Fy: Fu: Es:

3.3.2.2a Radial Girder Design

Type f'c Density Concrete Modulus of Elascticity Ec Modular ratio

Concrete Properties

Steel Properties

2574 ksi 11

Lightweight 4000 psi 115 pcf

50 ksi 65 ksi 29000 ksi

Created by: CJB / ADV

11/1/2011

C-69

3.3.2.2a Radial Girder Design

YES

Total Capacity*

V < Vn ?

m Vn

Distance from M0 to Mmax

306.525 YES

7

268

V

Total Shear Load

V'h

Adjusted Horizontal Shear

YES

268.15

Smin

Min. Req. Section Modulus

38%

122.33

Stens

Section Modulus for Tension

% Composite Action > 25% ?

137.21

Ss

Shear connectors, partial composite action Steel Section Modulus

% Composite Action

98

(i) (ii) Vh

703 810 703

277.3 0.962 1.8 YES

ksi

33.0

0.66*Fy

fb,1 < 0.66*Fy?

Mcomp f'c-comp 0.45*f'c-comp f'c < 0.45*f'c-comp ?

ksi

YES

32.8

fb,2

Option 1 Option 2 Horizontal Shear

Horizontal Shear Vh

Composite Moment Concrete compressive stress

Condition 2:

ft

kips

kips

in3

in

3

in3

kips kips kips

kip-ft ksi ksi

ksi

45.0

ksi

kip-ft

kip-ft

36.2

Post-Composite Moment

= ΣQn = (studs/rib)*Vstud*nribs*m/l ; AISC I3-1c

= V'h

wr wr/h # of Studs Stud capacity

Spacing

Length

Diameter

Postcomposite Defleciton

Camber

Precomposite Deflection

Effective Moment of Inertia

Unfactored Joist 3 Load

Unfactored Joist 2 Load

Pre Composite Unfactored Joist 1 Load Unfactored Joist 2 Load Unfactored Joist 3 Load Post Composite Unfactored Joist 1 Load

Deflection and Camber

Concrete Cover ≥ 1/2" Slab Thickness ≥ 2" Shear Stud Spacing ≤ 18"

Shear Stud Diamater ≤ 3/4" Shear Stud Length ≥ 1 1/2"

Nominal Rib height ≤ 3"

Stud Checks from AISC I3.2c.1:

Shear Stud Properties

3.3.2.2a Radial Girder Design

= Vh*(Smin - Ss / Savail - Ss)2 = N/A if 100% composite action

= MIN(i, ii)

= 0.85*f'c* Ac = As*Fy

= Mcomp/(n*St)

= (Mpre+ Mpost)/Str

= Mpre / Ss + Mpost/Str

Modulus for Tension

in3

0.9*Fy fb,1 < 0.9*Fy?

98.1

277.3

Mpre

Mpost

Pre-Comosite Moment

Steel Section

in3

fb,1

137.2

Str

Section Modulus for Tension

Allowable Stress Condition 1:

98.3

Ss

Steel Section Modulus

Stress Check

YES YES YES YES

YES

YES

0.00 0.129

Δpost OK?

YES

0.919

0.062

Δpre Δcamber

L/360

1068

Ieff

12.10

10.73

8.88

3.09 3.95 4.51

I3.2c.1.b I3.2c.1.b I3.2c.1.c I3.2c.1.d

I3.2c.1.b

I3.2c.1.a

in

in

in

in

in4

kips

kips

kips kips kips

2.125 in 1.417 67 18.3 AISC Table 3-21

5 in

3 in

0.75 in

Created by: CJB / ADV

References 3 Point Deflection Spreadsheet

References 3 Point Deflection Spreadsheet

= Ix + (Ic - Ix )*(V'h/Vh)2

11/1/2011

C-70

Created by:

CJB / ADV

11/1/2011

Selected Shape's Properties

0.295

6.99

56.5

448 36

tw

bf

Ss

Ix

Web Thickness

Flange Width

Steel Section Modulus

Moment of Inertia Weight

1234.15

83.42

241.75

Str

Sc

Section Modulus for Tension

Section Modulus for Comp.

5.11

yt

N.A. to top of beam

Icomp

14.79

yb

N.A. to bottom of beam

Composite Moment of Inertia

82.81 N/A 82.81

(a) (b) beff

Span/4 Beam Spacing Effective Flange Width

Composite Beam Properties

15.9 0.43

d tf

Overall Depth Flange Thickness

10.6

As

W 16 x 36

(24) 14 25%

Area of Steel

Section Type

Shear Stud Shear Stud Spacing % Composite Action

4.1 Residential Radial Girder Bank 4.1 W-Shape 16 x 36 Overall Check, Acceptable? YES

Bank: Type: Beam:

in

3

in3

in in4

in

in in in

plf

in

4

in in3

in

in in

in2

= Ic / y t

= Ic / y b

= MIN(a,b)

SDL LL

DL LL

B Total Composite Depth

T

Decking Type Slab thickness Rib Height C P

Slab and Decking Properties

Postcomposite

Text from Summary Precomposite

Joist Reaction Loads for 1 Joist

Precomposite Postcomposite Total w/o Construction

Radial Girder Column Moments

Radial Girder Beam Span:

Input from Bank Information

3.3.2.2a Radial Girder Design

Angled girder applies a point load at the midspan of the cantilever. The façade applies an additional point load at the end.

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

3.11 6.71

Joist 1 3.28 2.44

86.0 141.8 192.6

27.60

in in in in 1.75 in 19.9 in

3.5 in

1.5VL22 2.5 1.5 36 6

3.94 8.49

4.23 3.09

Shear Capacity

h

Joist 2

kip-ft kip-ft kip-ft

ft

kips kips

kips kips

18.3

1.5

from Tower Geometry

Design tool to calculate the W-Shape and Shear stud configuration for radial girders in the residential floors. The predetermined decking material runs parallel to the girders. Loads are applied as point loads from the joists. A separate spreadsheet calculates pre- and post-composite deflection

Radial Girder Design Tool for Residential Floors

C-71

2.19 1.60

34.6 25.3

17.3 12.6 Joist 2

5.84 12.58

2.04 4.40

32.2 69.4

16.1 34.7

4.86 3.61

13.4 10.0

26.8 20.0 Joist 1

1.61 3.48

4.61 9.94

12.7 27.4

25.4 54.9

2.74

86.0 79.5 141.8 131.2 192.6 70

Self Weight Moment (Core and Column)

Precomposite Column Moment Precomposite Core Moment Postcomposite Column Moment Postcomposite Core Moment Total Max Moment w/o Construction

Smin

6.27 4.58

1.70 1.27

kip-ft kip-ft kip-ft kip-ft kip-ft in3

kip-ft

Joist 2 18.40 9.20 Joist 2

Joist 1 9.20 18.40 Joist 1

Distance from Load to Core Distance from Load to Column Precomposite Column Reaction DL LL Core Reaction DL LL Column Moment DL LL Core Moment DL LL Postcomposite Column Reaction SDL LL Core Reaction SDL LL Column Moment SDL LL Core Moment SDL LL

Factored Moment Calculation

M / (0.66*Fy)

kip-ft kip-ft

kip-ft kip-ft

kips kips

kips kips

kip-ft kip-ft

kip-ft kip-ft

kips kips

kips kips

ft ft

3.3.2.2a Radial Girder Design

Concrete Properties

Steel Properties

Type f'c Density Ec Modular ratio

Fy: Fu: Es:

ksi ksi ksi

Lightweight 4000 psi 115 pcf 2574 ksi 11

50 65 29000

C-72

33.0

YES

0.66*Fy

fb,1 < 0.66*Fy?

83.42

70.03

133.88 25% YES

134 9

146.4 YES

Ss

Stens

Smin

V'h

V m

Vn V < Vn ?

Shear connectors, partial composite action Steel Section Modulus

Section Modulus for Tension

Min. Req. Section Modulus

Adjusted Horizontal Shear % Composite Action % Composite Action > 25% ?

Total Shear Load Distance from M 0 to Mmax

Total Capacity*

57

(i) (ii) Vh

704 530 530

141.8 0.640 1.8 YES

32.8

fb,2

Mcomp f'c-comp 0.45*f'c-comp f'c < 0.45*f'c-comp ?

YES

Option 1 Option 2 Horizontal Shear

Horizontal Shear Vh

Composite Moment Concrete compressive stress

Condition 2:

45.0

Post-Composite Moment

0.9*Fy fb,1 < 0.9*Fy?

141.8

Mpost

38.7

86.0

Mpre

Pre-Comosite Moment

fb,1

83.4

Str

Section Modulus for Tension

Allowable Stress Condition 1:

56.5

Ss

Steel Section Modulus

Stress Check

3

kips ft

kips

in

3

in3

in

3

kips kips kips

kip-ft ksi ksi

ksi

ksi

ksi

ksi

kip-ft

kip-ft

in

in

3

2

Concrete Cover ≥ 1/2" Slab Thickness ≥ 2" Shear Stud Spacing ≤ 18"

Shear Stud Diamater ≤ 3/4" Shear Stud Length ≥ 1 1/2"

Nominal Rib height ≤ 3"

Precomposite Deflection

Effective Moment of Inertia

Pre Composite Unfactored Joist 1 Load Unfactored Joist 2 Load Post Composite Unfactored Joist 1 Load Unfactored Joist 2 Load

Deflection and Camber

Postcomposite Defleciton

3.3.2.2a Radial Girder Design

= ΣQn = (studs/rib)*V stud*nribs*m/l ; AISC I3-1c

= V'h

wr wr/h # of Studs Stud capacity

Spacing

Length

Diameter

Stud Checks from AISC I3.2c.1:

= Vh*(Smin - Ss / Savail - Ss) = N/A if 100% composite action Camber

= MIN(i, ii)

= 0.85*f'c* Ac = As*Fy

= Mcomp/(n*St)

= (Mpre+ Mpost)/Str

= Mpre / Ss + Mpost/Str

Modulus for Tension

Steel Section

Shear Stud Properties

YES YES YES YES

YES

YES

0.00 0.149 0.920 YES

Δpost L/360 OK?

0.112

498 Δcamber

Δpre

Ieff

6.79 8.59

4.26 5.46

I3.2c.1.b I3.2c.1.b I3.2c.1.c I3.2c.1.d

I3.2c.1.b

I3.2c.1.a

2.125 in 1.417 24 18.3 AISC Table 3-21

14 in

3 in

0.75 in

in in

in

in

kips kips in4

kips kips

References 3 Point Deflection Spredsheet

References 3 Point Deflection Spredsheet

= Ix + (Ic - Ix )*(V'h/Vh)2

3.3.2.2b 2-Point Deflection Calculations

Created by:

ADV/CJB

11/1/2011

Calculates deflection under precomposite loads and under superimposed dead and live loads using principles of superposition. Gives deflection at 100 locations along the beam when it is subjected to two point loads. Input from Cantilever Worksheet

Maximum Deflection

Es Ieff

29000 498

ksi 4 in

Precomposite Postcomposite

Is Self Weight Length Spacing

448 0.0030 331 110

in kip/in in in

0.1121667 in 0.14934099 in

4

Unfactored Loads from Cantilever Worksheet Precomposite Post Composite 4.26 6.79 kips 5.46 8.59 kips

Joist 1 Joist 2

a 221 110

b 110 221

in in

a and b from AISC Manual

Precomposite Deflection from: (in) 0.0 3.3 6.6 9.9 13.3 16.6 19.9 23.2 26.5 29.8 33.1 36.4 39.8 43.1 46.4 49.7 53.0 56.3 59.6 62.9 66.3 69.6 72.9 76.2 79.5 82.8 86.1 89.4 92.8 96.1 99.4 102.7 106.0 109.3 112.6 115.9 119.3 122.6 125.9 129.2 132.5 135.8 139.1 142.4 145.8 149.1 152.4 155.7 159.0 162.3 165.6 168.9

C-73

Joist 1 (in) 0 4.36085E-05 0.000172375 0.00038321 0.000673027 0.001038735 0.001477247 0.001985473 0.002560325 0.003198715 0.003897554 0.004653753 0.005464224 0.006325877 0.007235625 0.008190379 0.00918705 0.010222549 0.011293788 0.012397679 0.013531131 0.014691058 0.01587437 0.017077979 0.018298796 0.019533732 0.0207797 0.022033609 0.023292372 0.0245529 0.025812104 0.027066896 0.028314187 0.029550888 0.030773911 0.031980167 0.033166568 0.034330025 0.035467449 0.036575751 0.037651844 0.038692638 0.039695045 0.040655976 0.041572342 0.042441055 0.043259027 0.044023168 0.044730391 0.045377605 0.045961724 0.046479657

Post Composite Deflection from: Joist 2 (in) 0 0.000111187 0.000437209 0.000966759 0.00168853 0.002591216 0.003663508 0.0048941 0.006271685 0.007784955 0.009422603 0.011173323 0.013025806 0.014968747 0.016990838 0.019080771 0.02122724 0.023418938 0.025644556 0.02789279 0.03015233 0.03241187 0.034660103 0.036885722 0.039077419 0.041223888 0.043313822 0.045335912 0.047278853 0.049131337 0.050882056 0.052519705 0.054032975 0.055410559 0.056641905 0.057725222 0.058664373 0.059463315 0.060126007 0.060656405 0.061058468 0.061336152 0.061493415 0.061534215 0.061462509 0.061282255 0.060997409 0.060611931 0.060129776 0.059554903 0.058891269 0.058142832

Self Weight (in)

Total

Joist 1 (in)

0 1.13535E-05 4.4501E-05 9.80942E-05 0.000170813 0.000261363 0.000368482 0.00049093 0.000627499 0.000777008 0.000938302 0.001110255 0.001291771 0.001481777 0.001679231 0.00188312 0.002092455 0.002306278 0.002523657 0.002743688 0.002965497 0.003188235 0.003411082 0.003633245 0.00385396 0.004072491 0.004288127 0.004500189 0.004708023 0.004911003 0.005108532 0.00530004 0.005484984 0.00566285 0.005833151 0.00599543 0.006149255 0.006294223 0.006429958 0.006556113 0.006672369 0.006778433 0.006874041 0.006958957 0.007032973 0.007095908 0.007147608 0.007187949 0.007216834 0.007234193 0.007239983 0.007234193

0 0.000166149 0.000654085 0.001448064 0.00253237 0.003891314 0.005509236 0.007370503 0.009459509 0.011760678 0.014258459 0.016937331 0.019781801 0.022776401 0.025905695 0.02915427 0.032506745 0.035947764 0.039462001 0.043034156 0.046648958 0.050291163 0.053945555 0.057596946 0.061230176 0.064830111 0.068381649 0.071869711 0.075279248 0.07859524 0.081802693 0.08488664 0.087832145 0.090624297 0.093248968 0.095700819 0.097980196 0.100087562 0.102023413 0.10378827 0.10538268 0.106807222 0.108062501 0.109149148 0.110067824 0.110819218 0.111404044 0.111823048 0.112077 0.112166701 0.112092976 0.111856681

(in) 0.0 3.3 6.6 9.9 13.3 16.6 19.9 23.2 26.5 29.8 33.1 36.4 39.8 43.1 46.4 49.7 53.0 56.3 59.6 62.9 66.3 69.6 72.9 76.2 79.5 82.8 86.1 89.4 92.8 96.1 99.4 102.7 106.0 109.3 112.6 115.9 119.3 122.6 125.9 129.2 132.5 135.8 139.1 142.4 145.8 149.1 152.4 155.7 159.0 162.3 165.6 168.9

3.3.2.2b 2-Point Deflection Calculations

(in) 0 6.24909E-05 0.000247013 0.00054914 0.000964447 0.001488506 0.002116893 0.002845181 0.003668944 0.004583757 0.005585192 0.006668825 0.007830228 0.009064977 0.010368645 0.011736807 0.013165035 0.014648905 0.01618399 0.017765863 0.0193901 0.021052275 0.02274796 0.024472731 0.02622216 0.027991823 0.029777293 0.031574144 0.03337795 0.035184286 0.036988724 0.03878684 0.040574207 0.042346399 0.04409899 0.045827554 0.047527665 0.049194898 0.050824826 0.052413022 0.053955062 0.055446519 0.056882967 0.058259981 0.059573133 0.060817999 0.061990151 0.063085165 0.064098614 0.065026072 0.065863113 0.066605311

Joist 2 (in) 0 0.00015741 0.00061898 0.00136869 0.00239054 0.00366852 0.00518662 0.00692883 0.00887914 0.01102156 0.01334006 0.01581864 0.0184413 0.02119202 0.0240548 0.02701362 0.03005249 0.03315539 0.03630631 0.03948925 0.04268819 0.04588714 0.04907008 0.052221 0.0553239 0.05836277 0.06132159 0.06418437 0.06693509 0.06955775 0.07203633 0.07435483 0.07649725 0.07844756 0.08019084 0.08172455 0.08305415 0.08418526 0.08512346 0.08587437 0.08644359 0.08683673 0.08705937 0.08711713 0.08701562 0.08676042 0.08635715 0.08581141 0.0851288 0.08431492 0.08337538 0.08231578

Total (in) 0 0.000219904 0.000865992 0.001917831 0.003354986 0.005157023 0.007303509 0.009774009 0.012548089 0.015605315 0.018925253 0.022487469 0.026271529 0.030256998 0.034423443 0.03875043 0.043217524 0.047804292 0.052490299 0.057255112 0.062078295 0.066939416 0.07181804 0.076693733 0.081546061 0.08635459 0.091098885 0.095758513 0.10031304 0.104742031 0.109025053 0.113141672 0.117071452 0.120793961 0.124289831 0.127552102 0.130581818 0.133380154 0.135948288 0.138287397 0.140398657 0.142283246 0.143942339 0.145377115 0.14658875 0.14757842 0.148347303 0.148896574 0.149227412 0.149340993 0.149238494 0.148921091

172.3 175.6 178.9 182.2 185.5 188.8 192.1 195.4 198.8 202.1 205.4 208.7 212.0 215.3 218.6 221.9 225.3 228.6 231.9 235.2 238.5 241.8 245.1 248.4 251.8 255.1 258.4 261.7 265.0 268.3 271.6 274.9 278.3 281.6 284.9 288.2 291.5 294.8 298.1 301.4 304.8 308.1 311.4 314.7 318.0 321.3 324.6 327.9 331.3

0.046928317 0.047304615 0.047605462 0.047827769 0.047968449 0.048024412 0.04799257 0.047869834 0.047653115 0.047339325 0.046925375 0.046408177 0.045784642 0.045051681 0.044206206 0.043245202 0.042170065 0.040989033 0.039710929 0.038344579 0.036898807 0.035382438 0.033804296 0.032173206 0.030497994 0.028787482 0.027050497 0.025295862 0.023532402 0.021768943 0.020014308 0.018277323 0.016566811 0.014891598 0.013260509 0.011682367 0.010165998 0.008720226 0.007353876 0.006075772 0.00489474 0.003819603 0.002859187 0.002022316 0.001317815 0.000754508 0.00034122 8.67757E-05 0

0.057313548 0.056407377 0.055428274 0.054380198 0.053267106 0.052092955 0.050861704 0.049577309 0.048243728 0.046864918 0.045444838 0.043987444 0.042496694 0.040976545 0.039430955 0.037863882 0.036279283 0.034681115 0.033073337 0.031459904 0.029844776 0.028231909 0.026625261 0.025028789 0.023446452 0.021882205 0.020340008 0.018823817 0.01733759 0.015885284 0.014470857 0.013098266 0.01177147 0.010494424 0.009271088 0.008105417 0.007001371 0.005962906 0.00499398 0.00409855 0.003280573 0.002544009 0.001892812 0.001330943 0.000862357 0.000491012 0.000220866 5.5876E-05 0

0.007216834 0.007187949 0.007147608 0.007095908 0.007032973 0.006958957 0.006874041 0.006778433 0.006672369 0.006556113 0.006429958 0.006294223 0.006149255 0.00599543 0.005833151 0.00566285 0.005484984 0.00530004 0.005108532 0.004911003 0.004708023 0.004500189 0.004288127 0.004072491 0.00385396 0.003633245 0.003411082 0.003188235 0.002965497 0.002743688 0.002523657 0.002306278 0.002092455 0.00188312 0.001679231 0.001481777 0.001291771 0.001110255 0.000938302 0.000777008 0.000627499 0.00049093 0.000368482 0.000261363 0.000170813 9.80942E-05 4.4501E-05 1.13535E-05 0

0.111458699 0.110899941 0.110181344 0.109303875 0.108268528 0.107076325 0.105728314 0.104225575 0.102569211 0.100760356 0.098800171 0.096689843 0.094430591 0.092023657 0.089470313 0.086771934 0.083934332 0.080970188 0.077892798 0.074715487 0.071451606 0.068114536 0.064717685 0.061274486 0.057798405 0.054302932 0.050801586 0.047307914 0.043835489 0.040397915 0.037008822 0.033681867 0.030430736 0.027269142 0.024210828 0.021269561 0.018459139 0.015793387 0.013286157 0.01095133 0.008802812 0.006854542 0.005120481 0.003614622 0.002350984 0.001343614 0.000606587 0.000154005 0

172.3 175.6 178.9 182.2 185.5 188.8 192.1 195.4 198.8 202.1 205.4 208.7 212.0 215.3 218.6 221.9 225.3 228.6 231.9 235.2 238.5 241.8 245.1 248.4 251.8 255.1 258.4 261.7 265.0 268.3 271.6 274.9 278.3 281.6 284.9 288.2 291.5 294.8 298.1 301.4 304.8 308.1 311.4 314.7 318.0 321.3 324.6 327.9 331.3

3.3.2.2b 2-Point Deflection Calculations

0.067248241 0.067787475 0.068218589 0.068537155 0.068738749 0.068818944 0.068773314 0.068597433 0.068286876 0.067837215 0.067244025 0.066502881 0.065609356 0.064559023 0.063347458 0.06197034 0.06042967 0.058737251 0.05690573 0.054947751 0.052875961 0.050703005 0.048441529 0.046104179 0.0437036 0.041252439 0.03876334 0.03624895 0.033721914 0.031194878 0.028680488 0.026191389 0.023740227 0.021339649 0.019002298 0.016740823 0.014567867 0.012496077 0.010538098 0.008706577 0.007014158 0.005473488 0.004097213 0.002897977 0.001888427 0.001081209 0.000488968 0.00012435 0

0.08114172 0.07985881 0.07847264 0.07698883 0.07541297 0.07375066 0.07200751 0.07018913 0.06830111 0.06634906 0.06433858 0.06227527 0.06016474 0.05801259 0.05582442 0.05360583 0.05136244 0.04909983 0.04682361 0.0445394 0.04225278 0.03996936 0.03769474 0.03543454 0.03319434 0.03097976 0.02879639 0.02664984 0.02454571 0.02248961 0.02048713 0.01854389 0.01666547 0.01485749 0.01312555 0.01147525 0.0099122 0.00844199 0.00707023 0.00580253 0.00464448 0.00360168 0.00267975 0.00188428 0.00122088 0.00069515 0.00031269 7.9107E-05 0

0.148389962 0.147646283 0.14669123 0.145525982 0.144151715 0.142569604 0.140780829 0.138786564 0.136587988 0.134186276 0.131582606 0.128778154 0.125774098 0.122571613 0.119171878 0.115576174 0.111792106 0.10783708 0.103729344 0.099487146 0.095128736 0.090672362 0.086136273 0.081538716 0.076897941 0.072232196 0.067559729 0.06289879 0.058267626 0.053684486 0.04916762 0.044735274 0.040405699 0.036197142 0.032127851 0.028216076 0.024480066 0.020938067 0.01760833 0.014509103 0.011658634 0.009075171 0.006776964 0.004782261 0.00310931 0.001776359 0.000801659 0.000203456 0

C-74

3.3.2.2c 3-Point Deflection Calculations

Created by:

ADV/CJB

11/1/2011

Calculates deflection under precomposite loads and under superimposed dead and live loads using principles of superposition. Gives deflection at 100 points along the beam when subjected to three point loads. Input from Cantilever Worksheet

Maximum Deflection

Es Ieff

29000 1068

ksi in4

Is Self Weight Length Spacing

890 0.0046 331 83

in4 kip/in in in

Precomposite Postcomposite

0.06 in 0.13 in

Unfactored Loads from Cantilever Worksheet Precomposite 3.09 3.95 4.51

Joist 1 Joist 2 Joist 3

Post Composite 8.88 10.73 12.10

kips kips kips

a 248 165 83

b 83 165 248

Precomposite Deflection from: (in) 0.0 3.3 6.6 9.9 13.2 16.5 19.8 23.2 26.5 29.8 33.1 36.4 39.7 43.0 46.3 49.6 52.9 56.2 59.5 62.8 66.2 69.5 72.8 76.1 79.4 82.7 86.0 89.3 92.6 95.9 99.2 102.5 105.9 109.2 112.5 115.8 119.1 122.4 125.7 129.0 132.3 135.6 138.9 142.2 145.5 148.9 152.2 155.5 158.8 162.1 165.4 168.7 172.0 175.3 178.6 181.9 185.2 188.5 191.9

C-75

in in in

a and b from AISC Manual

Post Composite Deflection from:

Joist 1 Joist 2 Joist 3 Self Weight Total (in) (in) (in) (in) (in) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.00E-05 3.42E-05 4.36E-05 8.68E-06 9.65E-05 3.97E-05 1.35E-04 1.71E-04 3.40E-05 3.79E-04 8.83E-05 2.99E-04 3.76E-04 7.50E-05 8.39E-04 1.55E-04 5.24E-04 6.55E-04 1.31E-04 1.46E-03 2.40E-04 8.08E-04 1.00E-03 2.00E-04 2.25E-03 3.41E-04 1.15E-03 1.41E-03 2.82E-04 3.18E-03 4.59E-04 1.54E-03 1.87E-03 3.75E-04 4.25E-03 5.92E-04 1.98E-03 2.39E-03 4.80E-04 5.44E-03 7.40E-04 2.47E-03 2.95E-03 5.94E-04 6.76E-03 9.03E-04 3.00E-03 3.56E-03 7.18E-04 8.18E-03 1.08E-03 3.57E-03 4.20E-03 8.49E-04 9.70E-03 1.27E-03 4.19E-03 4.87E-03 9.88E-04 1.13E-02 1.47E-03 4.84E-03 5.56E-03 1.13E-03 1.30E-02 1.68E-03 5.52E-03 6.28E-03 1.28E-03 1.48E-02 1.90E-03 6.23E-03 7.00E-03 1.44E-03 1.66E-02 2.14E-03 6.97E-03 7.74E-03 1.60E-03 1.85E-02 2.38E-03 7.74E-03 8.48E-03 1.76E-03 2.04E-02 2.63E-03 8.52E-03 9.22E-03 1.93E-03 2.23E-02 2.89E-03 9.33E-03 9.95E-03 2.10E-03 2.43E-02 3.16E-03 1.02E-02 1.07E-02 2.27E-03 2.63E-02 3.43E-03 1.10E-02 1.14E-02 2.44E-03 2.82E-02 3.71E-03 1.18E-02 1.21E-02 2.61E-03 3.02E-02 4.00E-03 1.27E-02 1.27E-02 2.78E-03 3.22E-02 4.29E-03 1.36E-02 1.33E-02 2.95E-03 3.41E-02 4.58E-03 1.44E-02 1.39E-02 3.11E-03 3.60E-02 4.88E-03 1.53E-02 1.44E-02 3.28E-03 3.79E-02 5.18E-03 1.62E-02 1.49E-02 3.44E-03 3.97E-02 5.48E-03 1.70E-02 1.54E-02 3.60E-03 4.15E-02 5.79E-03 1.79E-02 1.58E-02 3.76E-03 4.32E-02 6.09E-03 1.87E-02 1.61E-02 3.91E-03 4.48E-02 6.40E-03 1.95E-02 1.65E-02 4.05E-03 4.64E-02 6.70E-03 2.03E-02 1.68E-02 4.19E-03 4.80E-02 7.00E-03 2.11E-02 1.70E-02 4.33E-03 4.95E-02 7.30E-03 2.19E-02 1.72E-02 4.46E-03 5.09E-02 7.60E-03 2.26E-02 1.74E-02 4.58E-03 5.22E-02 7.90E-03 2.33E-02 1.75E-02 4.70E-03 5.35E-02 8.19E-03 2.40E-02 1.77E-02 4.81E-03 5.47E-02 8.47E-03 2.47E-02 1.77E-02 4.92E-03 5.58E-02 8.75E-03 2.53E-02 1.78E-02 5.01E-03 5.68E-02 9.03E-03 2.58E-02 1.78E-02 5.10E-03 5.78E-02 9.29E-03 2.64E-02 1.78E-02 5.18E-03 5.86E-02 9.55E-03 2.69E-02 1.77E-02 5.26E-03 5.94E-02 9.80E-03 2.73E-02 1.77E-02 5.32E-03 6.01E-02 1.00E-02 2.77E-02 1.76E-02 5.38E-03 6.07E-02 1.03E-02 2.80E-02 1.74E-02 5.43E-03 6.12E-02 1.05E-02 2.83E-02 1.73E-02 5.47E-03 6.16E-02 1.07E-02 2.85E-02 1.71E-02 5.50E-03 6.19E-02 1.09E-02 2.87E-02 1.69E-02 5.52E-03 6.21E-02 1.11E-02 2.88E-02 1.67E-02 5.53E-03 6.22E-02 1.13E-02 2.88E-02 1.65E-02 5.54E-03 6.21E-02 1.14E-02 2.88E-02 1.62E-02 5.53E-03 6.20E-02 1.16E-02 2.87E-02 1.59E-02 5.52E-03 6.18E-02 1.17E-02 2.85E-02 1.56E-02 5.50E-03 6.14E-02 1.18E-02 2.83E-02 1.53E-02 5.47E-03 6.10E-02 1.19E-02 2.80E-02 1.50E-02 5.43E-03 6.04E-02 1.20E-02 2.77E-02 1.47E-02 5.38E-03 5.98E-02 1.21E-02 2.73E-02 1.43E-02 5.32E-03 5.90E-02 1.21E-02 2.69E-02 1.39E-02 5.26E-03 5.82E-02

(in) 0.0 3.3 6.6 9.9 13.2 16.5 19.8 23.2 26.5 29.8 33.1 36.4 39.7 43.0 46.3 49.6 52.9 56.2 59.5 62.8 66.2 69.5 72.8 76.1 79.4 82.7 86.0 89.3 92.6 95.9 99.2 102.5 105.9 109.2 112.5 115.8 119.1 122.4 125.7 129.0 132.3 135.6 138.9 142.2 145.5 148.9 152.2 155.5 158.8 162.1 165.4 168.7 172.0 175.3 178.6 181.9 185.2 188.5 191.9

3.3.2.2c 3-Point Deflection Calculations

Joist 1 Joist 2 Joist 3 Total (in) (in) (in) (in) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.41E-05 7.73E-05 9.74E-05 1.99E-04 9.52E-05 3.05E-04 3.82E-04 7.82E-04 2.12E-04 6.77E-04 8.41E-04 1.73E-03 3.72E-04 1.19E-03 1.46E-03 3.02E-03 5.74E-04 1.83E-03 2.24E-03 4.64E-03 8.18E-04 2.60E-03 3.15E-03 6.56E-03 1.10E-03 3.48E-03 4.19E-03 8.77E-03 1.42E-03 4.48E-03 5.34E-03 1.12E-02 1.77E-03 5.59E-03 6.60E-03 1.40E-02 2.16E-03 6.79E-03 7.95E-03 1.69E-02 2.58E-03 8.09E-03 9.38E-03 2.01E-02 3.04E-03 9.48E-03 1.09E-02 2.34E-02 3.52E-03 1.10E-02 1.24E-02 2.69E-02 4.03E-03 1.25E-02 1.40E-02 3.06E-02 4.56E-03 1.41E-02 1.57E-02 3.43E-02 5.12E-03 1.58E-02 1.73E-02 3.82E-02 5.70E-03 1.75E-02 1.90E-02 4.22E-02 6.31E-03 1.93E-02 2.06E-02 4.62E-02 6.93E-03 2.11E-02 2.23E-02 5.03E-02 7.57E-03 2.30E-02 2.39E-02 5.44E-02 8.23E-03 2.49E-02 2.54E-02 5.85E-02 8.90E-03 2.68E-02 2.69E-02 6.27E-02 9.58E-03 2.87E-02 2.84E-02 6.67E-02 1.03E-02 3.07E-02 2.98E-02 7.08E-02 1.10E-02 3.27E-02 3.11E-02 7.47E-02 1.17E-02 3.46E-02 3.23E-02 7.86E-02 1.24E-02 3.66E-02 3.34E-02 8.23E-02 1.31E-02 3.85E-02 3.44E-02 8.60E-02 1.39E-02 4.04E-02 3.53E-02 8.96E-02 1.46E-02 4.23E-02 3.61E-02 9.30E-02 1.53E-02 4.42E-02 3.68E-02 9.63E-02 1.61E-02 4.60E-02 3.75E-02 9.95E-02 1.68E-02 4.78E-02 3.80E-02 1.03E-01 1.75E-02 4.95E-02 3.85E-02 1.06E-01 1.82E-02 5.12E-02 3.89E-02 1.08E-01 1.89E-02 5.28E-02 3.92E-02 1.11E-01 1.96E-02 5.44E-02 3.95E-02 1.13E-01 2.03E-02 5.58E-02 3.96E-02 1.16E-01 2.10E-02 5.72E-02 3.97E-02 1.18E-01 2.16E-02 5.85E-02 3.98E-02 1.20E-01 2.23E-02 5.97E-02 3.97E-02 1.22E-01 2.29E-02 6.08E-02 3.96E-02 1.23E-01 2.35E-02 6.18E-02 3.95E-02 1.25E-01 2.41E-02 6.27E-02 3.93E-02 1.26E-01 2.46E-02 6.35E-02 3.90E-02 1.27E-01 2.52E-02 6.41E-02 3.87E-02 1.28E-01 2.57E-02 6.46E-02 3.83E-02 1.29E-01 2.62E-02 6.50E-02 3.78E-02 1.29E-01 2.66E-02 6.52E-02 3.73E-02 1.29E-01 2.70E-02 6.53E-02 3.68E-02 1.29E-01 2.74E-02 6.52E-02 3.62E-02 1.29E-01 2.78E-02 6.50E-02 3.56E-02 1.28E-01 2.81E-02 6.46E-02 3.50E-02 1.28E-01 2.84E-02 6.41E-02 3.43E-02 1.27E-01 2.86E-02 6.35E-02 3.36E-02 1.26E-01 2.88E-02 6.27E-02 3.28E-02 1.24E-01 2.90E-02 6.18E-02 3.20E-02 1.23E-01 2.91E-02 6.08E-02 3.12E-02 1.21E-01

Precomposite Deflection from: (in) 195.2 198.5 201.8 205.1 208.4 211.7 215.0 218.3 221.6 224.9 228.2 231.5 234.9 238.2 241.5 244.8 248.1 251.4 254.7 258.0 261.3 264.6 267.9 271.2 274.5 277.9 281.2 284.5 287.8 291.1 294.4 297.7 301.0 304.3 307.6 310.9 314.2 317.6 320.9 324.2 327.5 330.8

Post Composite Deflection from:

Joist 1 Joist 2 Joist 3 Self Weight Total (in) (in) (in) (in) (in) 1.22E-02 2.64E-02 1.36E-02 5.18E-03 5.73E-02 1.22E-02 2.58E-02 1.32E-02 5.10E-03 5.63E-02 1.22E-02 2.53E-02 1.28E-02 5.01E-03 5.52E-02 1.21E-02 2.47E-02 1.24E-02 4.92E-03 5.41E-02 1.21E-02 2.40E-02 1.20E-02 4.81E-03 5.29E-02 1.20E-02 2.33E-02 1.15E-02 4.70E-03 5.16E-02 1.19E-02 2.26E-02 1.11E-02 4.58E-03 5.02E-02 1.18E-02 2.19E-02 1.07E-02 4.46E-03 4.88E-02 1.16E-02 2.11E-02 1.02E-02 4.33E-03 4.73E-02 1.15E-02 2.03E-02 9.78E-03 4.19E-03 4.58E-02 1.13E-02 1.95E-02 9.34E-03 4.05E-03 4.42E-02 1.11E-02 1.87E-02 8.89E-03 3.91E-03 4.26E-02 1.08E-02 1.79E-02 8.45E-03 3.76E-03 4.09E-02 1.05E-02 1.70E-02 8.01E-03 3.60E-03 3.91E-02 1.02E-02 1.62E-02 7.56E-03 3.44E-03 3.74E-02 9.89E-03 1.53E-02 7.13E-03 3.28E-03 3.56E-02 9.52E-03 1.44E-02 6.69E-03 3.11E-03 3.37E-02 9.12E-03 1.36E-02 6.26E-03 2.95E-03 3.19E-02 8.70E-03 1.27E-02 5.84E-03 2.78E-03 3.00E-02 8.26E-03 1.18E-02 5.42E-03 2.61E-03 2.81E-02 7.79E-03 1.10E-02 5.01E-03 2.44E-03 2.62E-02 7.31E-03 1.02E-02 4.61E-03 2.27E-03 2.43E-02 6.82E-03 9.33E-03 4.22E-03 2.10E-03 2.25E-02 6.32E-03 8.52E-03 3.84E-03 1.93E-03 2.06E-02 5.81E-03 7.74E-03 3.47E-03 1.76E-03 1.88E-02 5.30E-03 6.97E-03 3.12E-03 1.60E-03 1.70E-02 4.80E-03 6.23E-03 2.78E-03 1.44E-03 1.52E-02 4.30E-03 5.52E-03 2.45E-03 1.28E-03 1.36E-02 3.81E-03 4.84E-03 2.14E-03 1.13E-03 1.19E-02 3.33E-03 4.19E-03 1.85E-03 9.88E-04 1.04E-02 2.88E-03 3.57E-03 1.57E-03 8.49E-04 8.87E-03 2.44E-03 3.00E-03 1.32E-03 7.18E-04 7.47E-03 2.02E-03 2.47E-03 1.08E-03 5.94E-04 6.17E-03 1.64E-03 1.98E-03 8.64E-04 4.80E-04 4.96E-03 1.28E-03 1.54E-03 6.70E-04 3.75E-04 3.87E-03 9.65E-04 1.15E-03 4.98E-04 2.82E-04 2.89E-03 6.85E-04 8.08E-04 3.50E-04 2.00E-04 2.04E-03 4.48E-04 5.24E-04 2.27E-04 1.31E-04 1.33E-03 2.58E-04 2.99E-04 1.29E-04 7.50E-05 7.61E-04 1.17E-04 1.35E-04 5.80E-05 3.40E-05 3.44E-04 2.99E-05 3.42E-05 1.47E-05 8.68E-06 8.74E-05 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

(in) 195.2 198.5 201.8 205.1 208.4 211.7 215.0 218.3 221.6 224.9 228.2 231.5 234.9 238.2 241.5 244.8 248.1 251.4 254.7 258.0 261.3 264.6 267.9 271.2 274.5 277.9 281.2 284.5 287.8 291.1 294.4 297.7 301.0 304.3 307.6 310.9 314.2 317.6 320.9 324.2 327.5 330.8

3.3.2.2c 3-Point Deflection Calculations

Joist 1 Joist 2 Joist 3 Total (in) (in) (in) (in) 2.92E-02 5.97E-02 3.03E-02 1.19E-01 2.92E-02 5.85E-02 2.95E-02 1.17E-01 2.92E-02 5.72E-02 2.86E-02 1.15E-01 2.91E-02 5.58E-02 2.76E-02 1.13E-01 2.90E-02 5.44E-02 2.67E-02 1.10E-01 2.88E-02 5.28E-02 2.58E-02 1.07E-01 2.86E-02 5.12E-02 2.48E-02 1.05E-01 2.83E-02 4.95E-02 2.38E-02 1.02E-01 2.79E-02 4.78E-02 2.29E-02 9.86E-02 2.75E-02 4.60E-02 2.19E-02 9.54E-02 2.70E-02 4.42E-02 2.09E-02 9.21E-02 2.65E-02 4.23E-02 1.99E-02 8.87E-02 2.59E-02 4.04E-02 1.89E-02 8.52E-02 2.52E-02 3.85E-02 1.79E-02 8.16E-02 2.45E-02 3.66E-02 1.69E-02 7.80E-02 2.37E-02 3.46E-02 1.59E-02 7.42E-02 2.28E-02 3.27E-02 1.50E-02 7.04E-02 2.19E-02 3.07E-02 1.40E-02 6.66E-02 2.09E-02 2.87E-02 1.30E-02 6.26E-02 1.98E-02 2.68E-02 1.21E-02 5.87E-02 1.87E-02 2.49E-02 1.12E-02 5.48E-02 1.75E-02 2.30E-02 1.03E-02 5.08E-02 1.63E-02 2.11E-02 9.44E-03 4.69E-02 1.51E-02 1.93E-02 8.59E-03 4.30E-02 1.39E-02 1.75E-02 7.77E-03 3.92E-02 1.27E-02 1.58E-02 6.97E-03 3.55E-02 1.15E-02 1.41E-02 6.21E-03 3.18E-02 1.03E-02 1.25E-02 5.48E-03 2.83E-02 9.13E-03 1.10E-02 4.79E-03 2.49E-02 7.99E-03 9.48E-03 4.14E-03 2.16E-02 6.89E-03 8.09E-03 3.52E-03 1.85E-02 5.84E-03 6.79E-03 2.95E-03 1.56E-02 4.85E-03 5.59E-03 2.42E-03 1.29E-02 3.92E-03 4.48E-03 1.93E-03 1.03E-02 3.08E-03 3.48E-03 1.50E-03 8.06E-03 2.31E-03 2.60E-03 1.11E-03 6.02E-03 1.64E-03 1.83E-03 7.82E-04 4.25E-03 1.07E-03 1.19E-03 5.07E-04 2.77E-03 6.18E-04 6.77E-04 2.88E-04 1.58E-03 2.80E-04 3.05E-04 1.30E-04 7.15E-04 7.15E-05 7.73E-05 3.28E-05 1.82E-04 0.00E+00 0.00E+00 0.00E+00 0.00E+00

C-76

3.3.2.3 Rotated Radial Girder Beam Design

Created by:

DBL

4/30/2012

Calculation shown for Bank 3-4 Mechanical Floor - Top Girders Design of the radial girders at mechanical floor, which must bend about their weak axis. Girders oriented about their weak axis enable the gusset plate connections for outriggers.

Geometry and Applied Loads L1

Length of Shorter Joist

234

in

From Drawing

L2 L l TA1 TA2

276 300 100 21,963 27,792

in in in in2 in2

From Drawing

DL DL LL LL αDL

170 0.00118 100 0.00069 1.2

psf ksi psf ksi

αLL DLLTotal

1.6 0.00253

ksi

= αDL*DL + αLL*LL

P1 P2

28.0

kips

= (TA1*DLLTotal+αDL*Dsw1*L1)/2

35.4

kips

= (TA2*DLLTotal+αDL*Dsw2*L2)/2

Reaction at Support 1

R1

30.5

kips

= (P1 *(l-a)+P2*b)/l

Reaction at Support 2

R2

33.0

kips

= (P1 *a+P2*(l-b))/l

Shear Force in Section A

VA

39.6

kips

= (P1 *(l-a)+P2*b)/l

Shear Force in Section B

VB

2.5

kips

= R1-P1

Shear Force in Section C

VC

23.8

kips

= (P1 *a+P2*(l-b))/l

Moment at x=l

M1

3,657

kip-in

= R1*l

Moment at x=2l

M2

3,904

kip-in

= R1*l - P1(2*l-a)

Mmaxf

3,904

kip-in

= MAX(M1, M2)

Length of Longer Joist Length of Girder Unbraced Length of Girder Tributary Area of Shorter Joist Tributary Area of Longer Joist Applied Dead Load Applied Dead Load Applied Live Load Applied Live Load Dead Load Factor Live Load Factor

Total Factored Load Total Factored Load

From Drawing = L/3 From Drawing From Drawing

Reactions, Internal Forces, Moments

Maximum Bending Moment

C-77

3.3.2.3 Rotated Radial Girder Beam Design

Steel Strength Fy Φ ΦFy

Nominal Steel Strength Steel Reduction Factor Factored Steel Strength

50 0.9 45

ksi ksi

Selected Section and Checks Chosen Section for Joist 1

Wsection

Beam Self Weight Density

ρsw1

0.022

Sx

25.4

Section Modulus

W12 x 22

Chosen Section for Joist 2

Wsection

Beam Self Weight Density

ρsw2

0.022

Sy

25.4

Section Modulus Chosen Section for Girder Section Modulus Allowable Deflection

W12 x 22 kip/ft in3

Wsection W14 x 730

Beam Self Weight Density Max Deflection

kip/ft in3

ρsw

0.730

Sy

527

kip/ft in3

Δmax

0.229

in

MASTAN Analysis, attached

Δallowable

0.975

in

= L/240

= bf*tf ; AISC2005 G7 (for weak axis)

Δmax < Δallowable? Checks from moment, shear, and deflection

Yes Yes

Section Properties Area of Web Beam depth Web width

Adw d tw

87.89 22.4 3.07

in2

Web Height

h0

17.5

in

Flange Width

bf

17.9

in

Flange Thickness

tf

4.91

Moment of Inertia (Strong)

Ix

14,300

in in4

Moment of Inertia (Weak)

Iy

4,720

in4

Section Modulus (Strong)

Sx

1,280

in

Section Modulus (Weak)

Sy

527

in3

Radius of Gyration (Strong)

rx

8.17

in

Radius of Gyration (Weak)

ry

4.69

Plastic Section Modulus (Strong)

Zx

1,660

in in3

Plastic Section Modulus (Weak)

Zy

816

in3

Radius of Gyration (Torsion)

rts

5.68

J

1,450

in in4

Polar Moment of Inertia

in in

3

= ((I yh0)/(2Sx))

3.3.2.3 Rotated Radial Girder Beam Design

1/2

C-78

C-79

Created by:

DBL

4/30/2012

Disp y =

0.2991

in

3.3.2.3 Rotated Radial Girder Beam Design

The radial grder was modeled in MASTAN as a fixed-fixed beam with two point loads in order to find the maximum deflection at the center of the beam.

Mastan Analysis for Rotated Radial Girder

C-80

Created by:

CJB / ADV

0.26 5.03 35.3 245 26

d tf tw bf Sx Ix

Overall Depth Flange Thickness

Web Thickness

Flange Width

Steel Section Modulus

Moment of Inertia Weight

718 54.4

Icomp Str

Composite Moment of Inertia

Section Modulus for Tension 153

4.70

yt

Sc

13.20

yb

N.A. to bottom of beam

N.A. to top of beam

Section Modulus for Comp.

61 124 61

(a) (b) beff

Span/4 Beam Spacing Effective Flange Width

Composite Beam Properties

13.9 0.42

As

W 14 x 26 7.69

(80) 6 2 100%

2 Residential Circumferential Girder Bank 2 14 x 26 #N/A

Section Type Area of Steel

Steel Shape Properties

Shear Stud Shear Stud Spacing Studs Per Rib % Composite Action

W-Shape Overall Check, Acceptable?

Beam:

Bank: Type:

= Ic / yb = Ic / yt

in3

= MIN(a,b)

#N/A

in3

in in4

in

in in in

plf

in4

in in3

in

in in

in2

Fails in:

Yes No

211 10.3

20.4

SDL LL

Postcomposite

Precomposite

LL Total

SDL

DL LL Total

Joist End Reactions

Postcomposite

Construction LL

Beam Self Weight

Precomposite Slab and Decking

psf psf

psf

plf

9.26 13.56

4.30

kips kips

kips

Factored 4.49 kips 3.37 kips 7.86 kips

40.8 88

32

31.2

39.6

psf

psf psf

34 55

2

psf plf psf

ft ft

ft

33 26 20

Factored Loading Conditions

Precomposite Slab and Decking Beam Self Weight Construction LL Postcomposite SDL LL

Unfactored Loading Conditions

Beam Tributary Area Beam Spacing

Beam Span

Inputs from Bank Information

3.3.2.4 Circumferential Girder Design

Calc/Lookup Passes Check Fails Check

User Input Constant/Prev Calc.

11/1/2011

from Load Summary

from Slab & Deck Info

from Tower Geometry

Design tool to calculate the W-Shape and Shear stud configuration for circumferential girders in all banks and floor types with a predetermined decking type running perpendicular to the girder. The design method follows that found in Taranath's Steel, Concrete, & Composite Design of Tall Buildings .

3.3.2.4 Circumferential Girder Design

C-81

Moment Calculation

33.5

Smin

Min. Req. Section Modulus

54.4 40.1 69.2

Mpre

Mpost

Section Modulus for Tension

Pre-Comosite Moment

Post-Composite Moment

YES 24.1 33.0 YES 69 0.494

fb,2

0.66*Fy

fb,1 < 0.66*Fy?

Mcomp

f'c-comp

Composite Moment

Concrete compressive stress

Condition 2:

YES

1.8

45.0

0.45*f'c-comp f'c < 0.45*f'c-comp ?

28.9

fb,1

Condition 1:

0.9*Fy fb,1 < 0.9*Fy?

Allowable Stress

35.3

Ss Str

Steel Section Modulus

Stress Check

92

Mu

770 1,328 1,768

Max. Moment (at center)

Factored Precomposite load Factored Postcomposite load Total Load (w/o construction LL)

3

3

ksi

ksi

kip-ft

ksi

ksi

ksi

ksi

kip-ft

kip-ft

in

in

kip-ft 3 in

plf plf plf

= Mcomp/(n*St)

Concrete Properties

Slab and Decking Properties

Total Composite Depth

Rib Height

Slab thickness

Vulcraft Decking Type

B

T

C P

td

n

17.9

1.75

3.5

1.5 36 6

2.5

1.5VL22

11

2,574

Ec

Elastic Modulus Modular Ratio

115

4,000

ρc

Concrete Strength Density of concrete

Lightweight f'c

Concrete Type

29,000

65

Fu Es

Ultimate Strength Elastic Modulus

50

Fy

in

in

in

in in in

in

ksi

pcf

psi

ksi

ksi

ksi

CJB / ADV

Yield Strength

Steel Properties

3.3.2.4 Circumferential Girder Design

= (Mpre+ Mpost)/Str

= Mpre / Ss + Mpost/Str

= Mmax/(0.66*Fy)

2

= w*l /8

Created by:

= td+ts+d

= Es/Ec

0.5

= 33*ρc*f'c

11/1/2011

C-82

m Vn V < Vn ?

nribs

V

#N/A

#N/A

10

384.5 40

0.00

Δcamber

Precomposite loads Precomposite Deflection

Postcomposite loads Final Deflection Allowable Deflection OK?

L/360

0.172 0.681 YES

0.315

Δpre

Steel Moment of Inertia

Δpost

245.0

Ix

Camber

718.3

Ieff

Deflection & Camber

Effective Moment of Inertia

3

3

3

kips

ft

kips

in kips

in in

in

in

in4

in4

* total capacity = sum of nominal shear strengths between the point of maximum positive moment and the point of zero moment

Total Capacity*

Total Shear Load Number of Ribs Distance from M0 to Mmax

N/A 100% YES

V'h

Adjusted Horizontal Shear % Composite Action % Composite Action > 25% ?

54.43 33.49

in

Smin

in

33.49

Min. Req. Section Modulus

Shear connectors, partial composite action Ss Steel Section Modulus Stens Section Modulus for Tension

kips kips kips

2

# of Studs

# of Ribs studs / rib Stud capacity

Concrete Cover ≥ 1/2"

Post Composite

nribs Vstud

918

573

Service Loads (Unfactored) Pre Composite

3.3.2.4 Circumferential Girder Design

= 5*W*L4/(384*E*I)

= 5*W*L4/(384*E*I)

= Ix + (Ic - Ix )*(V'h/Vh)2

Shear Stud Spacing ≤ 18"

= ΣQn = (studs/rib)*Vstud*nribs*m/l ; AISC I3-1c Slab Thickness ≥ 2"

= V'h

Stud Checks from AISC I3.2c.1: Nominal Rib height ≤ 3" Shear Stud Diamater ≤ 3/4" Shear Stud Length ≥ 1 1/2"

= Vh*(Smin - Ss / Savail - Ss) = N/A if 100% composite action

= MIN(i, ii)

= 0.85*f'c* Ac = As*Fy

Shear Stud Properties 521 384.5 385

Diameter Length Spacing

(i) (ii) Vh

Horizontal Shear Vh

Option 1 Option 2 Horizontal Shear

Created by:

plf

plf

YES

YES

YES

YES YES YES

80

40 2 #N/A

0.75 3.00 6

I3.2c.1.d

I3.2c.1.c

I3.2c.1.b

I3.2c.1.b

I3.2c.1.a I3.2c.1.b

in in in

CJB / ADV

=Qn per rib; AISC Table 3-21

11/1/2011

C-83

Created by:

CJB / ADV

2

in

has one angled girder at midpoint, long

Precomposite Postcomposite Total

Radial Girder Moments

0.81 13 491 6260 192

tw bf Sx Ix

Web Thickness

Steel Section Modulus

Moment of Inertia Weight

DLP1 LLP1

Midpoint Dead Load

Midpoint Live Load

Distance to Point Load 1

11.04

= MIN(a,b)

= Ic / yt

in3

kips

30.20

Postcomposite 14.08

length / 2

= Ic / yb

in3

in in4

in

in in in

kips

Precomposite

kips kips

kips kips

kips

kips

kips

kips

kip-ft kip-ft kip-ft

ft ft

2

ft 2 ft ft

55 psf

Construction Load

Slab and decking Beam Self Weight

32 psf

38.136 kips 230.4 plf

34 psf

SDL

192 plf 20 psf

103.32 plf

31.78 psf

7.03 15.17

12.56 0.32

15.1

7.04

5.52

8.23

110.3 482.2 553.5

160.9 31.8

19.33 172.4 48.3

Live Load

Factored Loading Conditions

3.3.2.5a Cantilever Design Tool

kips

HSS Self Weight

DL

SDL LL

Cantilever Beam Self Weight LL Postcomposite

Precomposite

Unfactored Loading Conditions

Postcomposite

Precomposite

LL

SDL

LL

DL LL from Construction

Point Load 2 (factored)

plf

Postcomposite

in4

in

3

in

in

in in

9.66 ft Precomposite 16.46 kips

639.53

Sc

Section Modulus for Comp.

a

562.93

Str

Section Modulus for Tension

Factored Moment calculation

8832.14

13.81

yt

N.A. to top of beam Icomp

15.69

yb

N.A. to bottom of beam

Composite Moment of Inertia

57.98 N/A 57.98

(a) (b) beff

Span/4 Beam Spacing Effective Flange Width

Composite Beam Properties

Flange Width

25.5 1.46

d tf

Overall Depth Flange Thickness

56.3

As

Area of Steel

DL

HSS 2 Tributary Area: HSS 2 Length:

Precomposite

Angled girder applies a point load at the midspan of the cantilever. The façade applies an additional point load at the end.

Fails Check

Cantilever Beam Span: HSS 1 Tributary Area: HSS 1 Length:

Input from Bank Information

Point Load 1 (factored) W 24 x 192

No

Yes

User Input Constant/Prev Calc. Calc/Lookup Passes Check

Section Type

0.00 (29) 8 100%

24 x 192 YES

3 Residential Cantilever Long Bank 3

Selected Shape's Properties

Camber Shear Stud Shear Stud Spacing % Composite Action

W-Shape Overall Check, Acceptable?

Bank: Type: Beam:

Construction

Decking and slab

SDL over HSS Trib. Areas LL over HSS Trib. Areas

HSS Self Weight + DL (decking,slab) 200 lbs load at end point

HSS and Facade Reaction

LL over girder trib area

SDL over girder trib area

20 psf Construction LL

Girder Self Weight + DL(decking,slab)

Angled Girder Reactions

from Tower Geometry

Design tool to calculate the W-Shape and Shear stud configuration for cantilevers in all banks and floor types with a predetermined decking type running parallel to the cantilever. Loads are applied as point loads from the angled girders and the HSS beams. A separate spreadsheet calculates pre- and post-composite deflection

3.3.2.5a Cantilever Design Tool

11/1/2011

C-84

0.32

LLtot

Total Factored LL Moment from Dead Load Moment from Live Load Reaction Total Moment Total Moment w/ Radial Girder Continuity

557.6

Mpre Mpost

YES 31.1 33.0

fb,1 < 0.9*Fy? fb,2

0.66*Fy fb,1 < 0.66*Fy?

N/A 100% YES

314.62

Smin

Min. Req. Section Modulus V'h

562.93

Stens

Section Modulus for Tension

Adjusted Horizontal Shear % Composite Action % Composite Action > 25% ?

491

Ss

Shear connectors, partial composite action Steel Section Modulus

493 2815 493

900 1.535 1.8 YES

(i) (ii) Vh

Mcomp f'c-comp 0.45*f'c-comp f'c < 0.45*f'c-comp ?

45.0

0.9*Fy

YES

32.8

fb,1

Option 1 Option 2 Horizontal Shear

Horizontal Shear Vh

Composite Moment Concrete compressive stress

Condition 2:

Condition 1:

Allowable Stress

Post-Composite Moment

900.1

562.9

Str

Section Modulus for Tension

Pre-Comosite Moment

491

315

Smin

Ss

865

Mmax

104.4 865

Steel Section Modulus

Stress Check

Total Reaction Total Moment for Design

11.36 444.8 112.9 44.8 557.6 447.32

33.47

LLP2 Dltot

Endpoint Live Load

Total Factored DL

12.56

DLP2

Endpoint Dead Load

kips

in3

in3

in3

kips kips kips

kip-ft ksi ksi

ksi

ksi

ksi

ksi

kip-ft

kip-ft

in3

3

in

kip-ft 3 in

kips kip-ft

kips kip-ft kip-ft kips kip-ft kip-ft

kips

kips

kips

kips kip-ft kip-ft kips kip-ft kip-ft

kips

kips

kips

Postcomposite LL (Point)

SDL (Point)

Fy:

f'c Density

Shear Stud Properties

3.3.2.5a Cantilever Design Tool

Ec

Stud capacity

Diameter Length Spacing wr wr/h # of Studs

Modular ratio

Created by:

in in in in in

29000 ksi

65 ksi

50 ksi

1.75 in 29.5 in

1.5VL22 2.5 1.5 36 6 3.5

104.4 kips 865.2 kip-ft

88 kips

40.8 kips

in in in in

18.3 AISC Table 3-21

0.75 3 8 2.125 1.417 29

11

2574 ksi

115 pcf

4000 psi

TypeLightweight

Es:

Fu:

Concrete Modulus of Elascticity

Concrete Properties

Steel Properties

B Total Composite Depth

Decking Type Slab thickness Rib Height C P T

Slab and Decking Properties

Exterior Column Reaction Exterior Column Moment

Reactions and Moments

Includes beam self weight

midpoint, long cantilever has two

= Vh*(Smin - Ss / Savail - Ss)2 = N/A if 100% composite action

= MIN(i, ii)

= 0.85*f'c* Ac = As*Fy

= Mcomp/(n*St)

= (Mpre+ Mpost)/Str

= Mpre / Ss + Mpost/Str

Modulus for Tension

Steel Section

M / (0.66*Fy)

Does not include construction loads

45.37 315.0 585.0 70.9 900.1 417.88

25.57

15.17

7.03

CJB / ADV

11/1/2011

C-85 0.404 0.644 YES

Δpost

Postcomposite Defleciton L/360 OK?

0.00

Δcamber

Camber

8832 0.424

Ieff Δpre

in in

in

in

in4

kips kips

30.61 15.35

Precomposite Deflection

kips kips

kips ft

20.62 10.66

Effective Moment of Inertia

Pre Composite Unfactored Midpoint Load Unfactored Enpoint Load Post Composite Unfactored Midpoint Load Unfactored Enpoint Load

Deflection and Camber

530.7 YES

Vn

Total Capacity*

V < Vn ?

493 19

V m

Total Shear Load Distance from M0 to Mmax

Nominal Rib height ≤ 3" Shear Stud Diamater ≤ 3/4" Shear Stud Length ≥ 1 1/2" Concrete Cover ≥ 1/2" Slab Thickness ≥ 2" Shear Stud Spacing ≤ 18"

Stud Checks from AISC I3.2c.1:

3.3.2.5a Cantilever Design Tool

References Cantilever Deflection Spredsheet

References Cantilever Deflection Spredsheet

= Ix + (Ic - Ix )*(V'h/Vh)2

= ΣQn = (studs/rib)*Vstud*nribs*m/l ; AISC I3-1c

= V'h

YES YES YES YES YES YES

I3.2c.1.a I3.2c.1.b I3.2c.1.b I3.2c.1.b I3.2c.1.c I3.2c.1.d

Created by:

CJB / ADV

11/1/2011

3.3.2.5b Cantilever Deflection Tool

Created by: ADV/CJB

11/1/2011

Calculates deflection under precomposite loads and under superimposed dead and live loads using principles of superposition

Input from Cantilever Worksheet Es

29,000

Ieff

8,832

Is Self Weight Length Midpoint

6,260 0.0160 232 116

Maximum Deflection ksi in4

Precomposite

0.42 in

Postcomposite

0.40 in

in4 kip/in in in

Unfactored Loads from Cantilever Worksheet Midpoint Load Endpoint Load

Precomposite Post Composite 20.62 30.61 kips 10.66 15.35 kips

Precomposite Deflection from: (in) 0.0 2.3 4.6 7.0 9.3 11.6 13.9 16.2 18.6 20.9 23.2 25.5 27.8 30.1 32.5 34.8 37.1 39.4 41.7 44.1 46.4 48.7 51.0 53.3 55.7 58.0 60.3 62.6 64.9 67.3 69.6 71.9 74.2 76.5 78.8 81.2 83.5 85.8 88.1 90.4 92.8 95.1 97.4

Post Composite Deflection from:

Midpt Load Endpt Load Self Weight Total (in) (in) (in) (in) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.52E-05 3.65E-05 6.33E-06 7.80E-05 1.40E-04 1.46E-04 2.52E-05 3.10E-04 3.12E-04 3.26E-04 5.62E-05 6.95E-04 5.51E-04 5.78E-04 9.93E-05 1.23E-03 8.56E-04 9.01E-04 1.54E-04 1.91E-03 1.22E-03 1.29E-03 2.20E-04 2.74E-03 1.65E-03 1.75E-03 2.98E-04 3.71E-03 2.15E-03 2.28E-03 3.87E-04 4.81E-03 2.70E-03 2.88E-03 4.86E-04 6.06E-03 3.30E-03 3.54E-03 5.96E-04 7.44E-03 3.97E-03 4.27E-03 7.16E-04 8.96E-03 4.69E-03 5.06E-03 8.46E-04 1.06E-02 5.47E-03 5.92E-03 9.87E-04 1.24E-02 6.29E-03 6.85E-03 1.14E-03 1.43E-02 7.17E-03 7.83E-03 1.30E-03 1.63E-02 8.10E-03 8.88E-03 1.46E-03 1.84E-02 9.07E-03 9.99E-03 1.64E-03 2.07E-02 1.01E-02 1.12E-02 1.83E-03 2.31E-02 1.12E-02 1.24E-02 2.02E-03 2.56E-02 1.23E-02 1.37E-02 2.23E-03 2.82E-02 1.34E-02 1.50E-02 2.44E-03 3.09E-02 1.46E-02 1.64E-02 2.66E-03 3.37E-02 1.59E-02 1.79E-02 2.88E-03 3.66E-02 1.71E-02 1.94E-02 3.12E-03 3.97E-02 1.84E-02 2.10E-02 3.36E-03 4.28E-02 1.98E-02 2.26E-02 3.61E-03 4.60E-02 2.12E-02 2.43E-02 3.87E-03 4.93E-02 2.26E-02 2.60E-02 4.13E-03 5.27E-02 2.40E-02 2.78E-02 4.40E-03 5.63E-02 2.55E-02 2.97E-02 4.67E-03 5.98E-02 2.70E-02 3.16E-02 4.96E-03 6.35E-02 2.85E-02 3.35E-02 5.25E-03 6.73E-02 3.01E-02 3.55E-02 5.54E-03 7.11E-02 3.17E-02 3.75E-02 5.84E-03 7.50E-02 3.33E-02 3.96E-02 6.14E-03 7.90E-02 3.49E-02 4.18E-02 6.46E-03 8.31E-02 3.65E-02 4.40E-02 6.77E-03 8.73E-02 3.82E-02 4.62E-02 7.09E-03 9.15E-02 3.99E-02 4.85E-02 7.42E-03 9.58E-02 4.15E-02 5.08E-02 7.75E-03 1.00E-01 4.33E-02 5.32E-02 8.08E-03 1.05E-01 4.50E-02 5.56E-02 8.42E-03 1.09E-01

3.3.2.5b Cantilever Deflection Tool

(in) 0.0 2.3 4.6 7.0 9.3 11.6 13.9 16.2 18.6 20.9 23.2 25.5 27.8 30.1 32.5 34.8 37.1 39.4 41.7 44.1 46.4 48.7 51.0 53.3 55.7 58.0 60.3 62.6 64.9 67.3 69.6 71.9 74.2 76.5 78.8 81.2 83.5 85.8 88.1 90.4 92.8 95.1 97.4

Midpt Load (in) 0.00E+00 3.70E-05 1.47E-04 3.29E-04 5.80E-04 9.00E-04 1.29E-03 1.74E-03 2.26E-03 2.84E-03 3.48E-03 4.18E-03 4.94E-03 5.75E-03 6.62E-03 7.55E-03 8.52E-03 9.55E-03 1.06E-02 1.17E-02 1.29E-02 1.41E-02 1.54E-02 1.67E-02 1.80E-02 1.94E-02 2.08E-02 2.23E-02 2.38E-02 2.53E-02 2.68E-02 2.84E-02 3.00E-02 3.17E-02 3.33E-02 3.50E-02 3.67E-02 3.84E-02 4.02E-02 4.19E-02 4.37E-02 4.55E-02 4.73E-02

Endpt Load (in) 0.00E+00 3.72E-05 1.48E-04 3.33E-04 5.90E-04 9.18E-04 1.32E-03 1.79E-03 2.33E-03 2.94E-03 3.61E-03 4.36E-03 5.16E-03 6.04E-03 6.98E-03 7.99E-03 9.05E-03 1.02E-02 1.14E-02 1.26E-02 1.39E-02 1.53E-02 1.68E-02 1.82E-02 1.98E-02 2.14E-02 2.31E-02 2.48E-02 2.66E-02 2.84E-02 3.03E-02 3.22E-02 3.42E-02 3.62E-02 3.83E-02 4.04E-02 4.26E-02 4.48E-02 4.71E-02 4.94E-02 5.18E-02 5.42E-02 5.67E-02

Total (in) 0.00E+00 7.42E-05 2.96E-04 6.62E-04 1.17E-03 1.82E-03 2.61E-03 3.53E-03 4.58E-03 5.77E-03 7.09E-03 8.53E-03 1.01E-02 1.18E-02 1.36E-02 1.55E-02 1.76E-02 1.97E-02 2.20E-02 2.44E-02 2.69E-02 2.95E-02 3.21E-02 3.49E-02 3.78E-02 4.08E-02 4.39E-02 4.71E-02 5.03E-02 5.37E-02 5.71E-02 6.06E-02 6.42E-02 6.79E-02 7.16E-02 7.54E-02 7.93E-02 8.33E-02 8.73E-02 9.14E-02 9.55E-02 9.97E-02 1.04E-01

C-86

Precomposite Deflection from: (in) 99.7 102.0 104.4 106.7 109.0 111.3 113.6 116.0 118.3 120.6 122.9 125.2 127.5 129.9 132.2 134.5 136.8 139.1 141.5 143.8 146.1 148.4 150.7 153.1 155.4 157.7 160.0 162.3 164.7 167.0 169.3 171.6 173.9 176.2 178.6 180.9 183.2 185.5 187.8 190.2 192.5 194.8 197.1 199.4 201.8 204.1 206.4 208.7 211.0 213.4 215.7 218.0 220.3 222.6 224.9 227.3 229.6 231.9

C-87

Post Composite Deflection from:

Midpt Load Endpt Load Self Weight Total (in) (in) (in) (in) 4.67E-02 5.80E-02 8.77E-03 1.14E-01 4.84E-02 6.05E-02 9.12E-03 1.18E-01 5.02E-02 6.31E-02 9.47E-03 1.23E-01 5.19E-02 6.56E-02 9.83E-03 1.27E-01 5.37E-02 6.82E-02 1.02E-02 1.32E-01 5.55E-02 7.09E-02 1.05E-02 1.37E-01 5.72E-02 7.36E-02 1.09E-02 1.42E-01 5.90E-02 7.63E-02 1.13E-02 1.47E-01 6.08E-02 7.91E-02 1.17E-02 1.52E-01 6.26E-02 8.19E-02 1.20E-02 1.56E-01 6.43E-02 8.47E-02 1.24E-02 1.61E-01 6.61E-02 8.76E-02 1.28E-02 1.66E-01 6.79E-02 9.05E-02 1.32E-02 1.72E-01 6.96E-02 9.34E-02 1.36E-02 1.77E-01 7.14E-02 9.64E-02 1.40E-02 1.82E-01 7.32E-02 9.94E-02 1.44E-02 1.87E-01 7.50E-02 1.02E-01 1.47E-02 1.92E-01 7.67E-02 1.06E-01 1.51E-02 1.97E-01 7.85E-02 1.09E-01 1.55E-02 2.03E-01 8.03E-02 1.12E-01 1.59E-02 2.08E-01 8.20E-02 1.15E-01 1.63E-02 2.13E-01 8.38E-02 1.18E-01 1.67E-02 2.19E-01 8.56E-02 1.21E-01 1.72E-02 2.24E-01 8.73E-02 1.24E-01 1.76E-02 2.29E-01 8.91E-02 1.28E-01 1.80E-02 2.35E-01 9.09E-02 1.31E-01 1.84E-02 2.40E-01 9.27E-02 1.34E-01 1.88E-02 2.46E-01 9.44E-02 1.38E-01 1.92E-02 2.51E-01 9.62E-02 1.41E-01 1.96E-02 2.57E-01 9.80E-02 1.44E-01 2.00E-02 2.62E-01 9.97E-02 1.48E-01 2.04E-02 2.68E-01 1.02E-01 1.51E-01 2.09E-02 2.74E-01 1.03E-01 1.55E-01 2.13E-02 2.79E-01 1.05E-01 1.58E-01 2.17E-02 2.85E-01 1.07E-01 1.61E-01 2.21E-02 2.90E-01 1.09E-01 1.65E-01 2.25E-02 2.96E-01 1.10E-01 1.68E-01 2.30E-02 3.02E-01 1.12E-01 1.72E-01 2.34E-02 3.07E-01 1.14E-01 1.75E-01 2.38E-02 3.13E-01 1.16E-01 1.79E-01 2.42E-02 3.19E-01 1.17E-01 1.83E-01 2.47E-02 3.25E-01 1.19E-01 1.86E-01 2.51E-02 3.30E-01 1.21E-01 1.90E-01 2.55E-02 3.36E-01 1.23E-01 1.93E-01 2.59E-02 3.42E-01 1.25E-01 1.97E-01 2.63E-02 3.48E-01 1.26E-01 2.00E-01 2.68E-02 3.54E-01 1.28E-01 2.04E-01 2.72E-02 3.59E-01 1.30E-01 2.08E-01 2.76E-02 3.65E-01 1.32E-01 2.11E-01 2.80E-02 3.71E-01 1.33E-01 2.15E-01 2.85E-02 3.77E-01 1.35E-01 2.19E-01 2.89E-02 3.83E-01 1.37E-01 2.22E-01 2.93E-02 3.89E-01 1.39E-01 2.26E-01 2.97E-02 3.94E-01 1.40E-01 2.30E-01 3.02E-02 4.00E-01 1.42E-01 2.33E-01 3.06E-02 4.06E-01 1.44E-01 2.37E-01 3.10E-02 4.12E-01 1.46E-01 2.41E-01 3.14E-02 4.18E-01 1.48E-01 2.44E-01 3.19E-02 4.24E-01

3.3.2.5b Cantilever Deflection Tool

(in) 99.7 102.0 104.4 106.7 109.0 111.3 113.6 116.0 118.3 120.6 122.9 125.2 127.5 129.9 132.2 134.5 136.8 139.1 141.5 143.8 146.1 148.4 150.7 153.1 155.4 157.7 160.0 162.3 164.7 167.0 169.3 171.6 173.9 176.2 178.6 180.9 183.2 185.5 187.8 190.2 192.5 194.8 197.1 199.4 201.8 204.1 206.4 208.7 211.0 213.4 215.7 218.0 220.3 222.6 224.9 227.3 229.6 231.9

Midpt Load (in) 4.91E-02 5.10E-02 5.28E-02 5.47E-02 5.65E-02 5.84E-02 6.02E-02 6.21E-02 6.40E-02 6.58E-02 6.77E-02 6.96E-02 7.14E-02 7.33E-02 7.51E-02 7.70E-02 7.89E-02 8.07E-02 8.26E-02 8.45E-02 8.63E-02 8.82E-02 9.00E-02 9.19E-02 9.38E-02 9.56E-02 9.75E-02 9.94E-02 1.01E-01 1.03E-01 1.05E-01 1.07E-01 1.09E-01 1.11E-01 1.12E-01 1.14E-01 1.16E-01 1.18E-01 1.20E-01 1.22E-01 1.24E-01 1.25E-01 1.27E-01 1.29E-01 1.31E-01 1.33E-01 1.35E-01 1.37E-01 1.38E-01 1.40E-01 1.42E-01 1.44E-01 1.46E-01 1.48E-01 1.50E-01 1.52E-01 1.53E-01 1.55E-01

Endpt Load (in) 5.92E-02 6.17E-02 6.43E-02 6.69E-02 6.96E-02 7.23E-02 7.51E-02 7.78E-02 8.07E-02 8.35E-02 8.64E-02 8.93E-02 9.23E-02 9.53E-02 9.83E-02 1.01E-01 1.04E-01 1.08E-01 1.11E-01 1.14E-01 1.17E-01 1.20E-01 1.24E-01 1.27E-01 1.30E-01 1.34E-01 1.37E-01 1.40E-01 1.44E-01 1.47E-01 1.51E-01 1.54E-01 1.58E-01 1.61E-01 1.65E-01 1.68E-01 1.72E-01 1.75E-01 1.79E-01 1.83E-01 1.86E-01 1.90E-01 1.93E-01 1.97E-01 2.01E-01 2.04E-01 2.08E-01 2.12E-01 2.16E-01 2.19E-01 2.23E-01 2.27E-01 2.30E-01 2.34E-01 2.38E-01 2.42E-01 2.45E-01 2.49E-01

Total (in) 1.08E-01 1.13E-01 1.17E-01 1.22E-01 1.26E-01 1.31E-01 1.35E-01 1.40E-01 1.45E-01 1.49E-01 1.54E-01 1.59E-01 1.64E-01 1.69E-01 1.73E-01 1.78E-01 1.83E-01 1.88E-01 1.93E-01 1.98E-01 2.03E-01 2.09E-01 2.14E-01 2.19E-01 2.24E-01 2.29E-01 2.34E-01 2.40E-01 2.45E-01 2.50E-01 2.56E-01 2.61E-01 2.66E-01 2.72E-01 2.77E-01 2.82E-01 2.88E-01 2.93E-01 2.99E-01 3.04E-01 3.10E-01 3.15E-01 3.21E-01 3.26E-01 3.32E-01 3.37E-01 3.43E-01 3.48E-01 3.54E-01 3.60E-01 3.65E-01 3.71E-01 3.76E-01 3.82E-01 3.88E-01 3.93E-01 3.99E-01 4.04E-01

3.3.2.6 HSS Edge Beam Design

Created By:

DL 11/10/2012

Design tool to validate sellection HSS beam size on the building exterior This tool calculates loads applied to the section and the section capacity Beam Location 109th Floor - Mechanical

Color Key:

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

Summary Selected Section Does section pass all checks?

HSS20X12X1/2 Yes

Beam Geometries Side View Length of Beam Uncurved Length of Beam Angle of Curvature Radius of Curvature Eccentricity of Curvature Torque Coefficient Angular Twist Coefficient

L L' α r b A B

813 839.4 50 961.9 90.1 0.0255 0.0020

in in deg in in

See Diagram Below = α/360 * 2πr See Diagram Below See Diagram Below See Diagram Below regression from Blodgett regression from Blodgett

3.3.2.6 HSS Edge Beam Design

C-88

Applied Loads Live Load Dead Load Factored Floor Load Unfactored Floor Load Tributary Area Factored Distributed Load Unfactored Distributed Load End Torque Angular Twist

LL DL wf w Atrib wf w Tend θ

240 44.3 437 284.3 24,827

psf psf psf psf 2 in

= 1.6LL+1.2DL = LL+DL

89.8 58.4 2,361,639

lb/in lb/in lb*in

= wf*Atrib/L'

0.0064

deg

= B*r3*wtotal/Es*(b/t)

= w*L'/2

= w*Atrib/L' = A*r2*wftotal

Bending Moment Max Shear

Vmaxf

42.0

kip

Max Moment 1/4 Uncurved Length 1/2 Uncurved Length 3/4 Uncurved Length Bending Moment 1/4 Length

Mmaxf

5879 210 420 630 735

2 Kip-in = w*L' /12 in in in 2 2 Kip-in = wL'*(6L'x-L' -6x )/12

Bending Moment 1/2 Length

MB MC

2,939

2 2 Kip-in = wL'*(6L'x-L' -6x )/12

735

2 2 Kip-in = wL'*(6L'x-L' -6x )/12

Nominal Steel Strength

Fy

50

Steel Reduction Factor

Φy ΦyFy

0.9 45

ksi

= Φy*Fy

Smin

131

in3

= Mmaxf/ΦyFy

Bending Moment 3/4 Length

L'/4 L'/2 3L'/4 MA

Shear

Factored Steel Strength Minimum Required Section Modulus

ksi

Section Properties Selected Section Section Modulus (Strong)

HSS20X12X1/2

Sx

155

in3

W Ag

Yes 8.61 28.3

lb/in in2

Awt

17.7

in2

Ht b t h

20.0 12.0 0.465 19.1

R b/t Ht/t

1,674 22.8 40.0

in in in in in3

Passes check for S min < Sy? Self Weight Total Area Effective Shear Area Overall Depth Overall Width Design Wall Thickness Depth less corner radii Torsional resistance Slenderness Ratio Slenderness Ratio C-89

= Ht-2*t = 2*t*b2*Ht2/(b+Ht)

3.3.2.6 HSS Edge Beam Design

Slenderness Ratio Moment of Inertia (Strong)

h/t Ix

41.0 1,550.00

in

4

Moment of Inertia (Weak)

Iy

705

in4

Section Modulus (Weak)

Sy

117

in

Plastic Section Modulus

Zx

188

in

Radius of Gyration (Strong)

rx

7.39

in

Radius of Gyration (Weak)

ry

4.99

in

Web Plate Buckling Coefficient

kv

5

Cv

59.24 73.78 1

Limiting Thickness Ratio 1 Limiting Thickness Ratio 2 Web Shear Coefficient

3 3

G5 = 1.10*(kv*E/Fy)1/2 ; G2.1(b) = 1.37*(kv*E/Fy)1/2 ; G2.1(b) G2.1(b) 4

Polar Moment of Inertia

J

1,540

in

Torsional Shear Constant Young's Modulus Shear Modulus

C E Es

209 29,000 11,200

in3 ksi ksi

wftotal wtotal

100.1

lb/in

= wf+1.2*W

67.00

lb/in

= wf+W

Δmax

1.93

in

= wtotal*L'4/(384*E*Ix)

Δallowable

3.50

in

= L'/240

Total Loads Total Factored Load Total Unfactored Load

deflection for fixed-fixed

Deflection Max Deflection Allowable Deflection Passes for Δmax < Δallowable?

Yes

Compactness Uncurved Length of Beam Unbraced Length of Beam

L' Lb = L'

839 839

in in

Compactness Ratio

λp

27.0

= 1.12*(E/Fy)1/2 ; Table B4.1

Noncompact Ratio Compactness

λr

33.7 COMPACT

= 1.40*(E/Fy)1/2 ; Table B4.1 Section B4

Applied Load Summary Max Shear Force

Vmaxf

42.0

Kip

Max Bending Moment

Mmaxf

5,879

Kip-in

Bending Moment 1/4 Length

MA

735

Kip-in

Bending Moment 1/2 Length

MB

2,939

Kip-in

Bending Moment 3/4 Length

MC

735

Kip-in

Cb

2.4

Beam Bending Coefficient Torsion at Ends

Tend

2,362

12.5Mmax/(2.5Mmax+3MA+4MB+3MC) ; F1-3

Kip-in

3.3.2.6 HSS Edge Beam Design

C-90

Capacity Calculations Nominal Steel Strength

Fy

50.0

ksi

Nominal Yield Capacity

Mn = M p

9,400

Kip-in = FyZx ; (F7-1)

Flange Local Buckling

Mn

N/A

1/2 Kip-in = Mp-(Mp-FyS)(3.57(b/t)(Fy/E) -4.0 ; (F7-2)

Web Local Buckling

Mn

N/A

1/2 Kip-in = Mp-(Mp-FySx)(0.305(h/t)(Fy/E) -0.738) ; (F7-

Nominal Moment Capacity

Mn

9,400

Fcr

59.0 73.9 30.0

ksi

Max Bending Stress Max Shear Stress

fbf fvf

37.9 2.4

ksi ksi

Reduction Factor for Bending

Φy

0.9

Ch 4

Reduction Factor for Shear

Φv

0.9

G1

Reduction Factor fo Torsion

ΦT

0.9

H3

Bending Capacity

Fbf

54.6

ksi

= Φy*Mn/Sx

Available Strength in Shear

Fvf Tn

27.0

ksi

= Φv*0.6*Fy

5,643

Kip-in = ΦT *Fcr*C

Thickness Ratio Thickness Ratio Torsional Strength

5) Kip-in = MIN(above Mn's)

= 2.45(E/Fy)1/2 ; H3(b) = 3.07(E/Fy)1/2 ; H3(b)

Capacity Calculations

Torsional Capacity

= Mmax/Sx ; 2-9 = Vmax/Awt ; 2-21

Ratios of Applied Loads to Load Capacity Utilization Factor: Bending Utilization Factor < 100% ? Utilization Factor: Shear Utilization Facotr < 100% ? Utilization Factor: Torsion Utilization Factor < 100% ? Combined Effect Utilization Factor < 100% ?

C-91

Ub Uv Ut

69.5% Yes 8.8% Yes 41.9% Yes 95.1% Yes

= fbf/Fbf = fvf/Fvf = Tend/Tn 2 = (fbf/Fbf)+(fvf/Fvf + Tend/Tn) ; (H3-6)

3.3.2.6 HSS Edge Beam Design

3.3.3 Vibration Analysis

Created by:

SJR

5/9/2012

Vibration of the floor system was checked as a serviceability requirement. It was found that the selected decking and joists met the requirements for a residential building as demonstrated below.

Estimated Peak Accelerations Type Residential Mechanical Lobby Residential Mechanical Lobby Residential Mechanical Lobby Residential -1 Residential -2

Bank

ap/g

ao/g

ap/g < ao/g ?

1 1 1 2 2 2 3 3 3 4 4

0.332% 0.099% 0.199% 0.246% 0.040% 0.086% 0.194% 0.043% 0.073% 0.146% 0.130%

0.500% 0.500% 0.500% 0.500% 0.500% 0.500% 0.500% 0.500% 0.500% 0.500% 0.500%

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

3.3.3 Vibration Analysis

C-92

Vibration Analysis Calculations

Created by:

SJR

5/9/2012

Analyzes typical residential, mechanical, and lobby floor bays for each bank. Compares estimated peak acceleration to acceleration limit from AISC Design Guide 11 Floor Vibrations Due to Human Activity , Figure 2.1. Each element is considered separately and then the system as a whole is evaluated. Bank Floor Location

Color Key:

1 5 Lobby

Yes No Typical Bay:

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

Joist

Joist

Joist

Girder

Girder

Consistent Inputs Acceleration Limit

ao/g

0.5%

AISC Design Guide 11 Figure 2.1

Steel Modulus

Es 29,000,000 psi

Concrete Modulus Dynamic Modular Ratio

Ec 2,574,000 psi n 8.35

= Es/(1.35*Ec) ; AISC Design Guide 11 4.2 2

g

386

in/s

Po

lbs

β

65 0.2

ρc SDL LL

110 12 18

pcf psf psf

tc

3 2.5

in.

Corrugation Thickness

tcor

1.5

in

Vulcraft Decking Catalogue

Effective Concrete Depth

deff

3.25

in

= tc + tcor/2

Decking Weight

wd

1.78

Theoretical Conc. Volume Total Load

Vth

0.253 60

psf Vulcraft Decking Catalogue 3 2 ft /ft Vulcraft Decking Catalogue = SDL + LL + w d + ρc*Vth psf

Gravity Acceleration Constant Force Model Dampening Ratio Concrete Density Superimposed Dead Load Live Load

65 lb for floors ; AISC Design Guide 11 Table 4.1 AISC Design Guide 11 Table 4.1

Flooring Properties Number of Joists Concrete Thickness

C-93

3.3.3 Vibration Analysis

Joist 1 Details Joist Length

LJ1

183

Joist Tributary Area Steel Size Chosen Steel Weight

Atr

17,712 W12 x 22 22

Steel Area

As

6.48

Steel Moment Of Inertia (MOI) Steel Depth

Ixx d

156 12.3

Uniformly dist load / length

wl

41.9

Uniformly dist load / area

wa

0.433

lbs/in lbs/in2

Effective Concrete Width

beff

73.2

in

=min(tributary width , 0.4*L J1)

Distance to centroid

ybar

0.780

below top of form deck

in 2 in plf 2 in in4 in

Joist 1 Calculations

Transformed MOI

It

564

in in4

Mid-span Deflection Natural Frequency

Δ fn

0.0374 18.3

in /s

= 5wlLJ1 /384EsIt = 0.18*sqrt(g/Δ) ; AISC Design Guide 11 3.3

Joist Spacing

sj

6.98

AISC Design Guide 11 4.3a

Transformed Slab MOI

Ds

4.11

ft in4/ft

Transformed Joist MOI

Dj

80.8

in4/ft

= It/S ; AISC Design Guide 11 4.3a

Effective Width Factor

Cj

1

Effective Panel Width

Bj

86.9

in

= Cj(Ds/Dj) LJ1 ; AISC Design Guide 11 4.3a

Effective Panel Weight

Wj

6,887

lbs

= waBjLJ1 ; AISC Design Guide 11 4.2

Estimated Peak Acceleration

ap/g

0.008%

uses parallel axis theorem 4

= de3/12n ; AISC Design Guide 11 4.3a

AISC Design Guide 11 4.3a 1/4

= Poexp(-0.35fn)/βWj ; AISC Design Guide 11 4.1

3.3.3 Vibration Analysis

C-94

Joist 2 Details Joist Length

LJ2

212

Joist Tributary Area Steel Size Chosen Steel Weight

Atr

21,600 W12 x 22 22

Steel Area

As

6.48

Steel Moment Of Inertia (MOI) Steel Depth

Ixx d

156 12.3

Uniformly dist load / length

wl

44.0

Uniformly dist load / area

wa

0.432

lbs/in lbs/in2

Effective Concrete Width

beff

84.8

in

=min(tributary width , 0.4*L J2)

Distance to centroid

ybar

0.559

below top of form deck

in 2 in plf 2 in in4 in

Joist 2 Calculations

Transformed MOI

It

578

in in4

Mid-span Deflection Natural Frequency

Δ fn

0.0690 13.5

in /s

= 5wlLJ2 /384EsIt = 0.18*sqrt(g/Δ) ; AISC Design Guide 11 3.3

Joist Spacing Transformed Slab MOI

S Ds

6.98 4.11

ft in4/ft

AISC Design Guide 11 4.3a

Transformed Joist MOI

Dj

82.8

in4/ft

= It/S ; AISC Design Guide 11 4.3a

Effective Width Factor

Cj

1

Effective Panel Width

Bj

100

in

= Cj(Ds/Dj)1/4LJ2 ; AISC Design Guide 11 4.3a

Effective Panel Weight

Wj

9,164

lbs

= waBjLJ2 ; AISC Design Guide 11 4.2

Estimated Peak Acceleration

C-95

ap/g

0.032%

uses parallel axis theorem 4

= de3/12n ; AISC Design Guide 11 4.3a

AISC Design Guide 11 4.3a

= Poexp(-0.35fn)/βWj ; AISC Design Guide 11 4.1

3.3.3 Vibration Analysis

Joist 3 Details Joist Length

LJ3

241

Joist Tributary Area Steel Size Chosen Steel Weight

Atr

25,200 W12 x 40 40

Steel Area

As

11.7

Steel Moment Of Inertia (MOI) Steel Depth

Ixx d

307 11.9

Uniformly dist load / length

wl

46.6

Uniformly dist load / area

wa

0.446

lbs/in lbs/in2

Effective Concrete Width

beff

96.4

in

=min(tributary width , 0.4*L J3)

Distance to centroid

ybar

1.259

below top of form deck

in 2 in plf 2 in in4 in

Joist 3 Calculations

Transformed MOI

It

952

in in4

Mid-span Deflection Natural Frequency

Δ fn

0.074 13.0

in /s

= 5wlLJ3 /384EsIt = 0.18*sqrt(g/Δ) ; AISC Design Guide 11 3.3

Joist Spacing Transformed Slab MOI

S Ds

6.98 4.11

ft in4/ft

AISC Design Guide 11 4.3a

Transformed Joist MOI

Dj

136.4

in4/ft

= It/S ; AISC Design Guide 11 4.3a

Effective Width Factor

Cj

1

Effective Panel Width

Bj

100

in

= Cj(Ds/Dj)1/4LJ3 ; AISC Design Guide 11 4.3a

Effective Panel Weight

Wj

10,790

lbs

= waBjLJ3 ; AISC Design Guide 11 4.2

ap/g

0.032%

Estimated Peak Acceleration

uses parallel axis theorem 4

= de3/12n ; AISC Design Guide 11 4.3a

AISC Design Guide 11 4.3a

= Poexp(-0.35fn)/βWj ; AISC Design Guide 11 4.1

3.3.3 Vibration Analysis

C-96

Girder Details Joist Length Steel Size Chosen Steel Weight Steel Area Steel Moment Of Inertia (MOI) Steel Depth

LG

As Ixx

335 W16 x 67 67 19.7

in plf in2 in

4

d

954 16.3

Uniformly dist load / length

wl

89.9

Uniformly dist load / area

wa

0.424

Effective Concrete Width

beff

134

in

=min(tributary width , 0.4*L G)

Distance to centroid

ybar

2.34

below top of form deck

Transformed MOI

It

2,545

in in4

Mid-span Deflection Natural Frequency

Δ fn

0.254 18.3

in /s

= (4/π)*5wlLJ34/384EsIt = 0.18*sqrt(g/Δ) ; AISC Design Guide 11 3.3

Average Joist Length

Lj-avg

212

= de3/12n ; AISC Design Guide 11 4.3a

Average Joist MOI

Dj-avg

81.8

ft in4/ft

Transformed Girder MOI

Dg

9.00

Effective Width Factor

Cg

1.8

Effective Panel Width

Bg

141

in

= Cj(Ds/Dj) LJ3 ; AISC Design Guide 11 4.3a

Effective Panel Weight

Wg

20,069

lbs

= waBjLJ3 ; AISC Design Guide 11 4.2

ap/g

0.003%

in

Girder Calculations

Estimated Peak Acceleration

C-97

lbs/in lbs/in2

uses parallel axis theorem

= It/S ; AISC Design Guide 11 4.3a

AISC Design Guide 11 4.3a 1/4

= Poexp(-0.35fn)/βWg ; AISC Design Guide 11 4.1

3.3.3 Vibration Analysis

Combined System Calculations Total Joist Deflection Total Girder Deflection Total Deflection Total Natural Frequency

Δj Δg ΔT fnT

0.060 0.254 0.314 6.31

in in in /s

average of all joist deflections

Total Effective Joist Weight

Wj

8,947

lbs

average of all effective joist weights

Total Effective Girder Weight

Wg

20,069

lbs

Total Effective Weight

WT

17,939

lbs

Estimated Peak Acceleration

ap/g

0.199%

Acceleration Limit

ao/g

0.5%

ap/g < ao/g ?

Yes

= 0.18*sqrt(g/ΔT) ; AISC Design Guide 11 3.3

= Δj/(ΔT)*Wj + Δ g/(ΔT)*Wg ; AISC Design Guide 11 4.4 = Poexp(-0.35fnT)/βW ; AISC Design Guide 11 4.1

3.3.3 Vibration Analysis

C-98

3.4 Columns

99

3.4.1 Column Load Takedown

100

3.4.2 Composite Column Design 114 3.4.3 Steel Column Design

118

3.0 Gravity Design C-99

3.4.1 Column Load Takedown

Created by:

CTM

2/15/2012

This series of spreadsheets calculates the gravity loads via tributary areas on the columns and core segments summing over the height of the building to determine the axial load each column must resist under gravity.

General Information Notes: • The self weight of the columns has not been addressed • Live loads were assumed to be non-reducible • Safety factors of 1.2 for dead loads and 1.6 for live loads were used • Bank 4 has been divided into 4a and 4b to correspond to the two floor plans received. • Each bank has the same loads applied over its height so the values are input at the bottom of the bank and refenerenced on the higher levels. • The tributary area and function of each floor are input into the column spreadsheets, the spreadsheets expand to allow for multiple loads types in which case the percentage is input to indicate a fraction of the tributary area for each type. • Bank transitions have been shown on takedown sheets, omitted levels are identical to those immediately above and below. • Column transfers have been included as necessary and may not appear in the sample calculations shown. • As the core size decreases going up the building the walls are not aligned axially causing an eccentricity from the from the walls above. The core walls segments were checked as columns using an intaction diagram to identify area where the ececntricity will cause need for extra reinforcing. • The circular core has been modeled as a trapezoidal shape to be used in the interaction diagram, the plans and dimensions shown correspond to these models.

Loads Area Loads Core Lobby(non core) Open None Mechanical Residential

Line Loads Façade

DL (psf) 55 32 0

SDL (psf) 57 57 0

LL (psf) 100 100 0

39 32.5

10 55

240 34

DL (lbs/ft) 145

slab openings

this includes the hss on the edges, it is a very rough guess

3.4.1 Column Load Takedown

C-100

Column Load Summaries Exterior Steel Columns • In Banks 1 and 2 the exterior ring of 21 columns is composed of three columns that repeat seven times, so there are three load scenarios, labeled as columns 1, 3a, and 3b. • Banks 3 and 4 have 14 exterior columns, columns 1 and 2. • Column 1 extends the full height of the building • Column 2 exists in banks 3 and 4, it then splits in two columns for bank 2 and 1 to become 3a and 3b

set back in the column layout (going towards the core) have not been considered

Final Loads at Ground Level (factored) DL (kips) 5590 n/a 4242 4242

Column 1 Column 2 Column 3a Column 3b

SDL (kips) 7564 n/a 5800 5800

LL (kips) 7481 n/a 5837 5837

Core Concrete Columns • The core is divided into four columns, of two shapes, a large and small layout on each bank. • The layout of four columns is the same for Banks 1 through 3 but the dimensions decrease going up the building. • Bank 4 core geometry has two columns (Top Core) that transfer loads into the four columns of bank 3.

Final Loads at Ground Level (factored) E-W Core N-S Core Top Core

DL (kips) 9706 12096 n/a

SDL (kips) 13171 14203 n/a

LL (kips) 24221 43350 n/a

typical column plan

C-101

3.4.1 Column Load Takedown

Tributary Area Data

Created by: CTM/CYW

12/3/2012

This information was calculated based on the preliminary architectural drawings using AutoCAD. Associated hand calculations are included.

Exterior Steel Columns Color key:

Bank 1 Number of Columns Long Outer Radius Short Outer Radius Average Outer Radius Radius to Column Radius to Core Column/Core Boundary Radius Maximum Trib. Area Max ext. length Minimum Trib. Area Min ext. length Core Trib. Area Boundary Line

Bank 3 Number of Columns Long Outer Radius Short Outer Radius Average Outer Radius Radius to Column Radius to Core Column/Core Boundary Radius Maximum Trib. Area Max ext. length Minimum Trib. Area Min ext. length Core Trib. Area Boundary Line

User Input Used in column load takedown

21 96.0 84.1 90.1 75.5 41 58.3 1037.6 37.2 646.5 26.6 63.4

14 80.6 71.8 76.2 61 35.42 48.2 922.4 33.1 421.5 52.0

ft ft ft ft ft ft ft2 ft 2 ft ft ft

Bank 2 Number of Columns Long Outer Radius Short Outer Radius Average Outer Radius Radius to Column Radius to Core Column/Core Boundary Radius Maximum Trib. Area Max ext. length Minimum Trib. Area Min ext. length Core Trib. Area Boundary Line

ft ft ft ft ft ft ft2 ft ft2 ft ft

Bank 4a Number of Columns Long Outer Radius Short Outer Radius Average Outer Radius Radius to Column Radius to Core Column/Core Boundary Radius Maximum Trib. Area Max ext. length Minimum Trib. Area Min ext. length Core Trib. Area Boundary Line

3.4.1 Column Load Takedown

21 90.9 79.9 85.4 68.5 41 54.8 799.8 31.6 526.8 24.5 58.9

14 72.0 63.4 67.7 57.75 34.33 46.0 669.4 35.3 504.9 49.6

ft ft ft ft ft ft ft2 ft 2 ft ft ft

ft ft ft ft ft ft ft2 ft ft2 ft ft

C-102

Bank 4b Number of Columns 14 Long Outer Radius 65.3 ft Short Outer Radius 59.4 ft Average Outer Radius 62.4 ft Radius to Column 49.625 ft Radius to Core 33.6 ft Column/Core Boundary Radius 41.6 ft 2 Maximum Trib. Area 570.5 ft Max ext. length 32.1 ft 2 Minimum Trib. Area 441.3 ft Min ext. length ft Core Trib. Area Boundary Line 44.0 ft

Core Concrete Columns centroid distances are along the axis of symmetry, axis show in diagram to right

Bank 1 E-W Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area N-S Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area Open to Below

Area 2 (ft ) 218 1575 245 409

Centroid (ft) 4.4105 -6.6 11.39 13.00

Area (ft2) 323 1490 425 313 138

Centroid (ft) 5.55 -5.63 14.95 13.96

typical layout, dimensions vary per floor

C-103

3.4.1 Column Load Takedown

Bank 2 E-W Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area N-S Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area Open to Below

Area Centroid 2 (ft ) (ft) 145.88 3.4 1301 -5.8 245 9 335 12 Area (ft2) 231 1508 418 241 145

Centroid (ft) 4.578 -4.85 12.45 13.0154

Area 2 (ft ) 136.4 1185 222

Centroid (ft) 3.1 -5.6 7

Area (ft2) 247 1041 376 76 160

Centroid (ft) 4.61 -4.88 9.95 13.11

Bank 3 E-W Core Column Residential Tributary Area Lobby Tributary Area

N-S Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area Open to Below

3.4.1 Column Load Takedown

C-104

Bank 4a E-W Core Column Residential Tributary Area Lobby Tributary Area N-S Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area

Area 2 (ft )

Centroid (ft) 3.6684 956.275 -5.1164 189.96 8.5061 Area (ft2) 1172 590 113

Centroid (ft) 2.3315 -5.89 11.6333 11.57

Area 2 (ft ) 157 1367 728 196

Centroid (ft) 4.5649 5.7874 9.9475 22.308

Bank 4b Top Core Column Residential Tributary Area Mechanical Tributary Area Lobby Tributary Area

C-105

3.4.1 Column Load Takedown

Column 1

Loads From This Floor DL SDL LL

Function

MidasGen Loads DL+SDL LL

... 137 137 137 19 39 252 272 291 314 336 ...

905 960 1,014 1,078 1,142 ...

19 19 19 23 23 ...

55 55 55 64 64 ...

403 434 466 502 538 ...

531 568 606 650 694 ...

556 583 611 644 676 ...

252 272 291 314 336 ...

442 474 505 542 579 ...

463 486 509 536 563 ...

4.7 4.7 4.7 5.1 5.1 ...

Façade Façade Façade Façade Façade ...

32.1 32.1 32 35.3 35.3 ...

19.4 19.4 19.4 22.8 22.8 ...

31.4 31.4 31.4 36.8 36.8 ...

18.5 18.5 18.5 21.8 21.8 ...

100 100 100 100 100 ...

Residential Residential Residential Residential Residential ...

571 571 571 669 669 ...

132 131 130 129 128 ...

4 4 4 4 4 ...

...

... 130 163 196 250 305 ...

... 137 137 137 19 19 ...

... 33 33 33 55 55 ...

... 219 219 219 31 62 ...

... 27 34 41 79 116 ...

... 129 161 194 222 249 ...

... 137 137 137 19 39 ...

... 23 29 34 66 97 ...

... 108 135 161 185 208 ...

... 4.7 4.7 4.7 4.7 4.7 ...

Façade Façade Façade Façade Façade ...

32.1 32.1 32 32.1 32.1 ...

136.9 136.9 136.9 19.4 19.4 ...

5.7 5.7 5.7 31.4 31.4 ...

22.2 22.2 22.2 18.5 18.5 ...

100 100 100 100 100 ...

Mechanical Mechanical Mechanical Residential Residential ...

571 571 571 571 571 ...

147 146 145 144 143 ...

4 4 4 4 4 ...

...

(kips)

...

(kips)

Column Design Total DL LL unfactored DL + SDL (kips) (kips)

...

Factored Loads SDL LL = total = total SDL*1.2 LL*1.6 (kips) (kips)

...

DL = total DL*1.2 (kips)

...

loads taken from summary sheet (kips) (kips) (kips)

Total Loads DL SDL LL sum of: above, column transfer, exterior edge, and floor loads (kips) (kips) (kips)

...

%

Exterior Edge Loads Load Type DL: from summary sheet (kips)

...

Use

Ext. Lng from trib sheet (ft)

...

Trib Area from trib sheet ft^2

...

Level

...

Bank

4 4 4 3 3 3 3 3

114 113 112 111 110 109 108 107

669 669 669 669 922 922 922 922

Residential Residential Residential Lobby(non core) None Mechanical Residential Residential

100 100 100 100

21.8 21.8 21.8 21.4 0.0 36.0 30.0 30.0

36.8 36.8 36.8 38.2 0.0 9.2 50.7 50.7

22.8 22.8 22.8 66.9 0.0 221.4 31.4 31.4

35.3 35.3 35 35 33 33 33.1 33.1

Façade Façade Façade Façade Façade Façade Façade Façade

5.1 5.1 5.1 5.1 4.8 4.8 4.8 4.8

939 966 993 1,020 1,024 1,065 1,100 1,135

1,094 1,131 1,168 1,206 1,206 1,215 1,266 1,316

655 678 701 768 768 989 1,020 1,052

1,127 1,160 1,192 1,224 1,229 1,278 1,320 1,362

1,313 1,357 1,401 1,447 1,447 1,458 1,519 1,580

1,048 1,085 1,121 1,228 1,228 1,582 1,632 1,683

64 64 64 65 5 50 86 86

23 23 23 67 0 221 31 31

2,033 2,097 2,161 2,225 2,230 2,280 2,366 2,451

655 678 701 768 768 989 1,020 1,052 ... ...

Façade Façade Façade Façade Façade Façade Façade Façade

4.6 4.6 4.6 4.6 5.4 5.4 5.4 5.4

3,209 3,239 3,270 3,300 3,306 3,351 3,391 3,430

4,276 4,320 4,364 4,410 4,410 4,420 4,477 4,534

3,128 3,155 3,182 3,262 3,262 3,511 3,547 3,582

3,851 3,887 3,924 3,960 3,967 4,022 4,069 4,116

5,131 5,184 5,237 5,291 5,291 5,304 5,372 5,441

5,005 5,048 5,092 5,220 5,220 5,618 5,675 5,731

75 75 75 76 5 56 96 96

27 27 27 80 0 249 35 35

7,485 7,559 7,634 7,710 7,715 7,771 7,868 7,964

3,128 3,155 3,182 3,262 3,262 3,511 3,547 3,582 ...

... ...

31.6 31.6 32 32 37 37 37.2 37.2

...

... ...

27.2 27.2 27.2 80.0 0.0 249.0 35.3 35.3

...

... ...

44.0 44.0 44.0 45.6 0.0 10.4 57.1 57.1

...

... ...

26.0 26.0 26.0 25.6 0.0 40.5 33.7 33.7

...

... ...

100 100 100 100 100 100 100 100

...

... ...

Residential Residential Residential Lobby(non core) None Mechanical Residential Residential

...

... ...

800 800 800 800 1,038 1,038 1,038 1,038

...

... ...

43 42 41 40 39 38 37 36

...

... ...

2 2 2 1 1 1 1 1

...

... ...

1,992 2,024 2,055 2,147 2,147 2,339 2,367 2,394

...

...

5,016 5,102 5,187 5,274 5,279 5,323 5,397 5,472

...

31 31 31 92 0 192 27 27

...

...

86 86 86 87 5 44 75 75

...

3,188 3,238 3,288 3,436 3,436 3,743 3,786 3,830

...

...

3,406 3,467 3,528 3,591 3,591 3,600 3,653 3,706

...

2,614 2,656 2,697 2,738 2,744 2,787 2,824 2,860

...

...

1,992 2,024 2,055 2,147 2,147 2,339 2,367 2,394

...

2,838 2,889 2,940 2,992 2,992 3,000 3,044 3,088

...

...

2,178 2,213 2,248 2,282 2,287 2,322 2,353 2,384

...

4.8 4.8 4.8 4.8 4.6 4.6 4.6 4.6

...

...

Façade Façade Façade Façade Façade Façade Façade Façade

...

33.1 33.1 33 33 32 32 31.6 31.6

...

...

31.4 31.4 31.4 92.2 0.0 192.0 27.2 27.2

...

50.7 50.7 50.7 52.6 0.0 8.0 44.0 44.0

...

...

30.0 30.0 30.0 29.5 0.0 31.2 26.0 26.0

...

100 100 100 100 100 100 100 100

...

...

Residential Residential Residential Lobby(non core) None Mechanical Residential Residential

...

922 922 922 922 800 800 800 800

...

77 76 75 74 73 72 71 70

...

3 3 3 2 2 2 2 2

...

...

100 100 100

1 1 1 1 1 1 1

7 6 5 4 3 2 1

1,038 1,038 1,038

Residential Residential Residential

100 100 100

33.7 33.7 33.7

57.1 57.1 57.1

35.3 35.3 35.3

37.2 37.2 37 37.2 37.2 37.2

Façade Façade Façade Façade Façade Façade

5.4 5.4 5.4 5.4 5.4 5.4

4,564 4,603 4,642 4,648 4,653 4,659 4,659

6,189 6,246 6,303 6,303 6,303 6,303 6,303

4,605 4,640 4,676 4,676 4,676 4,676 4,676

5,477 5,524 5,571 5,577 5,584 5,590 5,590

7,427 7,495 7,564 7,564 7,564 7,564 7,564

7,368 7,424 7,481 7,481 7,481 7,481 7,481

96 96 96 5 5 5

35 35 35 0 0 0

10,753 10,849 10,946 10,951 10,956 10,962 10,962

4,605 4,640 4,676 4,676 4,676 4,676 4,676

3.4.1 Column Load Takedown

C-106

N-S Core Notes: • Baseline point is the left edge along the axis of symmetry, notated with a zero • Unless otherwise noted eccentricities are measured from the baseline • Column transfers are extimated based on geometry, some load is going to walls around elevators, not currently considered Bldg Centroid to Side Center to used as baseline Centroid Bank 1 Bank 2 Bank 3 Bank 4a

Bank

Level

(ft)

(ft)

5.5 4.578 4.61 2.3315

36.8 35.3 30.8 28.8

Trib Area

b2 (ft) 10.15 9.65

28.86

4.89

Function 1

Function 2

Function 3

levels where column size will be checked/designed

Total Loads By Function, Factored 1 2 3 4

Function 4

... 18,567 19,049 19,530 20,138 20,326 21,002 21,366 21,730

238 238 238

C-107

...

0.0 0.0 0

8,037 8,138 8,239 8,343 8,365 8,402 8,506 8,610

19,755 19,935 20,114 20,393 20,527 21,018 21,202 21,386

8,405 8,500 8,595 8,689 8,730 8,840 8,939 9,037

9,645 9,766 9,887 10,012 10,038 10,082 10,207 10,332

31,608 31,895 32,183 32,629 32,843 33,629 33,923 34,218

4.27 4.27 4.27 2.05 14.63 0.41 5.34 5.34

503.54 503.54 503.54 665.43 280.52 940.55 518.12 518.12

-0.003 -0.003 -0.003 1.426 0.050 -0.091 -0.002 -0.002

49,658 50,161 50,665 51,330 51,611 52,551 53,069 53,587 ...

5.8 5.8 5.8

...

Open Open Open

7,004 7,083 7,163 7,241 7,275 7,367 7,449 7,531

...

14.0 14.0 13.96

...

13.2 13.2 13.2

179.61 179.61 179.61 279.10 133.44 491.18 184.12 184.12

...

Core Core Core

...

15.0 15.0 14.95

100.96 100.96 100.96 103.98 22.06 36.97 104.04 104.04

...

18.0 18.0 18

...

Mechanical Mechanical Mechanical

79.17 79.17 79.17 78.41 33.79 91.92 82.23 82.23

...

-5.6 -5.6 -5.63

...

63.0 63.0 63

0 0 0 0 0 0 0 0

...

Residential Residential Residential

...

2366 2366 2366

71 71 71 71 92 92 92 92

...

7 6 5 4 3 2 1

...

1 1 1 1 1 1 1

192 192 192 192 189 189 189 189

...

240 240 240 402 0 660 238 238

...

0.0 0.0 0 0 0 0 0.0 0.0

...

5.6 5.6 5.6 5.6 5.8 5.8 5.8 5.8

...

Open Open Open Open Open Open Open Open

...

13.0 13.0 13.0154 13.0154 13.96 13.96 14.0 14.0

...

10.4 10.4 10.4 10.4 13.2 13.2 13.2 13.2

...

Core Core Core Core Core Core Core Core

...

12.5 12.5 12.45 12.45 14.95 14.95 15.0 15.0

...

18.8 18.8 18.8 18.8 18 18 18.0 18.0

...

Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical

...

-4.9 -4.9 -4.85 -4.85 -5.63 -5.63 -5.6 -5.6

...

65.2 65.2 65.2 65.2 63 63 63.0 63.0

...

Residential Residential Residential Lobby(non core) Open Mechanical Residential Residential

...

2312 2312 2312 2312 2366 2366 2366 2366

...

43 42 41 40 39 38 37 36

...

2 2 2 1 1 1 1 1

...

32,651 33,015 33,379 33,861 34,124 35,055 35,559 36,062

...

-0.021 -0.021 -0.021 4.373 0.062 -0.119 -0.004 -0.004

...

364.02 364.02 364.02 482.26 263.25 930.74 503.54 503.54

...

2.71 2.71 2.71 0.85 12.60 0.09 4.27 4.27

...

21,520 21,736 21,952 22,284 22,490 23,274 23,561 23,849

...

5,820 5,902 5,985 6,070 6,091 6,131 6,252 6,373

...

5,311 5,377 5,442 5,507 5,543 5,650 5,745 5,840

...

13,450 13,585 13,720 13,928 14,056 14,546 14,726 14,905

...

4,850 4,919 4,987 5,058 5,076 5,109 5,210 5,311

...

4,426 4,481 4,535 4,589 4,619 4,708 4,788 4,867

...

135.09 135.09 135.09 207.75 128.36 490.14 179.61 179.61

...

68.64 68.64 68.64 70.84 18.05 33.13 100.96 100.96

...

54.60 54.60 54.60 54.04 30.18 88.97 79.17 79.17

...

0 0 0 0 0 0 0 0

...

22 22 22 22 71 71 71 71

...

166 166 166 166 192 192 192 192

...

175 175 175 294 0 667 240 240

...

0.0 0.0 0 0 0 0 0.0 0.0

...

6.1 6.1 6.1 6.1 5.6 5.6 5.6 5.6

...

Open Open Open Open Open Open Open Open

...

8.5 8.5 8.5 8.5 13.0154 13.0154 13.0 13.0

...

4.6 4.6 4.6 4.6 10.4 10.4 10.4 10.4

...

Core Core Core Core Core Core Core Core

...

10.0 10.0 9.95 9.95 12.45 12.45 12.5 12.5

...

22.7 22.7 22.7 22.7 18.8 18.8 18.8 18.8

...

Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical

...

-4.9 -4.9 -4.88 -4.88 -4.85 -4.85 -4.9 -4.9

...

66.6 66.6 66.6 66.6 65.2 65.2 65.2 65.2

...

Residential Residential Residential Lobby(non core) Open Mechanical Residential Residential

...

1653 1653 1653 1653 2312 2312 2312 2312

...

77 76 75 74 73 72 71 70

...

3 3 3 2 2 2 2 2

...

...

... 0.065 0.063 0.062 1.870 0.048 -0.174 -0.032 -0.032 ...

481.45 481.45 481.45 607.31 188.54 676.02 364.02 364.02 ...

4.83 4.83 4.83 2.61 9.78 -0.79 2.71 2.71 ...

12,818 13,127 13,435 13,868 14,024 14,603 14,819 15,035 ...

2,873 2,965 3,057 3,152 3,161 3,184 3,267 3,349 ...

2,876 2,957 3,038 3,118 3,141 3,215 3,280 3,346 ...

8,011 8,204 8,397 8,667 8,765 9,127 9,262 9,397 ...

2,394 2,471 2,547 2,626 2,635 2,654 2,722 2,791 ...

2,397 2,464 2,532 2,598 2,617 2,679 2,734 2,788 ...

192.84 192.84 192.84 270.19 97.66 361.87 135.09 135.09 ...

76.77 76.77 76.77 79.12 8.09 19.10 68.64 68.64 ...

67.31 67.31 67.31 66.72 18.82 61.75 54.60 54.60 ...

0 0 0 0 0 0 0 0 ...

33 33 33 33 22 22 22 22 ...

262 262 262 262 166 166 166 166 ...

187 187 187 313 0 487 175 175 ...

0.0 0.0 0 0 0 0 0.0 0.0 ...

0.0 0.0 0 0 6.1 6.1 6.1 6.1 ...

None None None None Open Open Open Open ...

11.6 11.6 11.57 11.57 8.5 8.5 8.5 8.5 ...

6.0 6.0 6 6 4.6 4.6 4.6 4.6 ...

Core Core Core Core Core Core Core Core ...

11.6 11.6 11.6333 11.6333 9.95 9.95 10.0 10.0 ...

31.5 31.5 31.5 31.5 22.7 22.7 22.7 22.7 ...

Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical Mechanical ...

-5.9 -5.9 -5.89 -5.89 -4.88 -4.88 -4.9 -4.9 ...

62.5 62.5 62.5 62.5 66.6 66.6 66.6 66.6 ...

Residential Residential Residential Lobby(non core) Open Mechanical Residential Residential ...

1875 1875 1875 1875 1653 1653 1653 1653 ...

114 113 112 111 110 109 108 107 ...

4a 4a 4a 3 3 3 3 3 ...

...

(kips)

...

(ft)

...

(kips)

...

(ft)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

...

(kips)

Net Fact. Loads

...

(kips)

Net Eccentricity from centroid

...

(kips)

net factored loads per level

...

Dist to Baseline

eccen per level

...

%

Factored Loads DL SDL LL

...

Use

DL

Total Loads SDL LL

...

Dist to Baseline

Loads From This Floor (Unfactored) DL SDL LL

...

%

5.00 -1.01

...

Use

positive eccentricities eccentricities

...

Dist to Baseline

h4 (ft) 21.72 20.75 16.64 9.67

...

%

h3 (ft) 13.08 14.58 12.69 5.90

...

Use

h2 (ft) 5.08 2.52 3.95 1.00

...

Dist to Baseline

h1 (ft) 3.56 3.65 0.00 2.77

...

%

b4 (ft) 38.58 38.58 42.73 38.63

...

Use

b3 (ft) 1.00 1.00 3.08 1.00

...

ft^2

b1 (ft) 18.29 19.29

189 189 189

92 92 92

0 0 0

82.23 82.23 82.23

104.04 104.04 104.04

184.12 184.12 184.12

9,916 9,998 10,080 10,080 10,080 10,080 10,080

11,627 11,731 11,835 11,835 11,835 11,835 11,835

26,726 26,910 27,094 27,094 27,094 27,094 27,094

11,899 11,998 12,096 12,096 12,096 12,096 12,096

13,953 14,078 14,203 14,203 14,203 14,203 14,203

42,761 43,056 43,350 43,350 43,350 43,350 43,350

5.34 5.34 5.34

518.12 518.12 518.12

-0.001 -0.001 -0.001

68,613 69,131 69,649 69,649 69,649 69,649 69,649

3.4.1 Column Load Takedown

Core Columns to Evaluate

Created by: CTM

• These are the levels where we are going to check the columns on the interaction diagram • We are considering each bank to be one column since it is all the same shape • We selected the bottom of each bank where the loads are largest and the top where the eccentricity is greatest to plot on the interaction diagrams. This gives two points per core section per bank that need to be plotted.

E-W Core

Bank 1 Bank 2 Bank 3 Bank 4a

Bottom Top Bottom Top Bottom Top Bottom Top

Eccentricity (ft) 0.000 1.210 -0.015 5.895 0.047 0.834 -0.185 9.031

Load (kips) 47098 30211 29657 15818 15437 6069 5758 2217

Bottom Top Bottom Top Bottom Top Bottom Top

Eccentricity (ft) 0.000 1.426 -0.003 4.373 -0.021 1.870 0.062 4.836

Load (kips) 69649 51330 50665 33861 33379 20138 19530 11346

Bottom Top

Eccentricity (ft) 0.203 10.110

Load (kips) 14882 986

N-S Core

Bank 1 Bank 2 Bank 3 Bank 4a

Top Core

Bank 4b

3.4.1 Column Load Takedown

C-108

Column Interaction Diagrams for Core Segments Under Gravity These diagrams show where the initial wall size estimates need to be increased and reinforced to address the moments resulting from the eccentricity of the core walls above each bank. The core was evaluated with little to no rebar to understand the response of the concrete. Lateral loads have no yet been addressed the sizes will need to be adjusted further after these loads are considered.

E-W Bank 1

C-109

3.4.1 Column Load Takedown

E-W Bank 2

E-W Bank 3

3.4.1 Column Load Takedown

C-110

E-W Bank 4a

N-S Bank 1

C-111

3.4.1 Column Load Takedown

N-S Bank 2

N-S Bank 3

3.4.1 Column Load Takedown

C-112

N-S Bank 4a

C-113

3.4.1 Column Load Takedown

3.4.2 Composite Column Design This sheet summarizes the dimensions of the composite column with an embedded steel shape. It shows the different sizes for Column 1, 2, and 3A & 3B.

Summary Tables

Bank Level 145 134 4 123 111 100 87 3 74 64 2 52 40 29 17 1 5 Lobby

Column 1 C1 Width (in) W14X99 12 W14X99 12 W14X193 18 W14X342 18 W14X145 24 W14X342 24 W14X342 30 W14X99 36 W14X283 36 W14X426 36 W14X90 42 W14X342 42 W14X109 48 W14X132 48

Column Sizing Column 1 C1 Length (in) C1 Bar Size C1 # Bars C1 Tie Size 12 8 0 8 16 8 2 8 18 8 2 8 18 8 6 8 24 8 6 8 24 11 12 8 30 9 4 8 36 10 18 8 36 14 16 8 36 18 18 8 42 18 18 8 42 18 18 8 48 18 18 8 48 18 18 8

C1 Tie Spacing 6 6 9 9 12 12 15 18 18 18 21 21 24 24

Column Sizing Column 2 Bank Level 145 134 4 123 111 100 3 87 74 64 2 52 40 29 17 1 5 Lobby

Column 2 C2 Width (in) W14X99 12 W14X99 12 W14X193 18 W14X342 18 W14X145 24 W14X342 24 W14X342 30

C2 Length (in) 12 16 18 18 24 24 30

C2 Bar Size C2 # Bars C2 Tie Size 8 0 8 8 2 8 8 2 8 8 6 8 8 6 8 11 12 8 9 4 8

3.4.2 Composite Column Design

C2 Tie Spacing 6 6 9 9 12 12 15

C-114

Bank Level 145 134 4 123 111 100 3 87 74 64 2 52 40 29 17 1 5 Lobby

C-115

Column 3A & 3B

C3AB Width(in)

W14X99 W14X311 W14X455 W14X398 W14X605 W14X311 W14X342

24 24 24 30 30 36 36

Column Sizing Column 3A & 3B C3AB Length(in) C3 Bar Size C3 # Bars C3 Tie Size

24 24 24 30 30 36 36

9 9 9 14 14 18 18

3.4.2 Composite Column Design

5 4 9 5 9 9 8

8 8 8 8 8 8 8

C3 Tie Spacing

12 12 12 15 15 18 18

Composite Column Design

Created by:

DF/JL

12/9/2011

This spreadsheet calculates the compressive capacity of a W-shape embedded in concrete using AISC Chapter I2 Bank Location Column

2 Floor 40 1

Color Key:

Yes No

Overall Checks Limitations Pass? Axial Capacity Pass? % Capacity Used

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

YES YES 92.9%

Loading Sheet Factored Tributary Loads Weight of Steel above 52 Weight of Concrete above 52 Weight of Steel between 52-40 Weight of Concrete between 52-40 Total Factored Load

Pu

14,471 295 718 67 193 15,745

kips kips kips kips kips kips

Detailing Requirements 36 48 18 18 16

16*Reinforcing Diameter 48*Tie Diameter 0.5*Min Dimension Tie Spacing Minimum Shear Stud Spacing

in in in in in

AISC I2-1f AISC I2-1f AISC I2-1f AISC I2-1f AISC I2-1f

Inputs Steel Section Column Width Column Length Effective Length Factor Unbraced Height of Column Concrete Comp. Strength Concrete Density Reinforcing Bar Size Reinforcing Bar Diameter

b Lc K H f'c ρc

W14X426 36 in 36 in 1 158 in 14 ksi lbs/ft3 160

dbar

#18 2.257

in

Reinforcing Bar Area

Abar

4

in

Number of bars per side Tie Size Number of Ties Tie Spacing

nbars

9 #8 #5 18

in

nties

3.4.2 Composite Column Design

C-116

2

Tie Area

Atr

0.31

in

Tie Bar Diameter Shear Stud Spacing Cover

dtie

0.625 15 1.5

in in in

s c

Limitations Steel at least 1%? Minimum Transverse reinforcement ok? Reinforcement ratio ok?

YES YES YES

AISC I2-1a AISC I2-1a AISC I2-1a

Parameters 2

Area of Steel Section

As

125

in

Area of Rebar

Asr

72

in

Area of Ties Gross Area

Atr Ag

6 1,296

2

= Abar*nbar

2

in

= Atr * nties

2

in

= b*Lc

2

Area of Concrete

Ac

1,099

in

= Ag - As

Modulus of Elasticity Concrete

Ec

7,573

ksi

= ρc1.5* f'c0.5

Modulus of Elasticity Steel

Es

29,000 ksi

Min. Yield Stress Steel Section

Fy

50

ksi

Min. Yield Stress Bars

Fyr

60

Inertia of Steel Section

Is

1,110

ksi in4

Inertia of Steel Bars Inertia of Concrete

4 Isr 17,035 in 4 Ic 121,823 in

C1 Effective Stiffness

= 2*nbar* π*dbar4/64 + Abard2 = b*Lc3/12 - Is - Isr = 0.1 + 2*(As/ (Ac + As)) < 0.3; AISC I2-6

0.3 2

EIeff 5.56E+08 kip-in

= EsIs + 0.5*Es*Isr + C1*EC*IC; AISC I2-7

Compressive Strength Axial Strength of Steel Section

Ps

6,250

kips

= As*Fy

Axial Strength of Steel Rebar

Psr

4,320

kips

= Asr*Fyr

Axial Strength of Concrete

Pc 13,078 kips

= 0.85 * f'c * Ac

Axial Compressive Strength

Po 23,648 kips

= Ps + Psr + Pc; AISC I2-4

Effective Compressive Strength

Pe 219,799 kips

= π2*EIeff/(K*H)2; AISC I2-5

Nominal Compressive Strength

Pn

= PO*(0.658(Po/Pe)); AISC I2-2

LRFD Compressive Factor Factored Nominal Strength

C-117

Φc ΦcP n

22,607 kips 0.75 16,955 kips

3.4.2 Composite Column Design

3.4.3 Steel Column Design

Created by:

NC

12/9/2012

The steel column design tool assists in designing steel columns from W-shapes for pure axial load as per AISC Steel Construction Manual 13th Edition, Chapter E. Color Key: Bank Floors Column

4 134-150 1 Yes No

User Input Constant/Previous Calc Calc/Lookup Passes Check Fails Check

Material Properties Nominal Steel Strength Reduction Factor Length of Column Effective Length Factor Steel Modulus of Elasticity

Fy Φ L K Es

50 ksi 0.9 158 in 1.0 29,000,000 psi

Section Properties Chosen Section for Column

Wsection W14 x 99

Section Area Radius of Gyration (Strong)

A rx

29.1 6.17

in2 in

Radius of Gyration (Weak)

ry

3.71

Moment of Inertia (Strong)

Ix

1,110

in in4

Moment of Inertia (Weak)

Iy

402

in4

Plastic Section Modulus (Strong)

Zx

173

in3

Plastic Section Modulus (Weak)

Zy

83.6

in3

Section Modulus (Strong)

Sx

157

in3

Section Modulus (Weak)

Sy

55

in3

Polar Moment of Inertia

J

5.37

in4

P

1,042 0.099

kips kips/ft

Geometry and Loads Factored Load (from CLT) Column Self-Weight

wslf nfloors

16

Pself

21

kips

= nfloors*L*wslf

Pu

1,063

kips

= P+Pself

Effective Length (Strong)

Le,x

25.6

= K*L/rx

Effective Length (Weak)

Le,y Leff

42.6

= K*L/ry Max (Le,x , Le,y)

Number of Floors Load from Column Self-Weight Total Factored Load

Chosen Effective Length

42.6

3.4.3 Steel Column Design

C-118

Load Capacity Allowable Squash Stress Elastic Critical Buckling Stress Elastic Buckling Limit Flexural Buckling Stress Maximum Axial Load Reduction Factor Factored Max Axial Load Check:

C-119

ΦFy

45

ksi

Fe

158

kips

Flim

113

Fcr

43.8

ksi

Pmax

1,274

kips

Φ

0.9 1,147 Yes

kips

ΦPmax ΦPmax > Pu?

3.4.3 Steel Column Design

E3-4 4.71(E/Fy)

1/2

If Leff ≤ Flim use E3-2 else use E3-3 = Fcr*A

4.0 Lateral Design 4.1 Building as a Cantilever

121

4.2 MIDAS Gen FEA Summary

124

4.3 Preliminary Core Wall Thickness Calculation - No Outriggers 4.4 Final Core Wall Thickness Calculation - Outriggers 4.5 Core Rebar Design

125

128

131

4.5.1 Design of Core Rebar for Vertical and Horizontal Shear

132

4.5.2 Design of Core Rebar for Flexural Capacity

134

4.5.3 Mathcad for Bank 4 Strong Axis Bending

138

4.6 Energy Method Optimization

156

4.6.1 Optimization Calculations

158

4.6.2 Resizing of Built-Up Members

161

4.0 Lateral Design C-120

4.1 Preliminary Deflection Calculations

Created by:

CYW

5/11/2012

Generate sectional properties of the core wall for a simple cantilever deflection check in MASTAN. Bank: Location:

1 to 4 Core

Bank 1 Properties tc

Wall thickness Centerline radius Centerline circumference

Cc

7 40 251

ft ft ft

Rc

= 2*π*Rc

Outer radius

Ro

43.5

ft

= Rc+tc/2

Inner radius

Ri

36.5

= Rc-tc/2

Moment of inertia (100% solid wall) Opening length in core/gap Number of gaps Total open length in core Percentage of solid wall

Ic

1,418,209 15 4 60 76%

ft 4 ft

Log Ng Lo Ps

Transformed moment of inertia (with openings) Bank 1 height Concrete strength

It

h f'c Econc

Concrete modulus Total Bank 1 wind load from RWDI Distributed wind load

wtotal w

= π/4*(Ro2-Ri2)

ft ft

= Log*Ng

= 100% - L o/Cc 4

1,079,637 513.5 14,000

ft ft psi

= Ic*Ps

6,744,331 2,108 4.1

psi kips kips/ft

= 57,000*f'c1/2 ; ACI 318-08 8.5

= wtotal/h

Bank 2 Properties tc

Wall thickness Centerline radius Centerline circumference

Cc

4 39 245

ft ft ft

Rc

= 2*π*Rc

Outer radius

Ro

41.0

ft

= Rc+tc/2

Inner radius

Ri

37.0

= Rc-tc/2

Moment of inertia (100% solid wall) Opening length in core/gap Number of gaps Total open length in core Percentage of solid wall

Ic

747,385 15 4 60 76%

ft ft4

Log Ng Lo Ps

Transformed moment of inertia (with openings) Bank 2 height Concrete strength Concrete modulus Total Bank 2 wind load from RWDI Distributed wind load

C-121

It

h f'c Econc wtotal w

564,385 448 14,000 6,744,331 2,111 4.7

= π/4*(Ro2-Ri2)

ft ft

= Log*Ng

= 100% - L o/Cc ft4 ft psi

= Ic*Ps

psi kips kips/ft

= 57,000*f'c1/2 ; ACI 318-08 8.5

4.1 Preliminary Deflection Calculations

= wtotal/h

Bank 3 Properties tc

Wall thickness Centerline radius Centerline circumference

Cc

3 38 239

ft ft ft

Rc

= 2*π*Rc

Outer radius

Ro

39.5

ft

= Rc+tc/2

Inner radius

Ri

36.5

= Rc-tc/2

Moment of inertia (100% solid wall) Opening length in core/gap Number of gaps Total open length in core Percentage of solid wall

Ic

517,962 15 4 60 75%

ft 4 ft

Log Ng Lo Ps

Transformed moment of inertia (with openings) Bank 3 height Concrete strength

It

h f'c Econc

Concrete modulus Total Bank 3 wind load from RWDI Distributed wind load

wtotal w

387,800 487 14,000 6,744,331 2,544 5.2

2

2

= π/4*(Ro -Ri )

ft ft

= Log*Ng

= 100% - L o/Cc 4

ft ft psi

= Ic*Ps

psi kips kips/ft

= 57,000*f'c1/2 ; ACI 318-08 8.5

= wtotal/h

Bank 4 Properties tc

Wall thickness Centerline radius Centerline circumference

Cc

2 34 210

ft ft ft

Rc

= 2*π*Rc

Outer radius

Ro

34.5

ft

= Rc+tc/2

Inner radius

Ri

32.5

= Rc-tc/2

Moment of inertia (100% solid wall) Opening length in core/gap Number of gaps Total open length in core Percentage of solid wall

Ic

236,429 15 2 30 86%

ft ft4

Log Ng Lo Ps

Transformed moment of inertia (with openings) Bank 4 height Concrete strength Concrete modulus Total Bank 4 wind load from RWDI Distributed wind load

It

h f'c Econc wtotal w

202,732 448 14,000 6,744,331 2,394 5.3

= π/4*(Ro2-Ri2)

ft ft

= Log*Ng

= 100% - L o/Cc 4

ft ft psi

= Ic*Ps

psi kips kips/ft

= 57,000*f'c1/2 ; ACI 318-08 8.5

4.1 Preliminary Deflection Calculations

= wtotal/h

C-122

MASTAN Output

Undeformed

Maximum deflection

C-123

Deformed

10.79

ft

4.1 Preliminary Deflection Calculations

4.2 MIDAS Gen FEA Summary

Created by: CYW 5/11/2012

A detailed three dimensional structural analysis of the Spire was conducted using MIDAS Gen. All material properties and baseline element shapes were taken from initial lateral and gravity design. Vertical members, outriggers and belt trusses, and core wall thicknesses were resized throughout the iterative modeling process based on element forces and moments, and serviceability requirements.

Modeling Approach

Loading Conditions

• The model spans from the lobby at ground elevation to the top of level 144. • The mega-columns and core wall at the ground elevation are fixed to the ground. • All belt trusses and outriggers are modeled with pin-pin end-releases. • All other structural elements have been applied fixed-fixed end-releases. • Core walls are modeled as thick plate element with drilling DOF. • Outriggers are modeled as truss elements. • X-bracing belt trusses between Bank 1 and Bank 2 are modeled as beam elements. • All other belt trusses are modeled as truss elements. • Composite floor beams are modeled as W-Shape Steel Reinforced Concrete (SRC) in cross section properties. The width chosen in these SRC beams are based on the effective width of the composite beam from the gravity design. • Cantilevers and angled floor girders outside of the exterior column grid are not modeled. • Hypothetical tuned mass damper and mechanical floors at the Spire’s peak are not modeled. • Concrete strength of f'c = 14,000 psi is used in all vertical concrete elements. • Concrete strength of f'c = 4,000 psi is used in all horizontal concrete elements. • ASTM A992 standard with Fy = 50,000 psi steel is used.

• The wind data from wind tunnel testing is used directly for strength design. • The wind data from wind tunnel testing is reduced by a factor of 0.83 for serviceability design. • All lateral forces are applied along the z-axis at each floor. • Unfactored dead loads and live loads from the column load takedown were applied to nodes at column ends. • The total unfactored dead load and live load for the core was split equally into nodal forces to the nodes connecting the radial girders to the core walls or link beams. • MIDAS Gen calculates material self-weight in the analysis, thus no self-weight is considered in applied dead loads. • 54 load combinations are used for strength design checks. • 24 load combinations are used for serviceability design checks.

z x Undeformed Shape in MIDAS Gen model

C-124

4.2 MIDAS Gen FEA Summary

C-125

Created by: CJB & ADV

1/20/2012

160 13.2

Ec

ρc

h

14

6744331

f'c

626,016

983,313

Ac

Ic Vc

Concrete Area Concrete Moment of Inertia Concrete Volume

LL Wc

Mw Ms

Floor Live Load Core Self Weight Above

Wind Moment

9,410,000 8,821,667

84,464 354,663

81,958

6.93

Allowable Compression

-0.887

-3.610

Tapp

fcomp fr

Applied Tension

Allowable Tension

6.468

Applied Compression

1

Capp

Bank

59,908 197,333

56,024

ksi

-2.989

4.647

2

5,160,000 5,485,154

ksi

Maximum Applied Stresses and Allowable Stresses

Seismic Moment

DL

Floor Dead Load

Loads and Moments per Bank per Floor

961,063

1,394,364

t Ro

Thickness Outer Radius 1395

1910

Ri

2 40 34 6 40

1 1 34 8 42

pcf ft

ksi

ksi

Bank Floor Inner Radius

Core Properties per Bank per Floor

Density of concrete Floor-to-floor height

Concrete Strength Conc. Mod. of Elasticity

Concrete and Building Properties

-1.463

2.066

4a

570,000 802,276

21,238 30,395

15,356

125,278

175,954

500

4a 111 25 3 28 ft^2

ft ft ft

kip kip

kip

ft^3

-0.465

1.050

4b

ksi

ksi

120,000 kip-ft 225,348 kip-ft

13,496 10,351

6,810

64,692

110,597 ft^4

327

4b 130 25 2 27

Passes Check Fails Check

Calc/Lookup

Constant/Previous Calc.

User Input

= 7.5 * (f'c)^.5; ACI318 9.5.2.3 Modulus of Rupture

= 0.55*φ * f'c; ACI 318 14.5.2

These are the max values from the load combinations below. Green: value is less than allowable. Red: value is greater than allowable.

Unfactored moments from Seismic forces in Seismic Loads.xls

Unfactored moments From Wind Tunnel Loads in Wind Loads.xls

= ρc * Σ (Concrete Volume Above)

Unfactored loads calculated from cumulative forces on core wall sections found in "Column Load Takedown.xls"

= (# of floors) * Ac * h

= (π/4) * (Ro4 - Ri4)

= π * (Ro2 - Ri2)

= Ri + t

Core wall designed for critical stresses at the base of the listed floor (i.e. stresses from floor 40 dictate core wall design for floors 40-73)

Notes

Yes No

4.2 Preliminary Core Wall Thickness Calculation - No Outriggers

-2.698

3.552

3

2,420,000 2,859,767

37,076 97,170

33,366

417,344

495,618

855

3 74 32 4 36

= 57000*√(f'c); ACI318 8.5.1

COLORS KEY:

This spreadsheet uses inputed gravity loads and moments induced by lateral seismic and wind forces to calculate the required core thickness. The calculations are only based on the core for lateral resistance; outriggers are not included. For outriggers, see the sister sheet to this one, "Core Wall Calculation - Outriggers". The user can change the core properties to design for the moments, based on 6 of the ASCE7 load combinations.

4.2 Preliminary Core Wall Thickness Calculation - No Outriggers

C-126

FDL σc

FDL FLL σc

fb

ft

σc σt

Lateral Compression Stress

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

FLL fa

fb

ft

σc σt

Lateral Compression Stress

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

FDL FMs

Floor Factored Dead Load Factored Seismic Moment Factored Live Load Axial Compression Stress

Load Combination 5: 1.2D + 1.0E + L

LL fa

FDL FMw

Floor Factored Dead Load Factored Wind Moment Live Load Axial Compression Stress

Load Combination 4: 1.2D + 1.6W + L

Floor Factored Dead Load Factored Live Load Net Compression Stress

Load Combination 2: 1.2D + 1.6L

Floor Factored Dead Load Net Compression Stress

Load Combination 1: 1.4D

2.909 -0.262

N/A

-1.585

1.585

40 304,028 5,485,154 59,908 1.323

4.057

-1.845

1.845

1 523,945 8,821,667 84,464 2.212

4.198 -0.574

5.361

-2.386

2.386

-0.937

-3.149

3.149

40 304,028 8,256,000 59,908 1.812

1.991

2.396

1 523,945 15,056,000 84,464 2.212

40 304,028 95,853

40 354,700 1.766

1 523,945 135,142

1 611,269 2.222

-0.610

1.163

-0.887

0.887

111 54,901 802,276 21,238 0.277

N/A

2.066

-1.008

1.008

111 54,901 912,000 21,238 1.059

1.236

111 54,901 33,981

111 64,052 0.890

-0.258

0.506

-0.382

0.382

130 20,593 225,348 13,496 0.124

N/A

1.050

-0.326

0.326

130 20,593 192,000 13,496 0.725

0.897

130 20,593 21,594

130 24,025 0.511

ksi

ksi

ksi

ksi

kip kip-ft kip ksi

ksi

ksi

ksi

ksi

kip kip-ft kip ksi

kip kip ksi

kip ksi

= fa + ft

= fa + fb

= -fb

= FMs*Ro/Ic

= (FDL + FLL)/Ac

= 1.0 * (LL); ASCE 7-05 2.3.2

= 1.2 * (DL+Wc); ASCE 7-05 2.3.2 = 1.0 * (Ms); ASCE 7-05 2.3.2

= fa + ft

= fa + fb

= -fb

= FMw*Ro/Ic

= (FDL + FLL)/Ac

= 1.2 * LL; ASCE 7-05 2.3.2

= 1.2 * (DL+Wc); ASCE 7-05 2.3.2 = 1.6 * Mw; ASCE 7-05 2.3.2

= (FDL + FLL)/Ac

= 1.2* (DL+Wc); ASCE 7-05 2.3.2 = 1.6* LL; ASCE 7-05 2.3.2

= FDL/Ac

= 1.4* (DL+Wc); ASCE 7-05 2.3.2

4.2 Preliminary Core Wall Thickness Calculation - No Outriggers

-0.738

2.147

-1.443

1.443

74 156,643 2,859,767 37,076 0.704

-0.379

3.527

-1.953

1.953

74 156,643 3,872,000 37,076 1.574

1.755

74 156,643 59,322

74 182,751 1.485

Calculations of Net Compression and Net Tension Stresses at the base of each bank of the Spire, using ASCE 7-05 Load Combinations (ASCE 7-05 Section 2.3.2):

C-127

fb

ft

σc σt

Lateral Compression Stress

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

ft

σc σt

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress 2.414 -0.756

3.274

-1.585

1.585

0.829

-0.417

-1.845

1.845

1.429

fa

fb

Lateral Compression Stress

40 228,021 5,485,154

-2.989

-3.610

1 392,959 8,821,667

4.647

-3.818

3.818

0.829

40 228,021 13,209,600

6.468

-5.039

5.039

1.429

1 392,959 24,089,600

FDL FMs

Floor Factored Dead Load Factored Seismic Moment Axial Compression Stress

Load Combination 7: 0.9D + 1.0E

fa

FDL FMw

Load Combination 6: 0.9D + 1.6W

Floor Factored Dead Load Factored Wind Moment Axial Compression Stress

-0.737

1.036

-0.887

0.887

0.150

111 41,176 802,276

-1.463

1.762

-1.613

1.613

0.150

111 41,176 1,459,200

ksi

ksi

ksi

ksi

ksi

-0.326

0.438

-0.382

0.382

0.056

ksi

ksi

ksi

ksi

ksi

130 15,445 kip 225,348 kip-ft

-0.465

0.577

-0.521

0.521

0.056

130 15,445 kip 307,200 kip-ft

= fa + ft

= fa + fb

= -fb

= FMs*Ro/Ic

= (FDL + FLL)/Ac

= 0.9 * (DL+Wc); ASCE 7-05 2.3.2 = 1.0 * (Ms); ASCE 7-05 2.3.2

= fa + ft

= fa + fb

= -fb

= FMw*Ro/Ic

= (FDL + FLL)/Ac

= 0.9 * (DL+Wc); ASCE 7-05 2.3.2 = 1.6 * Mw; ASCE 7-05 2.3.2

4.2 Preliminary Core Wall Thickness Calculation - No Outriggers

-1.015

1.870

-1.443

1.443

0.427

74 117,483 2,859,767

-2.698

3.552

-3.125

3.125

0.427

74 117,483 6,195,200

C-128

Created by: ADV

1/25/2012

160 13.2

Density of concrete Floor-to-floor height

626,016

538,473 0.7

1,771,295

983,313

Io φo

It Vc

Column Moment of Inertia Outrigger Reduction Factor

Transformed Moment of Inertia Concrete Volume

9,410,000

8,821,667

LL Wc

Mw

Ms

Floor Live Load Core Self Weight Above

Wind Moment

Seismic Moment

84,464 354,663

DL

Floor Dead Load

Loads and Moments per Bank per Floor

81,958

1,098,964

1,394,364

Ic

Core Thickness Core Outer Radius

5,485,154

5,160,000

59,908 197,333

56,024

197,001 0.7

961,063

1395

1910

Ac

Concrete Area Core Moment of Inertia

2 40 34 6 40

Ri t Ro

pcf ft

ksi

ksi

1 1 34 8 42

Floor Core Inner Radius

Bank

Core and Outrigger Properties per Bank per Floor

6744331

Ec

ρc h

Conc. Mod. of Elasticity

14

f'c

Concrete Strength

Concrete and Building Properties

2,859,767

2,420,000

37,076 97,170

33,366

417,344

520,438

35,457 0.7

495,618

855

3 74 32 4 36

225,348

120,000

13,496 10,351

6,810

64,692

113,432

4,050 0.7

110,597

327

4b 130 25 2 27

kip-ft

kip-ft

kip kip

kip

ft^3

ft^4

ft^4

ft^4

ft^2

ft ft ft

User Input

Passes Check Fails Check

Calc/Lookup

Constant/Previous Calc.

Unfactored moments from Seismic forces in Seismic Loads.xls

Unfactored moments From Wind Tunnel Loads in Wind Loads.xls

= ρc * Σ Concrete Volume Above

Unfactored loads calculated from cumulative forces on core wall sections found in "Column Load Takedown.xls"

= (# of floors) * Ac * h

Itotal = Icore + φo*Icolumns

From "Column System Properties.xlsx"

= (π/4) * (Ro4 - Ri4)

= π * (Ro2 - Ri2)

= Ri + t

Core wall designed for critical stresses at the base of the listed floor (i.e. stresses from floor 40 dictate core wall design for floors 40-73)

Notes

Yes No

4.3 Final Core Wall Thickness Calculation - Outriggers

802,276

570,000

21,238 30,395

15,356

125,278

184,858

12,721 0.7

175,954

500

4a 111 25 3 28

= 57000*√(f'c); ACI318 8.5.1

COLORS KEY:

This spreadsheet uses inputed gravity loads and moments induced by lateral seismic and wind forces to calculate the required core thickness. The calculations are only based on the core for lateral resistance; outriggers are not included. For outriggers, see the sister sheet to this one, "Core Wall Calculation - Outriggers". The user can change the core properties to design for the moments, based on 6 of the ASCE7 load combinations.

4.3 Final Core Wall Thickness Calculation - Outriggers

C-129

Maximum Applied Stresses and Allowable Stresses

6.93 -0.887

fcomp

Allowable Compression Allowable Tension

ksi ksi

10% 16%

17% 30%

3% 6%

-2.549

3 3.434

2% 5%

-1.385

4a 2.018

1% 3%

-0.452

4b 1.042 ksi

ksi

FDL FLL σc

FDL σc

fb

ft

σc σt

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

FDL FMw LL fa

Lateral Compression Stress

1.6 * Wind Moment Live Load Axial Compression Stress

Floor Factored Dead Load

Load Combination 4: 1.2D + 1.6W + L

Floor Factored Dead Load Factored Live Load Net Compression Stress

Load Combination 2: 1.2D + 1.6L

Net Compression Stress

Floor Factored Dead Load

Load Combination 1: 1.4D

3.899 -0.275

-0.267

-2.087

2.087

8,256,000 59,908 1.812

40 304,028

40 304,028 95,853 1.991

40 354,700 1.766

4.691

-2.479

2.479

15,056,000 84,464 2.212

1 523,945

1 523,945 135,142 2.396

1 611,269 2.222

-0.286

3.434

-1.860

1.860

3,872,000 37,076 1.574

74 156,643

74 156,643 59,322 1.755

74 182,751 1.485

N/A

1.042

-0.317

0.317

192,000 13,496 0.725

130 20,593

130 20,593 21,594 0.897

130 24,025 0.511

ksi

ksi

ksi

ksi

kip-ft kip ksi

kip

kip kip ksi

kip ksi

= fa + ft

= fa + fb

= -fb

= FMw*Ro/Ic

= (FDL + FLL)/Ac

= 1.6 * Mw; ASCE 7-05 2.3.2 = 1.2 * LL; ASCE 7-05 2.3.2

= 1.2 * (DL+Wc); ASCE 7-05 2.3.2

= (FDL + FLL)/Ac

= 1.2* (DL+Wc); ASCE 7-05 2.3.2 = 1.6* LL; ASCE 7-05 2.3.2

= FDL/Ac

= 1.4* (DL+Wc); ASCE 7-05 2.3.2

= 0.55*φ * f'c; ACI 318 14.5.2 = 7.5 * (f'c)^.5; ACI318 9.5.2.3 Modulus of Rupture

These are the percent reductions in Maximum Applied Stresses when including the outriggers

These are the max values from the load combinations below. Green: value is less than allowable. Red: value is greater than allowable.

4.3 Final Core Wall Thickness Calculation - Outriggers

N/A

2.018

-0.959

0.959

912,000 21,238 1.059

111 54,901

111 54,901 33,981 1.236

111 64,052 0.890

Calculations of Net Compression and Net Tension Stresses at the base of each bank of the Spire, using ASCE 7-10 Load Combinations (ASCE 7-10 Section 2.3.2):

fr

-2.510

-2.538

Tapp

Applied Tension % Reduction with Outriggers In Applied Compression In Applied Tension

2 4.168

1 5.395

Capp

Bank Applied Compression

C-130

ft

σc σt

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

ft

σc σt

Lateral Compression Stress

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

fa

fb

ft

σc σt

Axial Compression Stress

Lateral Compression Stress

Lateral Tensile Stress

Net Compression Stress Net Tensile Stress

FDL FMs

Floor Factored Dead Load Factored Seismic Moment

Load Combination 7: 0.9D + 1.0E

fa

fb

Axial Compression Stress

FDL FMw

Floor Factored Dead Load Factored Wind Moment

Load Combination 6: 0.9D + 1.6W

fb

Lateral Compression Stress

Factored Live Load Axial Compression Stress

FDL FMs FLL fa

Load Combination 5: 1.2D + 1.0E + L

Floor Factored Dead Load Factored Seismic Moment

2.215 -0.557

-0.024

-1.386

1.386

0.829

2.881

-1.453

1.453

1.429

40 228,021 5,485,154

-2.510

-2.538

1 392,959 8,821,667

4.168

-3.339

3.339

0.829

5.395

-3.967

3.967

1.429

40 228,021 13,209,600

N/A

N/A

1 392,959 24,089,600

2.840

-1.386

1.386

40 304,028 5,485,154 95,853 1.454

3.849

-1.453

1.453

1 523,945 8,821,667 135,142 2.396

-0.947

1.801

-1.374

1.374

0.427

74 117,483 2,859,767

-2.549

3.403

-2.976

2.976

0.427

74 117,483 6,195,200

-0.589

2.159

-1.374

1.374

74 156,643 2,859,767 59,322 0.785

-0.316

0.429

-0.372

0.372

0.056

130 15,445 225,348

-0.452

0.564

-0.508

0.508

0.056

130 15,445 307,200

-0.219

0.526

-0.372

0.372

130 20,593 225,348 21,594 0.153

ksi

ksi

ksi

ksi

ksi

kip kip-ft

ksi

ksi

ksi

ksi

ksi

kip kip-ft

ksi

ksi

ksi

ksi

kip kip-ft kip ksi

= fa + ft

= fa + fb

= -fb

= FMs*Ro/Ic

= (FDL + FLL)/Ac

= 0.9 * (DL+Wc); ASCE 7-05 2.3.2 = 1.0 * (Ms); ASCE 7-05 2.3.2

= fa + ft

= fa + fb

= -fb

= FMw*Ro/Ic

= (FDL + FLL)/Ac

= 0.9 * (DL+Wc); ASCE 7-05 2.3.2 = 1.6 * Mw; ASCE 7-05 2.3.2

= fa + ft

= fa + fb

= -fb

= FMs*Ro/Ic

= (FDL + FLL)/Ac

= 1.0 * (LL); ASCE 7-05 2.3.2

= 1.2 * (DL+Wc); ASCE 7-05 2.3.2 = 1.0 * (Ms); ASCE 7-05 2.3.2

4.3 Final Core Wall Thickness Calculation - Outriggers

-0.694

0.994

-0.844

0.844

0.150

111 41,176 802,276

-1.385

1.685

-1.535

1.535

0.150

111 41,176 1,459,200

-0.521

1.167

-0.844

0.844

111 54,901 802,276 33,981 0.323

C-131

Bank 4

Bank 3

Bank 2

Bank 1

4.1 4.2

NS EW

NS EW

NS EW

Rebar Summary

18 8

14 14

18 18

18 18

Horizontal Shear Bar Size Spacing in

7 17

10 9

8 9

6 6

6 6

8 7

18 18

10 10

14 as vertical shear 14 as vertical shear

16 as vertical shear 12 as vertical shear

9 as vertical shear 10 as vertical shear

12 as vertical shear 12 as vertical shear

Flexural Note: in all cases, vertical shear rebar was

4.5 Core Rebar Design

Vertical Shear Bar Size Spacing in

In Banks 1, 2, and 3, the cores work in pairs to resist moment. The North-South cores work together to resist moment about the x-axis, while the East-West cores work together to resist moment about the yaxis. On the 4th Bank, there are only two cores, North and South. They work together to resist the moment about the x-axis, but have to work individually to resist the moment about the y-axis.

In all cases, the vertical reinforcing bars were sufficient for flexure as well.

Each core section is designed for the shear in it's particular direction; the North-South Core Sections are design for shear in the North-South direction, etc.

Notes

4.5 Core Rebar Design

Y

4.5.1 Design of Core Rebar for Vertical and Horizontal Shear Created by:

KMC

5/9/2012

Typical calculation shown for Bank1, North-South Core Section. • Spreadsheet takes the loads (shear and axial) from MIDAS, and, using the sizes of MIDAS' representation of the core, calculates the required rebar to resist horizontal shear. • There is no vertical shear, so the vertical reinforcing is determined purely from the code regulations. The shears chosen are the worst case, as are the axial loads. The form of the hand calc was taken from PCA Notes on ACI 318-08, page 21-27 through 21-29; all references are to ACI 318-08

Inputs Max Horizontal Shear

Vu,hor

23,996

kips

Max Vertical Shear

Vu, ver

0

kips

Axial Force

Pu

38,521

kips

Compressive Strength of Concrete

f'c

14,000

psi

Wall Thickness

h

84

in

Wall Length

lw

503

in

Wall Height

hw

6,162

in

d

402

in

Approximate Structural Depth

= 0.8lw; 11.9.4

Maximum Permitted Concrete Shear Strength φ Max Shear Strength φVn okay?

φ Vn φVn>Vu, hor?

0.75 29984 Yes

11.9.3 kips

= φ10sqrt(f'c)hd; 11.9.3

4.5.1 Design of Core Rebar for Vertical and Horizontal Shear

C-132

Shear Strength Provided by Concrete lw/2

251

in

hw/2

3,081

in

Position of critical shear Moment at Critical Section

y in 251 Mu 141,830,758 kips-in kips Shear Strength Provided by Concrete Vc 2,843

= min(lw/2, hw/2); 11.9.7 = (Vu, hor)(hw - y) *see below

Horizontal Shear Reinforcement Horizontal shear designed in accordance with 11.9.9

Fy

Yield Strength of Steel

Av/s

Steel Area/Spacing Ratio Bar Size

#

60 1.21

ksi in2/in

= (Vu, hor - φVc)/(φFyd); eq. 11-29

18

Area of Chosen Bar Size

Abar

4.00

in2

Max Spacing

smax

6.62

in

= min(lw/5, 3h, 18); 11.9.9.3

6

in in2

= h*sselected

sselected

Selected Spacing

Ag

Gross Area Ratio of Steel to Concrete spacing small enough? enough rebar?

504

ρsteel sselected Pu?

YES

Web Local Yielding at 3 Column Node (Top) (AISC J.10.1) Reduction Factor Location of force from edge Dist. from flange to web weld Bearing Length Factored Design Strength

Φ x k N ΦRn

1.0 144 7.00 36 42,600

ΦRn > Pu/(# stiffeners + 1) ?

in in in kips

= L*12 /2 = bf-MC = (5k + N)*Fy*tw*Φ ; J10-2

YES

Web Crippling at Top from Mega-Columns (AISC J.10.3) Reduction Factor Location of Force from Edge Bearing Length Nominal Strength Factored Design Strength

Φ x N Rn

0.75 144.00 36.00 61,653

in in kips

= L*12 /2 = bf-MC

ΦRn

46,240

kips

((E*Fy*tf)/tw)0.5 ; J10-4

ΦRn > Pn/(# stiffeners + 1) ?

= Φ*0.80*tw2*(1+3(N/d)*(tw/tf)1.5)*

YES

Check Bearing Strength at Bottom from Shaft Column (AISC J7) Reduction Factor Projected Bearing Area Nominal Strength Design Strength

Φ Apb

0.75 720

in2

= DMC*bf-MC

Rn

64,800

kips

= 1.8*Apb*Fy ; J7-1

ΦRn

48,600

kips

= Φb*Rn

ΦRn > Pu?

YES

Web local Yielding at Bottom from Shaft Column (AISC J.10.1) Reduction Factor Location of force from edge Dist. from flange to web weld Bearing Length Factored Design Strength

Φ x k N ΦRn

ΦRn > Pu/(# stiffeners + 1) ?

1.00 100 7.00 20.0 33,000

in in in kips

= bf-MC = (5k + N)*Fy*tw*Φ ; J10-2

YES

C-192

5.2.1 Mega-Column to Caisson Connection

Web Crippling at Bottom from Shaft Column (AISC J.10.3) Reduction Factor Location of Force from Edge Bearing Length Nominal Strength Factored Design Strength

Φ x N Rn

0.75 20 6.0 61,653

in kips

= bf-MC = Φ*0.40*tw2*(1+3(N/d)*(tw/tf)1.5)*

ΦRn

46,240

kips

((E*Fy*tf)/tw)0.5 ; J10-4

ΦRn > Pn/(# stiffeners + 1) ?

YES

Check Shaft Column Welds in Tension Permeter of Column Length of Weld

P Lw

144 144

in in

Throat Thickness

wt

2.50

in

Nominal Strength of Weld

Fw

70

ksi

Effective Area of Weld Reduction Factor Strength Capacity of Weld

Aw Φ ΦRn

360 0.80 12,096

in2

= L*w

kips

= Φ*0.60*FEXX*Aw ; Table J2.5

Tu

11,744

kips

Required Tension Force Check ΦRn > *

Tu*

YES

Compare Against half of the tension since there are Two "Shaft Columns"

Checkout Shaft Column for Pullout and Tension Forces Area of Steel Shape Reduction Factor Tensile Strength Factored Tensile Strength Required Tensile Strength Check ΦPn> *

A Φ Pn

272 0.9 13,600

in2

ΦtPn

12,240

kips

Tu

11,744

kips

Tu*

= Fy*A ; D2-1

kips

YES

Compare Against half of the tension since there are Two "Shaft Columns"

Determine the Embedment Length of Column in Shaft Diameter of Column* Yield Strength of Shaft Column

d Fy

36 50

in ksi

Concrete Compressive Strength

f'c

14

ksi

Embedment Length

ld

761

in

ld Embedment Length Is Current Embedment Length Okay? *Assume Column is a circle, diameter = depth

63.4

ft YES

= Dsc

= fy*db/(25*(f'c)0.5) ; ACI 318 - Chapter D

C-193

5.2.1 Mega-Column to Caisson Connection

5.2.2 Caisson Cap Moment Reinforcement

Created By:

JL

4/29/2012

Calculates the required reinforcing area based on the loads generated from Midas Gen. The area of steel is calculated using the Whitney Stress Block for concrete and is then checked against minimum steel equations found in CRSI 2008 Design Guide. Color Key Location Bottom of Mega-Column User Input Connection Typ. Connection Constant/Previous Calc. Calc/Lookup Moment Coming Down from Mega-Column Yes Passes Check Mu-x 3,486 kips-ft Moment - X No Fails Check MegaMu-x 41,832 kips-in Moment - X Column 3 Column Mu-y 2,902 kips-ft Moment - Y Load Node Beam Mu-y 34,824 kips-in Moment - Y

Caisson Cap Dimensions and Properties Width of Caisson Length of Caisson Height of Caisson Concrete Compressive Strength

b L h f'c

18 28 22 14

Density of Concrete

ρc

150

Modulus of Elasticity of Concrete

Ec 213,274 ksi

Rebar Yield Strength

fyr

Modulus of Elasticity of Steel Bar Size of rebar Diameter of rebar Area of Reinforcing bar

60

ft ft ft ksi lb/ft3

Caisson Cap Shaft Column = 57,000*f'c0.5

ksi

Es 29,000 ksi #18 dbar 2.257 in Abar 4.00 in2

Calculate the Required Number of Bars Along the x Direction (Short Bars) Depth to centroid of rebar Reduction Factor for Moment Required Area of Steel

dx Φ Asr-req 4/3*Asr-req

Asr min Calculations

254 0.9 3.05 4.07

160 160

Required Number of Bars

nb

40

Spacing

sx

5.99

Spacing < Min( db or 1")?

in2 in

in

* See equation at the end of sheet

2

= 4/3 * As-req

2

= (3*(f'c)0.5*L*dx)/fy

i 15,958 in ii 284,336 in2 iii Asrmin

Controlling Asr-min

= H - 6" - 3" - d b/2

in

2

in2

= (200*L*dx)/fy = 0.0018*L*H = Min(i,ii,iii) = As-min/As

in

= (L - nb*db) / db +1

YES

C-194

5.2.2 Caisson Cap Moment Reinforcement

Calculate the Required Number of Bars Along the Y direction (Long Bars) dy Φ

Depth to centriod of rebar in Y Reduction Factor for Moment Required Area of Steel

Asr-req 4/3*Asr-req

252 0.9 2.56 3.42

= H - 6" - 3" - d b -db/2

in

** See equation at end of sheet

in

2 2

i 10,168 in 2 ii 281,808 in

Asr min Calculations

iii Controlling As-min Required Number of Bars

Asr min

103 103

nb

26

sy

Spacing Spacing < Min( db or 1")?

3.07

2

in in2

= 4/3 * As-req = (3*(f'c)0.5*b*dy)/fy = (200*b*dy)/fy = 0.0018*b*H = Min(I,ii,iii) = As-min/As

in

2

= (b - nb*db) / (db +1)

YES

* Equation for As-req for Moment about X axis (Short Bars) ( ∗

∗

=

∗ fy2 ) 2 − 4 ∗ ( ) ∗ Mux 2 ∗ 0.85 ∗ f c ∗ ∗ fy2 2∗( ) 2 ∗ 0.85 ∗ f c ∗

)− ( ∗

∗

** Equation for As-req for Moment about the Y axis ( Long Bars) ( ∗ =

∗

∗ fy2 ) 2 − 4 ∗ ( ) ∗ Muy 2 ∗ 0.85 ∗ f c ∗ ∗ fy2 2∗( ) 2 ∗ 0.85 ∗ f c ∗

)− ( ∗

∗

C-195

5.2.2 Caisson Cap Moment Reinforcement

5.3 Outrigger Connections 5.3.1 Bottom of Outrigger to Column Connection

197

5.3.2 Top of Outrigger to Core

199

Outriggers

5.3 Outrigger Connections C-196

5.3.1 Bottom of Outrigger to Column Connection

Created by: JD

4/21/12

Design tool for the outrigger truss to the exterior columns using welds. The radial girder will be designed using the moment resisting girder connection spreadsheet. Bank: 4 Location: Typical Column

Color Key:

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

Plates Outrigger Column

Girder

Outrigger to Column Connection PASS

Design Adequate? Vertical Load at Connection

Ru

2500

Kips

From Midas Gen Model

Girder Properties Girder section Beam flange width Beam flange thickness

Wsection 14 x 730 bf 17.9 in tf 4.91 in tw d K1

3.07 22.4 2.75

in in in

Plate thickness

tp

3.50

in

Plate length

Lp

26.0

in

Plate width

wp

20.0

in

plate yielding strength

Fy

50

ksi

plate ultimate strength

Fu

65

ksi

2730

kips

Beam web thickness Beam depth Beam k1

Plate Properties

Plate Shear Yielding Shear yielding strength

ΦRn ΦRn ≥ Ru?

= 0.6*Fy*Lp*tp ; AISC J4-1

YES

C-197

5.3.1 Bottom of Outrigger to Column Connection

Plate Shear Rupture Net area of shear plane Plate shear rupture strength

Anv

91.00

ΦRn

2662

ΦRn ≥ Ru?

YES

in2 kips

= (Lp-(n*db+1/8))*tp

in2

= Lp*MIN(tp,tw)

= (0.75*0.6*Fu*Anv) ; AISC J4-4

Block Shear Rupture Agv

Gross area of shear plane

79.82

Ant

61.4

ΦRn

2

= (wp-(db+1/8))*MIN(tp,tw)

5655

in kips

ΦRn

4789

kips

= 0.75(0.6*Fy*Agv+Fu*Ant) ; AISC J4-5

MIN ΦRn ≥ Ru?

YES

Net area of tension plane Block shear rupture strength (min ΦRn)

= 0.75(0.6*Fu*Anv+Fu*Ant) ; AISC J4-5

Weld- Fillet Weld Electrode classification number Size of weld Number of Welds Type 1 Throat thickness Length of the weld type 1

FEXX 70 size 2 2 wt 1.414 Lw 25.00

Weld 1 strength Number of welds type 2 Length of the weld type 2

ΦRn1

Weld 2 strength

ΦRn2

891

ΦRn

3118

ΦRn ≥ Ru?

YES

Total weld strength

Lw

2227 2 10.00

ksi in in

= 0.707*size

in

one side of plate

kips

= 0.75*te*Lw*0.6*FEXX ; AISC J2-4

in Kips

= 0.75*te*Lw*0.6*FEXX ; AISC J2-4 = ΦRn1+ΦRn2

C-198

5.3.1 Bottom of Outrigger to Column Connection

5.3.2 Top of Outrigger to Core 5.3.2.1

Gusset Plate Design Inputs

200

5.3.2.2

Single Bolt Shear Capacity

203

5.3.2.3

Bolt and Plate Checks for Outrigger Connection

204

5.3.2.4

Bolt and Plate Checks for Girder Connection

207

5.3.2.5

Weld Design for Gusset Plate to Embedded Steel Frame 210

5.3.2.6

Steel Frame Embedded in Concrete Core Design

211

5.3.2.7

Embedded Steel Frame Shear Stud Spacing

217

Weld

Gusset Plate On Each Side

Radial Girder

Outrigger Embedded Steel Frame Within Concrete Core

5.3.2 Top of Outrigger to Core C-199

5.3.2.1 Gusset Plate Design Inputs Input dimensions for gusset plate, outrigger member, column member, floor girder, and bolts Column Section selected section specified minimum yield stress

Fy

specified minimum tensile strength

Fu

65

ksi

web thickness

tw

0.635

in

flange thickness

tf d bf

0.855 33.5 11.6

in in in

k1

1.125

in

depth width distance from web center to line of flange toe of fillet

W33 x 152 50 ksi

Girder Section selected section specified minimum yield stress

Fy

specified minimum tensile strength

Fu

65

ksi

web thickness

tw

3.07

in

flange thickness

tf d bf

4.91 22.4 17.9

in in in

k1

2.75

in

Ru Ru/2

224

kips

112

kips

depth width distance from web center to line of flange toe of fillet required loads load per gusset plate

W14 x 730 50 ksi

C-200

5.3.2.1 Gusset Plate Design Inputs

number of horizontal bolt groups

ngh

min. spacing between horizontal bolt groups sgv

2 7

in in

in

selected spacing between horizontal bolt groups spacing check number of rows of bolts per group

nbv

8 Yes 1

vertical bolt spacing

sbv

0

number of columns of bolts horizontal bolt spacing

nbh sbh

3 3

in

Leh Lev

3

in

3

in

Leh Lev

4

in

4.95

in

= 2*k1+F

Edge Spacing on Plate horizontal edge distance vertical edge distance

Edge Spacing on Girder horizontal edge distance vertical edge distance

= (bf-sgv-2*(nbv-1)*sbv)/2

Outrigger Section selected section specified minimum yield stress

Fy

specified minimum tensile strength

Fu

65

ksi

web thickness

tw

3.07

in

flange thickness

tf d bf

4.52 22.4 17.9

in in in

k1

2.75

in

ngv

2

depth width distance from web center to line of flange toe of fillet number of horizontal bolt groups min. spacing between horizontal bolt groups

W14 x 730 50 ksi

7

in in

in

selected spacing between horizontal bolt groups

sgv

spacing check number of rows of bolts per group

nbv

8 Yes 2

vertical bolt spacing

sbv

3

number of columns of bolts horizontal bolt spacing

nbh sbh

8

required loads load per gusset plate

Pu Pu /2

4

in

2190

kips

1095

kips

C-201

5.3.2.1 Gusset Plate Design Inputs

= 2*k1+F

Edge Spacing on Plate horizontal edge distance vertical edge distance

Leh Lev

6

in

6

in

Leh Lev

3

in

1.95

in

Edge Spacing on Outrigger horizontal edge distance vertical edge distance

=(bf-sgv-2*(nbv-1)*sbv)/2

Plate Dimensions plate thickness

tp

1.5

in

width at outrigger

Lout

26

in

width at girder

Lgird

18

in

Fy Fu

36

ksi

70

ksi

specified minimum yield stress specified minimum tensile strength

Bolt Properties bolt type bolt diameter bolt head size

5) Group B (e.g., A490) bolts, when threads are excluded from shear planes bd 7/8 in F

1 7/16

in

C-202

5.3.2.1 Gusset Plate Design Inputs

5.3.2.2 Single Bolt Shear Capacity Determine if the bolts slip and fail in shear available slip resistance bolt diameter mean slip coefficient pretension multiplier

ΦRn Φ db µ Du

16.6 1.00 7/8 0.30 1.13

factor for fillers

hf

1

min. fastener tension number of slip planes required to permit the connection to slip

Tb

49

ns

1

available shear strength reduction factor nominal shear stress nominal unthreaded body area of bolt

ΦRn Φ Vn

37.9 0.75 84

Ab 0.601 shear strength greater than slip resistance?

kips

ΦµDuhfTbns

in for Class A surfaces for one filler btwn connected parts

kips

Table J3.1

kips

ΦVnAb (J3-1)

ksi in2

πda 2/4

Yes

C-203

5.3.2.1 Gusset Plate Design Inputs

5.3.2.3 Bolt and Plate Checks for Outrigger Connection Checking failure modes for bolts and plate at the connection between gusset plate and outrigger connection

Strength Check Pu

1,095

kips

ΦRn

1,212 Yes

kips

nmin

29

bolts min # for bolt shear

nb

32 Yes

bolts

tp

1.5

in

Lout

26

in

specified minimum yield stress

Fy

36

ksi

specified minimum tensile strength

Fu

70

ksi

horizontal edge distance

Leh Lev

6

in

6

in

db

7/8

in

number of horizontal bolt groups

ngh

2

selected spacing between horizontal bolt groups

sgv

8

number of rows of bolts per group

nbv

2

vertical bolt spacing

sbv

3

number of columns of bolts

nbh sbh

8 4

in

specified minimum yield stress

Fy

50

ksi

specified minimum tensile strength

Fu

65

ksi

flange thickness

tf

4.52

in

Leh Lev

3

in

1.95

in

required strength design strength does it pass?

Bolt Check min. # of bolts actual number of bolts does it pass?

Plate Properties plate thickness width at outrigger

vertical edge distance

Bolt Group Properties bolt diameter

horizontal bolt spacing

in in

Outrigger Properties

horizontal edge distance vertical edge distance

C-204

5.3.2.1 Gusset Plate Design Inputs

Gross Area of Plate gross area

Ag

39.0

in2

= min( Aw, Agp)

Whitmore Section width

lw

46.3

Whitmore area

Aw

69.5

in in2

= l wtp

gross area from plate dimensions

2

Agp

39.0

in

ΦRn

1,212

kips

= ΦFnvAbnb (J3-1)

ΦRn Φ Fy

1,264 0.90 36

kips

= ΦFyAg (J4-1)

Ag

39.0

ΦRn Φ Fu

1,752 0.75 70

Ae U An

33.4 1.0 33.4

ΦRn Φ Ubs

1,692 0.75 1.0

kips ΦUbsFuAnt+Φ0.60min(FuAnv,FyAgv);(J4-5)

Agv

51.0

in2

= Louttp

Bolt Shear Strength design strength

Tensile Yielding of Gusset Plate design strength specified minimum yield stress gross area

ksi in2

Tensile Rupture of Gusset Plate design strength specified minimum tensile strength effective net area shear lag factor net area

kips

= ΦFuAe (J4-2)

ksi in2

AnU (D3-1) Table D3.1

in2

Block Shear Rupture of Gusset Plate available strength reduction coefficient gross area subject to shear net area subject to shear net area subject to tension

2

= [Lev+(nbh-1)*sbh]tp

39.8

in

Ant

16.5

in2

ΦRn Φ Ubs

3,066 0.75 1.0

kips ΦUbsFuAnt+Φ0.60min(FuAnv,FyAgv); (J4-5)

Agv

135.4

in2

Anv

= [Leh+(nbh-1)*sbh-(nbh-0.5)(da+.125)]tp = 2[Lev-0.5(da+0.125)]tp

Block Shear Rupture of Flange available strength reduction coefficient gross area subject to shear net area subject to shear net area subject to tension

Anv Ant

106.2 13.1

in

2

in

2

= [Lev+(nbh-1)*sbh]tf = [Leh+(nbh-1)*sbh-(nbh-0.5)(da+.125)]tf = 2[Lev-0.5(da+0.125)]tf

C-205

5.3.2.1 Gusset Plate Design Inputs

Bolt Bearing on Gusset Plate ΦRn Φ

3,186 0.75

clear distance, in dir. of force, between edge of hole and edge of material

l c edge

5.5

in

clear distance, in dir. of force, between edge of hole and edge adjacent hole

l c int

3.1

in

Σ 1.51l c nb3.0da

40.5

in

84.0

in

ΦRn Φ

1,798 0.75

kips

clear distance, in dir. of force, between edge of hole and edge of material

l c edge

2.5

in

clear distance, in dir. of force, between edge of hole and edge adjacent hole

l c int

3.1

in

Σ 1.51l c nb3.0da

8.2

in

84.0

in

available bearing strength

kips

= ΦtpFuMIN(Σ 1.51l c,nb3.0da) ; (J3-6b)

Bolt Bearing on Flange available bearing strength

= ΦtfFuMIN(Σ 1.51l c,nb3.0da) ; (J3-6b)

C-206

5.3.2.1 Gusset Plate Design Inputs

5.3.2.4 Bolt and Plate Checks for Girder Connection Checking failure modes for bolts and plate at the connection between gusset plate and outrigger Strength Check required strength design strength does it pass?

Ru

112

kips

ΦRn

227 Yes

kips

nmin

3

Bolt Check min. # of bolts

bolts min # for bolt shear

nb

6 Yes

bolts

plate thickness

tp

1.5

in

width at girder

Lgird

18

in

specified minimum yield stress

Fy

36

ksi

specified minimum tensile strength

Fu

70

ksi

horizontal edge distance

Leh Lev

3

in

3

in

da

7/8

in

number of horizontal bolt groups selected spacing between horizontal bolt groups

ngh

2

sgv

8

number of rows of bolts per group

nbv

1

vertical bolt spacing

sbv

0

number of columns of bolts

nbh sbh

3 3

in

specified minimum yield stress

Fy

50

ksi

specified minimum tensile strength

Fu

65

ksi

flange thickness

tf

actual number of bolts does it pass?

Plate Properies (from Inputs)

vertical edge distance

Bolt Group Properties bolt diameter

horizontal bolt spacing

in in

Girder Properties

horizontal edge distance vertical edge distance

Leh Lev

4.91 in 4

in

4.95 in

C-207

5.3.2.1 Gusset Plate Design Inputs

Gross Area of Plate gross area

Ag

Whitmore Section width

lw

Whitmore area

Aw Agp

gross area from plate dimensions

2 22.4 in

= MIN(Aw, Agp)

14.9 in 2 22.4 in

= l wtp

27.0 in

2

= Louttp

Bolt Shear Strength design strength

ΦRn

227

ΦRn Φ Fy

726 kips 0.90 36 ksi 2 22.4 in

= ΦFyAg (J4-1)

ΦRn 1270 kips Φ 0.75 Fu 70 ksi 2 Ae 24.2 in

= ΦFuAe (J4-2)

kips

= ΦFnvAbnb (J3-1)

Tensile Yielding of Gusset Plate design strength specified minimum yield stress

Ag

gross area

Tensile Rupture of Gusset Plate design strength specified minimum tensile strength effective net area shear lag factor net area

U An

= AnU (D3-1)

1.0 2 24.2 in

Table D3.1

464 kips 0.75 1.0 2 16.5 in

= ΦUbsFuAnt+Φ0.60min(FuAnv,FyAgv) ; (J4-5)

Block Shear Rupture of Gusset Plate available strength reduction coefficient gross area subject to shear

ΦRn Φ Ubs Agv

net area subject to shear

Anv

net area subject to tension

Ant

2

= [Lev+(nbh-1)*sbh]tp

14.3 in 2 3.8 in

= [Leh+(nbh-1)*sbh-(nbh-0.5)(da+.125)]tp

560 kips 0.75 1.0 2 24.3 in

= ΦUbsFuAnt+Φ0.60min(FuAnv,FyAgv) ; (J4-5)

= 2[Lev-0.5(da+0.125)]tp

Block Shear Rupture of Flange available strength reduction coefficient gross area subject to shear

ΦRn Φ Ubs Agv

net area subject to shear

Anv

net area subject to tension

Ant

2

21.8 in 2 17.2 in

= [Lev+(nbh-1)*sbh]tf = [Leh+(nbh-1)*sbh-(nbh-0.5)(da+.125)]tf = 2[Lev-0.5(da+0.125)]tf

C-208

5.3.2.1 Gusset Plate Design Inputs

Bolt Bearing on Gusset Plate ΦRn Φ

available bearing strength clear distance, in dir. of force, between edge of hole and edge of material clear distance, in dir. of force, between edge of hole and edge adjacent hole

786 kips 0.75

l c edge

2.5

in

l c int

2.1

in

Σ 1.51l c nb3.0da

= ΦtpFuMIN(Σ 1.51l c,nb3.0da) ; (J3-6b)

10.0 in 15.8 in

Bolt Bearing on Flange ΦRn 3770 kips Φ 0.75

available bearing strength clear distance, in dir. of force, between edge of hole and edge of material clear distance, in dir. of force, between edge of hole and edge adjacent hole

l c edge

4.5

in

l c int

2.1

in

Σ 1.51l c nb3.0da

= ΦtfFuMIN(Σ 1.51l c,nb3.0da) ; (J3-6b)

18.9 in 15.8 in

C-209

5.3.2.1 Gusset Plate Design Inputs

5.3.2.5 Weld Design for Gusset Plate to Embedded Steel Frame Design of weld of gusset plates to embedded steel frame

Weld Specifications Weld Size Weld Size in sixteenths of inch Electrode Strength of Weld Electrode Coeffiencient

D D FEXX C1

0.75 12 E70 70

in 1/16 in

=w * 16

ksi

Table 8-3

1

Table 8-3

Vector Addition of Loads Outrigger Force X Component

Fx

1,602

kips

Outrigger Force Y Component Shear Force Net Load X Component

Fy V Fx

1,494 224 1,602

kips kips kips

V+Fy

1,718

kips

Ru

2,348 77

kips degrees

43 69.3

degrees in

25.4 0.367 42 0.606 4.135 2,579

in

2,348 Yes

kips

Net Load Y Component Resultant Load Angle of Load Net Load Design Outrigger Angle Length of Weld Distance Between Welds Value for C Tables Outrigger Force Eccentricity Lookup Value for C Tables Tabular Value Strength of Weld Group Required Strength Does it pass strength requirements?

Lw k*Lw k ex a C φRn Ru

= (Fx2 + (V+Fy)2).5 with respect to vertical

with respect to horizontal plane

=k*Lw/Lw

in

From Drawing S-2.005

kips

=ex/Lw Table 8-4 Angle = 75 degrees =φ*C*C1*D*Lw

C-210

5.3.2.1 Gusset Plate Design Inputs

5.3.2.6 Steel Frame Embedded in Concrete Core Design Resulting steel sizes from model of steel frame embedded inside concrete core to take load from outriggers • All members were assumed to be fully braced, simulating the frame’s embedment in concrete. • All beams and columns are connected by moment connections. • All beams and columns are made of A992 Steel. • The top and bottom nodes of the frame are assumed to be fixed in all directions and rotations.

Tensile Load

2190

kips

applied axially from points where outrigger connects to frame

Final Sizes Beams Columns Ficticious Braces

W14 x 665 W33 x 152 W24 x 103 act in compression only

Local Coordinates

Z

X

Y

C-211

5.3.2.1 Gusset Plate Design Inputs

MIDAS Steel Code Check Results

Check

Member Number

Section Number

Length (ft)

Unbraced Length (ft)

Combined Shear Unbraced Unbraced Check Utilization Utilization Length (ft) Length (ft) Ratio Ratio OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

2 0.388 4 0.513 7 0.381 8 0.539 9 0.488 12 0.386 13 0.55 14 0.497 17 0.386 19 0.493 22 0.385 23 0.547 24 0.49 27 0.384 28 0.547 29 0.489 32 0.385 33 0.547 34 0.49 37 0.385 38

2 0.002 2 0.012 2 0.002 2 0.01 2 0.011 2 0.002 2 0.011 2 0.012 2 0.002 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2

13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Lateral Torsional Buckling Factor Lateral Torsional Buckling Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Effective Length Factor Effective Length Factor 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65

Bending Axial Load Moment y (kips) (k-ft)

Bending Moment y (k-ft)

Nominal Nominal Nominal Axial Moment Moment Strength Capacity z (k- Capacity z (k(kips) ft) ft) -679 1,904 752 2,016 -669 1,904 -821 1,904 744 2,016 -678 1,904 -824 1,904 751 2,016 -680 1,904 752 2,016 -677 1,904 -824 1,904 750 2,016 -676 1,904 -824 1,904 750 2,016 -676 1,904 -824 1,904 750 2,016 -676 1,904 -824

4.54 2,096 47.54 2,096 -3.10 2,096 2.26 2,096 -9.96 2,096 -2.61 2,096 -5.32 2,096 -8.53 2,096 -2.03 2,096 -1.07 2,096 -0.55 2,096 -0.20 2,096 0.82 2,096 -0.43 2,096 -0.77 2,096 -0.89 2,096 -0.90 2,096 -1.28 2,096 -1.52 2,096 -1.17 2,096 -1.53

8.73 265.5 -35.86 265.5 8.57 265.5 -32.01 265.5 -34.11 265.5 8.65 265.5 -34.39 265.5 -36.15 265.5 8.36 265.5 -35.67 265.5 8.57 265.5 -34.06 265.5 -34.94 265.5 8.71 265.5 -33.96 265.5 -34.90 265.5 8.68 265.5 -34.07 265.5 -35.17 265.5 8.65 265.5 -34.02

C-212

5.3.2.1 Gusset Plate Design Inputs

Check

Member Number

Section Number

Unbraced Length (ft) Length (ft)

Combined Shear Unbraced Unbraced Check Utilization Utilization Length (ft) Length (ft) Ratio Ratio OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

0.547 39 0.49 42 0.385 43 0.547 44 0.49 47 0.385 48 0.547 49 0.49 52 0.385 53 0.548 54 0.491 57 0.385 58 0.548 59 0.491 62 0.385 63 0.547 64 0.489 67 0.387 68 0.556 69 0.493 90 0.019 91 0.019

0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 2 0.002 2 0.011 2 0.011 1 0 1 0

0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 16.4576 0 16.4576 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Lateral Torsional Buckling Factor Lateral Torsional Buckling Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Effective Length Factor Effective Length Factor 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65

C-213

5.3.2.1 Gusset Plate Design Inputs

Bending Axial Load Moment y (kips) (k-ft)

Bending Moment y (k-ft)

Nominal Nominal Nominal Axial Moment Moment Strength Capacity z (k- Capacity z (k(kips) ft) ft) 1,904 750 2,016 -676 1,904 -824 1,904 750 2,016 -676 1,904 -824 1,904 750 2,016 -677 1,904 -824 1,904 750 2,016 -677 1,904 -824 1,904 750 2,016 -677 1,904 -824 1,904 750 2,016 -681 1,904 -826 1,904 754 2,016 182 8,820 182 8,820

2,096 -1.50 2,096 -1.38 2,096 -1.81 2,096 -1.77 2,096 -1.58 2,096 -2.16 2,096 -2.30 2,096 -1.55 2,096 -2.28 2,096 -2.32 2,096 -1.55 2,096 -1.67 2,096 -1.23 2,096 -1.15 2,096 -2.04 2,096 -3.42 2,096 -1.68 2,096 6.05 2,096 -11.97 2,096 -45.39 5,550 -45.61 5,550

265.5 -35.04 265.5 8.67 265.5 -34.07 265.5 -35.10 265.5 8.66 265.5 -34.00 265.5 -34.98 265.5 8.62 265.5 -34.12 265.5 -35.22 265.5 8.64 265.5 -34.16 265.5 -35.20 265.5 8.60 265.5 -33.98 265.5 -34.40 265.5 8.73 265.5 -35.62 265.5 -34.15 265.5 0.14 2655 -0.32 2655

Check

Member Number

Section Number

Unbraced Length (ft) Length (ft)

Combined Shear Unbraced Unbraced Check Utilization Utilization Length (ft) Length (ft) Ratio Ratio OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

92 0.019 93 0.019 94 0.019 95 0.019 96 0.021 97 0.02 98 0.02 99 0.019 100 0.019 101 0.019 102 0.019 103 0.018 104 0.374 105 0.374 106 0.374 107 0.374 108 0.374 109 0.377 110 0.403 111 0.073 112 0.393 113

1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0.003 1 0.988 1 0.002 1

16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.5834 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.5172 0 0.06624 0 16.5172 0 0.06624

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Lateral Torsional Buckling Factor Lateral Torsional Buckling Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Effective Length Factor Effective Length Factor 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65

Bending Axial Load Moment y (kips) (k-ft)

Bending Moment y (k-ft)

Nominal Nominal Nominal Axial Moment Moment Strength Capacity z (k- Capacity z (k(kips) ft) ft) 182 8,820 182 8,820 182 8,820 183 8,820 183 8,820 180 8,820 182 8,820 182 8,820 182 8,820 182 8,820 182 8,820 182 8,820 3,295 8,820 3,295 8,820 3,295 8,820 3,295 8,820 3,294 8,820 3,293 8,820 3,291 8,820 322 8,820 3,284 8,820 4

-45.86 5,550 -45.65 5,550 -45.68 5,550 -45.20 5,550 -49.57 5,550 -44.66 5,550 -47.45 5,550 -47.01 5,550 -44.75 5,550 -43.93 5,550 -44.88 5,550 -45.18 5,550 2.32 5,550 2.27 5,550 2.12 5,550 2.19 5,550 2.43 5,550 3.62 5,550 67.33 5,550 -108.23 5,550 -55.65 5,550 -88.16

0.23 2655 0.32 2655 -1.19 2655 0.59 2655 4.55 2655 -4.30 2655 -2.14 2655 1.25 2655 -0.76 2655 -0.76 2655 0.33 2655 -0.06 2655 0.93 2655 -1.11 2655 -1.11 2655 1.14 2655 -1.31 2655 -10.34 2655 57.37 2655 -94.19 2655 -36.39 2655 -0.05

C-214

5.3.2.1 Gusset Plate Design Inputs

Check

Member Number

Section Number

Unbraced Length (ft) Length (ft)

Combined Shear Unbraced Unbraced Check Utilization Utilization Length (ft) Length (ft) Ratio Ratio OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

0.016 114 0.376 116 0.374 117 0.374 118 0.374 119 0.374 127 0 129 0.001 130 0.565 131 0.409 132 0.41 133 0.41 134 0.409 135 0.407 136 0.408 137 0.408 138 0.408 139 0.408 140 0.408 141 0.409 142 0.409 143 0.407

0.988 1 0 1 0 1 0 1 0 1 0 1 0 1 0.001 2 0.011 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003 2 0.003

0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 0.06624 0 0.06624 0 13 0 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

Lateral Torsional Buckling Factor Lateral Torsional Buckling Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Effective Length Factor Effective Length Factor 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

C-215

5.3.2.1 Gusset Plate Design Inputs

Bending Axial Load Moment y (kips) (k-ft)

Bending Moment y (k-ft)

Nominal Nominal Nominal Axial Moment Moment Strength Capacity z (k- Capacity z (k(kips) ft) ft) 8,820 3,286 8,820 3,295 8,820 3,295 8,820 3,295 8,820 3,295 8,820 0 8,820 -1 8,330 -823 1,904 751 2,016 746 2,016 751 2,016 751 2,016 750 2,016 750 2,016 750 2,016 750 2,016 750 2,016 750 2,016 750 2,016 750 2,016 750 2,016

5,550 5.31 5,550 3.18 5,550 2.47 5,550 2.60 5,550 2.35 5,550 0.00 4,298 -3.74 5,550 43.36 2,096 1.30 1,916 2.99 1,916 -2.59 1,916 -2.76 1,916 -0.63 1,916 0.02 1,916 -0.70 1,916 -1.28 1,916 -1.42 1,916 -1.51 1,916 -1.83 1,916 -2.22 1,916 -0.83 1,916

2655 8.77 2655 0.68 2655 -1.31 2655 1.24 2655 1.24 2655 0.00 1771.95 -0.22 2655 -33.96 265.5 10.74 265.5 11.47 265.5 10.88 265.5 10.30 265.5 10.40 265.5 10.65 265.5 10.69 265.5 10.62 265.5 10.60 265.5 10.61 265.5 10.65 265.5 10.61 265.5 10.24 265.5

Check

Member Number

Section Number

Unbraced Length (ft) Length (ft)

Combined Shear Unbraced Unbraced Check Utilization Utilization Length (ft) Length (ft) Ratio Ratio OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

144 0.408 145 0.009 146 0.009 147 0.009 148 0.009 149 0.009 150 0.01 151 0.009 152 0 153 0.01 154 0.001 155 0.01 156 0.01 157 0.009 158 0.009 159 0.009 160 0.009 161 0 162 0 173 0.377 333 0.013 341 0.003 393 0.549

2 0.002 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0.001 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0.064 1 0.006 2 0.011

13 13 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.5172 0 0.06624 0 16.5172 0 0.06624 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 16.4576 0 0.06624 0 0.06624 0 16.4576 0 0.08416 0.08416 0.08416 0.08416 13 0

13 13 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.5172 16.5172 0.06624 0.06624 16.5172 16.5172 0.06624 0.06624 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 16.4576 0.06624 0.06624 0.06624 0.06624 16.4576 16.4576 0.08416 0.08416 0.08416 0.08416 0 0

Lateral Torsional Buckling Factor Lateral Torsional Buckling Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Effective Length Factor Effective Length Factor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.65 0.65

Bending Axial Load Moment y (kips) (k-ft)

Bending Moment y (k-ft)

Nominal Nominal Nominal Axial Moment Moment Strength Capacity z (k- Capacity z (k(kips) ft) ft) 753 2,016 14 8,820 14 8,820 14 8,820 14 8,820 14 8,820 14 8,820 12 8,820 0 8,820 16 8,820 -1 8,330 14 8,820 14 8,820 14 8,820 14 8,820 14 8,820 14 8,820 0 8,820 0 8,820 3,293 8,820 -149 8,330 -45 8,330 -824 1,904

4.55 1,916 44.87 5,550 44.92 5,550 45.43 5,550 45.14 5,550 44.65 5,550 45.82 5,550 43.96 5,550 0.00 4,298 50.54 5,550 -3.74 5,550 49.84 5,550 46.77 5,550 43.49 5,550 43.40 5,550 44.41 5,550 44.54 5,550 0.00 4,298 0.00 4,298 1.97 5,550 9.11 5,550 -0.21 5,550 -1.83 2,096

9.73 265.5 0.09 2655 0.00 1771.95 0.02 2655 -0.59 2655 -0.63 2655 2.39 2655 2.40 2655 0.00 1771.95 1.00 2655 -0.22 2655 0.82 2655 1.70 2655 1.70 2655 -0.63 2655 -0.04 2655 0.11 2655 0.00 1771.95 0.00 1771.95 8.77 2655 5.10 2655 -1.39 2655 -34.42 265.5

C-216

5.3.2.1 Gusset Plate Design Inputs

5.3.2.7 Embedded Steel Frame Shear Stud Spacing Design of shear studs for the columns and beams in the embedded steel frame to transfer loads to concrete Beam Shear Studs Selected Section Concrete Compressive Strength Diameter of Shear Stud Area of Shear Stud Connector

f'c d Asc

W14 x 665 14.0 0.50 0.20

ksi in in2

= π*d /4

lbs/ft3 ksi

=ρc1.5*( f'c) 0.5

2

Weight of Concrete per Unit Volume Modulus of Elasticity of Concrete

ρc Ec

160 7,573

Minimum Tensile Strength of a Shear Stud

Tu

65

Coefficient

Rg Rp

1.00

Shear Strength of Shear Stud

Qn1

32.0

kips

= 0.5* Asc*(Ec f'c)0.5

Shear Strength of Shear Stud

Qn2

12.8

kips

=Asc * Rg*Rp *Tu

Controlling Shear Strength of Shear Stud

Qn

12.8

kips

= MIN(QN1, QN2)

Flange Width Number of Rows of Shear Studs Shear Force Number of Shear Studs Per Row Member Length Spacing Minimum Spacing

bf r V n L s

17.7 4 3,364 66 16.5 3.00 3.00

in rows kips ft in in

AISC I3.2.(6)

36.0

in

AISC I3.2.(6)

slong

3.0

in

s min ≤ slong ≤ smax ?

Yes

strans s min ≤ strans ≤ smax ?

3.0

Coefficient

ksi

1.00

Shear Stud Specifications

Maximum Spacing

smin smax

Selected Shear Stud Spacings Longitudinal Spacing Spacing Check Transverse Spacing Spacing Check

in

Yes

C-217

5.3.2.1 Gusset Plate Design Inputs

Axial Load in Member =V/(Qn*r) =L/N

Column Shear Studs Selected Section Concrete Compressive Strength Diameter of Shear Stud Area of Shear Stud Connector

f'c d Asc

W33 x 152 14.0 0.38 0.11

Weight of Concrete per Unit Volume

wc

160

Modulus of Elasticity of Concrete

Ec

7,573

ksi

Minimum Tensile Strength of a Shear Stud

Tu

65

ksi

Coefficient

Rg Rp

1.00

Shear Strength of Shear Stud

Qn1

17.98

kips

= 0.5* Asc*(Ec f'c)0.5

Shear Strength of Shear Stud

Qn2

7.18

kips

=Asc * Rg*Rp *Tu

Controlling Shear Strength of Shear Stud

Qn

7.18

kips

= MIN(QN1, QN2)

Flange Width Number of Rows of Shear Studs Shear Force Number of Shear Studs Member Length Spacing Minimum Spacing

bf r V n L s

11.60 3 774 36 13.0 4.33 2.25

in rows kips ft in in

AISC I3.2.(6)

36.0

in

AISC I3.2.(6)

slong

4.00

in

s min ≤ slong ≤ smax ?

Yes

strans s min ≤ strans ≤ smax ?

2.25

Coefficient

ksi in in2

2

=π*d /4

lbs/ft3 =wc1.5*( f'c) 0.5

1.00

Selected Shear Stud Spacings

Maximum Spacing

smin smax

Axial Load in Member =V/(Qn*r) =L/N

Selected Shear Stud Spacings Longitudinal Spacing Spacing Check Transverse Spacing Spacing Check

in

Yes

C-218

5.3.2.1 Gusset Plate Design Inputs

6.0 Foundation Design 6.1 Retaining Wall

220

6.1.1 Soil Profile at Site

221

6.1.2 Effective Soil Pressure Calculations

222

6.1.3 Retaining Wall Design

224

6.1.4 Retaining Wall Mastan Analysis

228

6.2 Parking Garage

230

6.2.1 Two-Way Slab Using WWR

231

6.2.2 Parking Garage Columns 6.2.2.1

Parking Garage Column with Rebar

247

6.2.2.2

Parking Garage Column with W-Shape

248

6.2.3 Belled Caisson Design

6.3 Tower Foundation

250

6.3.1 Abaqus Analysis of Caissons

251

6.3.2 Mega-Column Caisson Design

253

6.3.3 Ring Beam Design

255

6.3.4 Core Caisson Design

257

6.3.5 Caisson Rebar

259

6.0 Foundation Design C-219

249

6.1 Retaining Wall 6.1.1 Soil Profile at Site

221

6.1.2 Effective Soil Pressure Calculations

222

6.1.3 Retaining Wall Design

224

6.1.4 Retaining Wall Mastan Analysis

228

6.1 Retaining Wall C-220

C-221

Created By: NT 5/11/2012

6.1.1 Soil Profile at Site

The job site is located next to Lake Michigan and the Chicago River so the water table is very high. The soil consists of a varitey of sands and clays that were called out in the geotechnical report.

6.1.1 Soil Profile at Site

6.1.2 Effective Soil Pressure Calculation

Created by NT: 4/27/2012

Calculating effective pressure and horizontal force to be used in retaining wall design. Note: Ground water table is at 5 ft depth as stated in the geotechnical report

User Input Depth (d) (ft) 0 25 35 44 50 55 65 71 72

Density (ρ) (pcf) Effective Pressure (psf)* Horizontal Force (plf/ft run)** 0 0 0 135 1,815 2,838 70 1,891 1,955 70 1,823 1,845 70 1,868 1,690 70 1,906 1,654 70 1,982 2,019 70 2,028 1,802 70 2,035 1,495

Density of Water Density of sand Density of clay For Firm/Stiff Clay Earth Pressure Coefficient

62.4 135 70

pcf pcf pcf K a 0.704

Fourmulas Porewater pressure (PP) = 62.4*H H- height in ft * Effective Pressure = (DP *ρ) + Effective pressure from layers above - PP ** Horizontal force = Effective Pressure*K a + Pore Pressure

Reference -C.R.I Clayton, J. Milititsky and Woods, Earth Pressure and Earth-Retaining Structures, 2nd Ed., Conference Publication New York : American Society of Civil Engineers, 1993, Pg 149, Pg 377

6.1.2 Effective Soil Pressure Calculation C-222

Effective pressure [psf] 0

500

1000

1500

2000

2500

0

Depth below ground [ft]

10

Sand

20 30 40

Clay

50 60 70 80

6.1.2 Effective Soil Pressure Calculation C-223

6.1.3 Retaining Wall Design

Created By: NT 5/11/2012

Design tool for a retaining wall to resist soil pressures around the exterior of the roundation. Wall has been designed as a simply supported concrete slab, braced by the parking garage levels. The top two storys are modeled as a cantilever due to uncertainty in soil conditions.

Yes No

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

Dimensions of Wall Designing for 12 in vertical strip of wall Maximum Unsupported Height L ts,min Minimum Wall Thickness ts, act Actual Wall Thickness

23 28

ft in

30

in

Cantilever at top of wall, 2 Stories + 2 Slabs =L/10

ACI 318 Table 9.5 (a)

At Spans Bar Size Area of Bar

Abar

Diameter of bar

dbar 1.69 in

Yield Strength of Bars Bar Spacing

#

14 2 2.25 in

Fy

60

ksi

sspan

6

in

L

Supports

Vertical Steel Bar Properties

At Supports Bar Size Area of Bar

# 14 2 Abar 2.25 in

Diameter of bar

dbar 1.69 in

Yield Strength of Bars Bar Spacing

Fy

60

ksi

ssuport

16

in

Horizontal Shrinkage steel Minimum steel ratio Area of Steel Required Bar Size Area of Bar No. of bars required No. of bars provided Spacing

ρg 0.0018 As # Abar

sshrink

per ACI 318 2

19 in 6 2 0.44 in 42 43 20 in

=ρg*L*ts, act

=As/Abar

6.1.3 Retaining Wall Design

C-224

Check for Moments At Center of Spans 2

As 4.50 in 2 Asmin 0.65 in

Area of steel Minimum Steel Required

As > As min ? Tension Compression Concrete Strength

β1 0.75 c 2 d 27 a 7 d-(a/2) 24 Mn 537

in in in in kip-ft

εs 0.006

Strain in Steel

As < As max ? Strength Reduction Factor

Mm 305 kip-ft FS 1.5 FS * Mm 458 kip-ft Φ*Mn > FS*Mm ? OK

C-225

ACI 318 08- 7.12.2.1

=As*fy =T

ACI - 318-08 - 7.7.1 = h-c-dbar =C/(0.85*f'c*b) =T*(d-a/2) Using Similar Triangles

OK

Φ 0.90 OK Φ *M 483 kip-ft

Maximum Moment on Wall Factor of Safety for Overturning

=ρg*b*h

OK

T 270 kips C 270 kips f'c 4,000 psi

Beta 1 Concrete Cover Structural Depth Height of compression face Moment Arm Nominal Moment

=Abar*12/Sspan

ok when ɛs > 0.005 From MASTAN Principles of Foundation Engineering. By- Braja M. Das

6.1.3 Retaining Wall Design

Check for Moments At Supports As 1.69 in2

Area of steel

Asmin 0.65 in2

Minimum Steel Required

As > As min ? Tension Compression Concrete Cover Concrete Strength

β1 0.75 d 26 a 2.48 d - (a/2) 25 Mn 210

in in in ft-kips

ϵs 0.021

Strain in Steel

ϵs > 0.005? Strength Reduction Factor

= ρg*b*h

ACI 318 08- 7.12.2.1

OK

T 101 Kips C 101 Kips c 2 in f'c 4,000 psi

Beta 1 Structural Depth Height of compression face Moment Arm Nominal Moment

per 12 in width

=As*fy =T

= h-c-dbar =C/(0.85*f'c*b) =T*(d-a/2) Similar Triangles

OK

Φ 0.90 OK Φ*Mn 189 ft-kips

Maximum Moment on Wall Factor of Safety for Overturning

Mm

98 ft-kips From MASTAN FS 1.5 FS * Mm 147 ft-kips Principles of Foundation Engineering. By- Braja M. Das Φ*Mn > FS*Mm ? OK

Reference - Braja M. Das, Principles of Foundation Engineering, Monterey, Calif, 1984, pg 199

6.1.3 Retaining Wall Design

C-226

Calculating Factor of Safety For Sliding Ht

Total Retaining Height

84

ft

7 Stories + 8 Slabs

Ω 0.52 radians ρclay 70 psf Geotechnical Report

Angle of friction for soil Density Of Clay Angle of Backfill Above The Wall Rankine's Coefficient For Passive Earth Pressure

α 0.17 radians =(tan(45+ Φ/2))2 kp 0.1

Rankine's Passive Earth Pressure

Pp 25.3 kips

=0.5*ρclay*H2*kp

ρc 145 psf P 113 kips V 30.5 kips FS 2.2 FS > 1.5 ? OK

Designing per ft.

Density of Reinforced concrete Factored Horizontal Sliding Force * Vertical Force, Self Weight of Wall Calculated Factor of Safety For Sliding

per foot =(V *tan(2*Ω/3))+Pp / (Pcosα))

* Worse Case From Effective Pressure Calculation, ( Horizontal Force*Height) NOTE - Checking for running length of 1 feet Reference - Braja M. Das, Principles of Foundation Engineering, Monterey, Calif, 1984, pg 199

Bearing Capacity Check Undrained Shear Strength of Very Stiff Clay

Su

15

ksf

Geotechnical Report

Density Of Clay Vertical Stress in Soil Adjacent To The Wall Ultimate Bearing Capacity of Clay Vertical Pressure Due To Wall

ρclay

70 6 21 12 OK

psf ksf ksf ksf

Geotechnical Report

σ UBC VBP UBC > VBP ?

= ρclay*height

=σ+Su =ρcomcrete*Ht*h*1/h

NOTE - Checking for running length of 1 feet Reference -C.R.I Clayton, J. Milititsky and Woods, Earth Pressure and Earth-Retaining Structures, 2nd Ed., Conference Publication New York : American Society of Civil Engineers, 1993, , pg 54

C-227

6.1.3 Retaining Wall Design

6.1.4 Retaining Wall Mastan Analysis A 2-D Mastan model was created to obtain the induced moments and deflected shape of the parking garage retaining wall. Loads on the structure were obtained from the Effective Soil Pressure Calculation. They were modeled as resultant point loads of the distributed loads contributed by each of the different soil layers (sand, clay, hard pan) from the Soil Profile along the height of the retaining wall. Parking floors provided supports and were modeled as fixities resisting the earth pressures. The bottom of the wall, on very hard clay, was modeled as fixed and the top of the wall acted as a cantilever with a maximum deflection of 0.00146 in. Figures of the Mastan output are included below. See also the Retaining Wall Design spreadsheet.

Retaining Wall Mastan Moment

6.1.4 Retaining Wall Mastan Analysis C-228

Retaining Wall Mastan Deformed Shape

6.1.4 Retaining Wall Mastan Analysis C-229

6.2 Parking Garage 6.2.1 Two-Way Slab Using WWR

231

6.2.2 Parking Garage Columns 6.2.2.1

Parking Garage Column with Rebar

247

6.2.2.2

Parking Garage Column with W-Shape

248

6.2.3 Belled Caisson Design

249

6.3 Tower Foundation C-230

6.2.1 Two-Way Slab Using WWR

Created by: MZ

5/10/2012

Notes: • WWR (Welded Wire Reinforcement) is used instead of traditional rebars for parking garage design. • In the following WWR Refenrence Table, "D" denoted a deformed wire. The number following "D" gives a cross-sectional area in hundredths of a square inch (ACI 318 - Appendix E) • Bar Size column indicates size of bars used to form WWR steel mesh.

WWR Reference Table Nominal WWR Size D11 D20 D31 D44 D60 D79

Bar Size #3 #4 #5 #6 #7 #8

2

Area [in ] 0.11 0.20 0.31 0.44 0.60 0.79

Diameter [in] 0.375 0.500 0.625 0.750 0.875 1.000

Level 1 Underground NS Direction (30 ft Span) Total Factored Moment Width of Strip WWR Area per Linear Foot WWR Selected Bar Spacing for WWR mesh Bars Needed for WWR mesh

Mu [kip-ft] [ft] As [in2] s

[in]

EW Direction (28.5 ft Span) Total Factored Moment Width of Strip WWR Area per Linear Foot WWR Selected Bar Spacing for WWR mesh Bars Needed for WWR mesh

C-231

Mu [kip-ft] [ft] As [in2] s

[in]

Column Strip Negative Positive -82.6 46.3 14.3 14.3 0.88 0.88 D44 D44 6.0 6.0 29 29

Middle Strip Negative Positive -27.5 14.3 14.3 14.3 0.33 0.33 D44 D44 16.0 16.0 11 11

Column Strip Negative Positive -71.6 38.3 14.3 14.3 0.88 0.88 D44 D44 6.0 6.0 29 29

Middle Strip Negative Positive -21.6 11.5 15.8 15.8 0.33 0.33 D44 D44 16.0 16.0 12 12

6.2.1 Two-Way Slab Using WWR

Level 2-7 Underground NS Direction (30 ft Span) Total Factored Moment Width of Strip WWR Area per Linear Foot WWR Selected Bar Spacing for WWR mesh Bars Needed for WWR mesh

Mu [kip-ft] [ft] As [in2] s

[in]

EW Direction (28.5 ft Span) Total Factored Moment Width of Strip WWR Area per Linear Foot WWR Selected Bar Spacing for WWR mesh Bars Needed for WWR mesh

Mu [kip-ft] [ft] As [in2] s

[in]

Column Strip Negative Positive -30.3 16.5 14.3 14.3 0.31 0.31 D31 D31 12 12 15 15

Middle Strip Negative Positive -10.1 5.5 14.3 14.3 0.31 0.23 D31 D31 12 16 15 11

Column Strip Negative Positive -28.0 14.5 14.3 14.3 0.31 0.31 D31 D31 12 12 15 15

Middle Strip Negative Positive -8.4 4.4 15.8 15.8 0.31 0.23 D31 D31 12 16 16 12

6.2.1 Two-Way Slab Using WWR

C-232

Parking Garage Reinforced Slab Design Design tool for WWR (Welded Wire Reinforcement) of garage slab Notes: • Slab for parking garage is designed using equivalent frame method • Pick positive and negative moment at critical sections respectively in each direction to design • All the slab panels are split into column strips and middle strips. For each way’s design (NS and EW), critical moments are proportionally distributed to column and middle strips • Slab is designed with drop panels and without interior beams or edge beams

Material Properties Concrete Density Concrete Strength

ρc f'c

Concrete Modulus WWR Yield Strength WWR Elastic Modulus

Ec 2,410 ksi Fy 80 ksi Es 29,000 ksi

110 4,000

pcf psi =ρc1.5*33*f'c1/2; ACI 318-08 8.5, 8.6

Load Cases Summary Parking Floor Slab Self Weight Superimposed Dead Load Live Load Total Factored Load

wslf SDL LL wu

110 42 40 246

psf psf psf psf

Parking Roof Slab Self Weight Superimposed Dead Load Live Load Snow Load Total Factored Load

wslf SID LL SL wu

110 271 100 20 627

psf psf psf psf psf

C-233

= ρc*h

=1.2(SW+SID)+1.6LL, ASCE7-10 2.3.2

=1.2(SW+SID)+1.6LL+0.5SL, ASCE7-10 2.3.2

6.2.1 Two-Way Slab Using WWR

Basic Dimensions Grid Span, NS Direction Grid Span, EW Direction Clear Span, whichever smaller

LNS LEW Ln

30.0 28.5 26.1

ft ft ft

Column Strip Width Middle Strip Width, NS Direction Middle Strip Width, EW Direction

bcol bm,NS bm,EW

14.3 14.3 15.8

ft ft ft

dcol deq

32.0 28.4

in in

=0.89*dcol, ACI 318-08 13.6.2.5

h

12.0 10.5 Yes 2.0

in in

=Ln/30, ACI Table 9.5 (c)

Column Column Diameter Diameter of Equi. Section Slab Slab Thickness Minimum Slab Thickness Concrete Cover on Top and Btm

hmin h>hmin? c

w/ each side 0.25min(LNS, LEW) ACI 318-08 13.2.1

in

Diagram showing breakdown of slab strips:

Column Grid

Column Strip Middle Strip

6.2.1 Two-Way Slab Using WWR

C-234

Drop Panel Drop Panel Thickness Minimum Thickness

hdr

7.0

in

hdr,min

3.0 11.5

in

=0.25h, ACI 318-08 13.2.5 (a)

in

=0.25(dext-deq/2) ACI 318-08 13.3.7

Maximum computing thickness hdr>hdr,min?

Yes

Ldr

10.0

ft

distext distext,min

5.0 4.75

ft

distext>distext,min?

Yes

Length of Square Drop Panel Extent dist. from Center Support

ft

=(1/6)min(L NS,LEW), ACI 318-08 13.2.5 (b)

h hdr dext

Cut Section of Column with Drop Panel

C-235

6.2.1 Two-Way Slab Using WWR

Summary Table for Design Moments at Critical Section Notes: • Moment Coefficient are from MASTAN analysis, using one foot slab applied with unit load. • Design for two typical level, level 1 underground and level 2-7 underground. Use parking roof load for level 1 underground; parking floor load for level 2-7 underground. • For each typical level, design for EW and NS two directions. • For each direction, deisgn for column strip and middle strip, based on one foot slab.

Level 1 Underground EW Direction

Span

28.5 ft

Critical Positive Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Column Strip Moment Distribution Coeff. Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

38.7 727 0.75 545 182 38.3 11.5

unit lb-ft kip-ft

Mastan Analysis wu*30ft

kip-ft kip-ft kip-ft kip-ft

ACI 318-08 13.6.4.1 Total Moment*0.75 Total Moment*(1-0.75) Moment at Column Strip/b col Moment at Column Strip/b m,EW

Critical Negative Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

-72.3 -1359 -1020 -340 -71.6 -21.6

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

NS Direction

Span

30.0 ft

Critical Positive Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

49.2 879 659 220 46.3 14.3

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

Critical Negative Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

-87.8 -1569 -1177 -392 -82.6 -27.5

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

wu*28.5ft Total Moment*0.75 Total Moment*(1-0.75) Moment at Column Strip/b col Moment at Column Strip/b m,NS

6.2.1 Two-Way Slab Using WWR

C-236

Level 2-7 Underground EW Direction

Span

28.5 ft

Critical Positive Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

37.3 276 207 69 14.5 4.4

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

Critical Negative Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

-71.9 -531 -399 -133 -28.0 -8.4

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

NS Direction

Span

30.0 ft

Critical Positive Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

44.7 314 235 78 16.5 5.5

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

Critical Negative Moment Moment Coefficient under Unit Load Total Moment at Panel Strip Moment at Column Strip Moment at Middle Strip Moment at Column Strip, Plf Moment at Middle Strip, Plf

-82.0 -576 -432 -144 -30.3 -10.1

unit lb-ft kip-ft kip-ft kip-ft kip-ft kip-ft

C-237

6.2.1 Two-Way Slab Using WWR

MASTAN Output One foot width of slab applied with unit load, showing critical design moment coefficients. -72.25

38.65

Level 1 Underground, EW Direction -87.83

49.17

Level 1 Underground, NS Direction

-71.90

37.29

Level 2-7 Underground, EW Direction -82.01

44.70

Level 2-7 Underground, NS Direction

6.2.1 Two-Way Slab Using WWR

C-238

Design Calculations for WWR Concrete Slab

Created by:

MZ

5/10/2012

• Level 1 North-South direction calculations have been included as representative of the typical calculations. It consists of positive and negative moment reinforcement design for column and middle strip respectively. Shear was also checked when ever negative moment is considered. • The East-West direction of level 1 and both directions of all other levels are calculated in the same manner but with their individual inputs. • All the reinforcement design are based on one foot slab.

C-239

6.2.1 Two-Way Slab Using WWR

Level 1 Underground NS Direction, Column Strip, Positive Moment LNS

Span Length Critical Moment

Mu

30 46.3

ft kip-ft

4,000 3400 #6 D44 0.44 0.750 80

psi psi

Material Properties Concrete Strength Average Concrete Strength Bar Size for WWR Nominal WWR Size Rebar Area Nominal Diameter WWR Yield Strength

f'c f'c,avg

Abar dbar Fy

2

in in ksi

Flexural MMR Calculation (Per Foot Width) Slab Thickness Concrete Cover Slab Effective Depth Width Bar Spacing WWR Area Tension at Yield Depth of Equi. Comp. Stress Block Nominal Moment Strength Adjustment Factor for Moment Design Moment Strength Minimum Required Steel Area

h c d b s As T a Mn φ ΦMn ΦMn>Mu ? As,min As>As,min?

12.0 2.0 9.6 12.0 6.0 0.88 70 1.73 51.4 0.9 46.3 Yes 0.19 Yes

in in in in in

=h-c-dbar/2

in2 kips in. kip-ft

max.s=16in. ACI 318-08 3.5.3.7

=FyAs =T/(b*f'c,avg) =T(d-a/2)

kip-ft in

2

6.2.1 Two-Way Slab Using WWR

=0.0018bh*60/Fy, for Fy > 60 ksi ACI 318-08 7.12.2.1

C-240

Level 1 Underground NS Direction, Column Strip, Negative Moment LNS

Span Length Critical Moment

Mu

30 -82.6

ft kip-ft

4,000 3400 #6 D44 0.44 0.750 80

psi psi

Material Properties f'c

Concrete Strength Average Concrete Strength Bar Size for WWR Nominal WWR Size Rebar Area Nominal Diameter WWR Yield Strength

f'c,avg

Abar dbar Fy

in2 in ksi

Flexural MMR Calculation (Per Foot Width) Slab Thickness Concrete Cover Slab Effective Depth Drop Panel Thickness Total Effective Depth Total Slab Thickness Slab Beam Width Bar Spacing WWR Area Tension at Yield Depth of Equi. Comp. Stress Block Nominal Moment Strength Adjustment Factor for Moment Design Moment Strength Minimum Required Steel Area

C-241

h c d hdr dtot htot b s As T a Mn φ ΦMn ΦMn>Mu ? As,min As>As,min?

12.0 2.0 9.6 7.0 16.6 19.0 12.0 6.0 0.88 70 1.73 92.5 0.9 83.2 Yes 0.31 Yes

in in in in in in in in in2 kips in kip-ft

=h-c-dbar/2 =d+hdr =h+hdr

max.s=16in. ACI 318-08 3.5.3.7

=FyAs =T/(b*f'c,avg) =T(d-a/2)

kip-ft in2

6.2.1 Two-Way Slab Using WWR

=0.0018bh*60/Fy, for Fy > 60 ksi ACI 318-08 7.12.2.1

MMR Shear Check Beam Shear Check Total Factored Load Length of Equi. Column Section Shear at dtot Distance from Col. face Adjustment Factor for Shear Shear Strength

Punching Shear Check Tributary Area for one Column Punching Shear at dtot/2 from Col. face Punching Shear Perimeter Punching Shear Strength

wu deq Vu Φ ΦVc ΦVc>Vu?

627 28.4 7.8 0.75 18.9

psf in kips/ft

=wu(LNS/2-deq/2-dtot) =Φ(2*sqrt(f'c)*b*dtot),

kips/ft

ACI 318-08 11.2.1.1

Yes =wu*LNS*LEW

Atri Vu b0 ΦVc ΦVc>Vu?

855 527 180 567 Yes

2

ft kips in kips

6.2.1 Two-Way Slab Using WWR

=wu(Atri-(deq+dtot)2) =4(deq+dtot) =Φ(4*sqrt(f'c)*b0*dtot)

C-242

Level 1 Underground NS Direction, Middle Strip, Positive Moment

Span Length Critical Moment

LNS Mu

30 14.3

ft kip-ft

f'c

4,000

psi

f'c,avg

3400 #6 D44 0.44

psi

Material Properties Concrete Strength Average Concrete Strength Bar Size for WWR Nominal WWR Size Rebar Area

Abar

2

0.750

in in

80

ksi

h c d b s As

12.0 2.0 9.6 12.0 16.0 0.33

in in in in in

Yield Tension

T

Depth of Equi. Comp. Stress Block

Nominal Diameter WWR Yield Strength

dbar Fy

Flexural MMR Calculation (Per Foot Width) Slab Thickness Concrete Cover Slab Effective Depth Width Bar Spacing WWR Area

Nominal Moment Strength Adjustment Factor for Moment Design Moment Strength Minimum Required Steel Area

max.s=16in. ACI 318-08 3.5.3.7

26

in2 kips

a

0.65

in.

=T/(b*f'c,avg)

Mn φ ΦMn

20.5 0.9 18.4

kip-ft

=T(d-a/2)

ΦMn>Mu ?

Yes 0.19 Yes

As,min As>As,min?

C-243

=h-c-dbar/2

=FyAs

kip-ft in2

6.2.1 Two-Way Slab Using WWR

=0.0018bh*60/Fy, for Fy > 60 ksi ACI 318-08 7.12.2.1

Level 1 Underground NS Direction, Middle Strip, Negative Moment LNS

Span Length Critical Moment

Mu

30 -27.5

ft kip-ft

4,000 3400 #6 D44 0.44 0.750 80

psi psi

Material Properties f'c

Concrete Strength Average Concrete Strength Rebar Size for WWR Nominal WWR Size One Bar Area Nominal Diameter WWR Yield Strength

f'c,avg

Abar dbar Fy

in2 in ksi

Flexural MMR Calculation (Per Foot Width) Slab Thickness Concrete Cover Slab Effective Depth Drop Panel Thickness Total Effective Depth Total Slab Thickness Slab Beam Width Bar Spacing WWR Area Yield Tension Depth of Equi. Comp. Stress Block Nominal Moment Strength Adjustment Factor for Moment Design Moment Strength Minimum Required Steel Area

h c d hdr dtot htot b s As T a Mn φ ΦMn ΦMn>Mu ? As,min As>As,min?

12.0 2.0 9.6 7.0 16.6 19.0 12.0 16.0 0.33 26 0.65 36 0.9 32 Yes 0.31 Yes

in in in in in in in in in2 kips in kip-ft

=h-c-dbar/2 =d+hdr =h+hdr

max.s=16in. ACI 318-08 3.5.3.7

=FyAs =T/(b*f'c,avg) =T(d-a/2)

kip-ft in2

6.2.1 Two-Way Slab Using WWR

=0.0018bh*60/Fy, for Fy > 60 ksi ACI 318-08 7.12.2.1

C-244

MMR Shear Check Beam Shear Check Total Factored Load Length of Equi. Column Section Shear at dtot Distance from Col. face Adjustment Factor for Shear Shear Strength

Punching Shear Check Tributary Area for one Column Punching Shear at dtot/2 from Col. face Punching Shear Peremeter Punching Shear Strength

C-245

wu deq Vu Φ ΦVc ΦVc>Vu?

627 28.4 7.8 0.75 18.9 Yes

psf in kips/ft

=wu(LNS/2-deq/2-dtot) =Φ(2*sqrt(f'c)*b*dtot),

kips/ft

ACI 318-08 11.2.1.1

=wu*LNS*LEW

Atri Vu b0 ΦVc ΦVc>Vu?

855 527 180 567 Yes

2

ft kips in kips

6.2.1 Two-Way Slab Using WWR

=wu(Atri-(deq+dtot)2) =4(deq+dtot) =Φ(4*sqrt(f'c)*b0*dtot)

C-246

1 2 3 4 5 6 7 Caisson

psi

psf psf psf ft2 kips

psf psf psf ft2 kips

Column Height

in 274 120 106 106 106 106 106 180

Column Area

in2 452 452 707 707 707 1018 1018 1018

in 12 12 15 15 15 18 18 18 kips 314.0 798.5 1196.4 1594.2 1992.0 2393.2 2794.2 3202.1

Load on column

3 0.0839 lb/in 1.5 in 3.0 in

4000

170 165 468 834 390.3

170 100 364 834 304

Column Radius

ρc c c

Garage level

f'c

Concrete Density Cover for Columns Cover for Caissons

P

DL LL

P

DL LL

Concrete Strength

Concrete Properties

Dead Load Parking Garage Live Load Parking Garage Load Tributary Area Load on Column

Loads Levels 1-7

Dead Load Terrace Live Load Roof Load Tributary Area Load on Column

Roof Loads

12 12 12 12

x x x x

14 14 53 170

W shape

Steel Shape

= 1.2DL+1.6LL

= 1.2DL+1.6LL

This is the summary for the parking garage column geometries and reinforcing

6.2.2 Summary of Parking Garage Columns

# 6 6 6 12

Size #6 #6 #6 #6

Rebar in 21 21 27 27 27 33 33 30

Dc

Color Key:

5/9/2012

Size #3 #3 #3 #3 #3 #3 #3 #3

Spiral Rebar

Yes No

in 2.24 2.24 2.28 2.28 2.28 2.31 2.31 1.10

Spiral Spacing (kips) 1004.1 1004.1 1518.9 1607.8 2592.6 2592.6 2993.4 3884.1

Column Capacity

User Input Constant/Previous Calc. Calc/Lookup Passes Check Fails Check

6.2.2 Summary of Parking Garage Columns

ρs 0.009 0.009 0.007 0.007 0.007 0.006 0.006 0.013

Spiral Reinforcement ratio

Created by: KLS

% 219.8 25.7 27.0 0.9 30.1 8.3 7.1 21.3

Over Designed

(in2) 2.64 2.64 2.64 5.28 4.71 4.71 17.0 44.7

Area of Steel

(kips) 0.034 0.015 0.013 0.013 0.013 0.013 0.013 0.023

Weight from Steel

(in2) 449.7 449.7 704.2 701.6 702.1 1013.2 1000.9 973.2

Area of Concrete

(kips) 10.3 4.5 6.3 6.2 6.2 9.0 8.9 14.7

Weight from Concrete

(kips) 10.4 4.5 6.3 6.3 6.3 9.0 8.9 14.7

Weight of Column

6.2.2.1 Parking Garage Column with Rebar

Created by: KLS

Design tool for concrete columns in parking garage reinforced with rebar. Used for the Roof and Levels 1-3 Color key with summary.

5/9/2012

P

Load on Column - Roof Dead Load Terrace Live Load Roof Load Tributary Area Load on Column Moment

DL LL

P M

170 100 364 834 304 0

psf psf psf 2 ft

L = 1.2DL+1.6LL

kips kip-ft Dc

Concrete Properties Concrete Strength

f'c

4,000

psi

Concrete Density Cover for Columns

ρc

0.08 1.5

lb/in3 in

ccol ccais

Cover for Caissons

3

r

in

Column Design - Roof Load Garage level Column Radius Column Area Column Height Load on column Quantity of Rebar Rebar Size

r Ag

1 12

Cover in

452 274 314 6 6

in2 in kips

21.0

in

60.0 0.01 3

ksi Size

0.375

in in2

s ɸ ɸPn

0.11 2.24 0.7 937

Area of Steel

As

0.66

kips in2

Weight from Steel

ws

Area of Concrete

Ac

0.03 452

kips in2

= n*h*1.502lbs/ft for #6 bars = Ag-As

Weight from Concrete

wc

10.4

kips

wslf

10.4

kips

= ρc*h*Ac = wc+ws

ɸPn>P?

Yes

h P n # Dc

Steel Yield Stength

Fy

Spiral Reinforcement ratio Spiral Rebar Diameter of Spiral Rebar

ρs # ds

Area of single Rebar

Asr

Spiral Spacing Column Capacity

Weight of Column

C-247

= πr2 includes self-weight Minimum 6 ; ACI 10.3 = 2r-2(Cover) 2

= 0.45(Ag/(πDc /4)-1)f'c/Fy

in

= Asr*π(Dc-ds)/(πDc2/4)ρs ; ACI 10.9.3 ACI 10.3.5.1 = 0.85ɸ[0.85f'c(Ag-As)+FyAs] ; ACI 10.3.5.1 = n*Asr

6.2.2.1 Parking Garage Column with Rebar

6.2.2.2 Parking Garage Column with W-Shape

Created by: KLS

5/9/2012

Design tool for columns with embedded shapes under pure axial load Reference: Chapter I AISC Steel Construction Manual Color key on summary.

Loads Pu

Total Load

3,766

kip

h

Section Type W12x170

Column Properties Radius of column Area of cross-section Yield Strength of Steel Shape

r A Fy

18 1,018 50

Cross-Sectional Area

As

49.91

Concrete Stength

f'c

4

Area of Concrete

Ac

968

Yield Strength of Rebar

Fysr

60

Cross-Sectional Area of rebar

Abar

0.00

Modulus of Elasticity of Steel

Es

29,000

Moment of Inertia (Strong)

Ix

1,639

ksi in4

Moment of Inertia (Weak)

Iy

517

in4

Moment of Inertia of Steel

Is

517

in4

Moment of Inertia of rebar

Isr

0

in4

Effective Rigidity

C1

0.20

≤0.3

Density of Concrete

ρc

145

psf

Modulus of Elasticity of Concrete

Ec

3,492

= wc sqrt(f'c)

Moment of Inertia of Concrete

Ic

81,931

psi 4 in k-in2

= EsIs+0.5EsIsr+C1EcIc

Effective EI Effective Length Factor Length of Column

EIeff K h

7.16E+07 1 180

in in2 ksi in2 ksi in2

W 12 x 170

ksi in2 r

= 0.1+2(As/Ac+As) 1.5

= pin-pin connection

in

Column Capacity Euler Buckling of Column

Compressive Stength Reduction Factor Ultimate Compressive Stress

2

2

Pe

21,825

Pno

5,787

kips

= FyAs+FysrAbar+0.85f'cAc

Pno/Pe

0.27

≤2.25

= if Pno≤2.25 Pn=Pno[0.658^(Pno/Pe)]

Pn Φ ΦPn

5,179 0.75 3,884 Yes

kips

= if Pno>2.25 Pn=0.877*Pe

ɸPn>Pu?

= π EIeff/(Kh)

kips

6.2.2.2 Parking Garage Column with W-Shape

C-248

6.2.3 Belled Caisson Design Belled caissons distribute the load from the parking garage columns over a larger area to lower the pressure to below the allowable bearing pressure of the soil, 45 ksf.

Load at bo om of caisson P := 3767kip

Parking Garage Columns.xls

Net Allowable Bearing Pressure on hardpan σ := 45ksf per Geotechnical Report

Area of Belled Caisson Area :=

P σ

= 83.711 ⋅ ft Area

radius :=

π

2

= 5.162 ⋅ ft

radius := 5.5ft rshaft := 18in R := radius − rshaft = 4 ⋅ ft y :=

R tan ( 30deg)

y := 7ft

C-249

= 6.928 ⋅ ft

Angle must less than or equal to 30 degrees per Chicago Building Code

6.3 Tower Foundation 6.3.1 Abaqus Analysis of Caissons

251

6.3.2 Mega-Column Caisson Design

253

6.3.3 Ring Beam Design

255

6.3.4 Core Caisson Design

257

6.3.5 Caisson Rebar

259

6.1 Retaining Wall C-250

6.3.1 Abaqus Analysis of Caissons

Created By: NT/JAC 5/11/2012

A finite element analysis using Abaqus was performed to obtain the maximum stresses experienced by the rock-socketed caissons. There were two main types of caissons, each requiring different Abaqus models. These were the caissons transmitting loads from the concrete core down to the bedrock and the caissons transmitting loads from the mega-columns. In either case, the caissons were modeled as quartered cylinders embedded into the corners bedrock cubes, taking advantage of the symmetry in the geometry. In the Abaqus results, bluer colors indicate lower stresses, whereas red colors indicate higher stresses.

Core Caissons The core caissons experienced only axial loads in the form of gravity loads from the concrete core. No shear forces were applied on these caissons. As can be seen in the figure below, there was a slight stress concentration at the top of the caisson where the load was applied. The maximum Von-Mises compression stress was 4.7 ksi, corresponding to a need for minimum reinforcing steel.

Abaqus model of stresses in the rock-socketed caissons under the concrete core

6.3.1 Abaqus Analysis of Caissons C-251

Mega-Column Caissons The mega-column caissons experienced both axial loads and shear forces, in the form of lateral and gravity loads from the mega-columns. As such, the stresses in these caissons were higher. This can be seen in the figure below, where darker red colors indicate higher stress concentration at the top surface of the caisson. The maximum Von-Mises compression stress was 4.9 ksi, corresponding to a need for a higher amount of reinforcing steel.

Abaqus model of stresses in the rock-socketed caissons under the mega columns

6.3.1 Abaqus Analysis of Caissons C-252

6.3.2 Mega-Column Caisson Design

Created by: KLS 5/9/2012

Design tool for rock-socketed caissons supporting the mega-column Acceptible? % Overdesigned

YES 5.47%

See bottom of calculation for diagram.

Material Properties Concrete Compressive Strength

f'c

14

ksi

Steel Yield Strength Young's Modulus Bedrock Poisson's Ratio Bedrock Emperical Constant

Fy

35 3500 0.28 0.5

ksi ksi

1152 102 120 114

in in in in

dc dd

102 0.9 1

in in in

0.0625

in

Mega Column Total Base Reaction Weight of Connection Column Caisson Base Reaction Allowable Stress in Concrete

P σc

53,852 1,228 56,214 4.61

kips kips kips ksi

Allowable Stress in rock

σr

4.16

ksi

Ref. 4

Allowable Stress

σall

4.16

ksi

Minimum of σc,σr

Actual Stress per Caisson Factor of Safety

σact

2.38 2

ksi

= P/(πd2/4)

E ν n

Chicago Building Code Ref. 1 Ref. 2 Ref. 3

Dimensions Depth to Bedrock Depth in Bedrock Diameter of Caisson Diameter of Caisson socket Length of Socket Minimum Steel Casing Actual Steel Casing Diameter Deduct steel thickness for durability

L Lo d bs Ls

= 0.0075*d

Forces and Stresses

FS

from Midas Gen = 0.3f'c+(Fy1.5(dc-dd))/d

= σall/σact

0.43

Settlements Settlement in Rock Settlement in Shaft

0.118 0.443

= (π/2*σact(1-ν2)(d/2))/(n*Ebedrock) = (σact(Lb+Lo))/(57*f'c)

in in 0.05

C-253

6.3.2 Mega-Column Caisson Design

Uplift Check Tmax

Maximum Tension Reaction

As

Area of Steel Weight of Steel

23488 672 491

kip in2

Midas Gen

kip

13.6 lb/ft for #18 bars

2

ρc

10638 160

in pcf

Weight of Caisson

wc

1135

kip

Compressive Strength Socket Shear

f 0.7 ksi Vs 25571.31 kips

Resistance Against Uplift Ru>Tmax?

Ru

26706 Yes

kips 0.12

Theoretical upperbound Horizontal Subgrade Modulus

k kh

9 2,150

ksf/ft

Shear Strength of rock Lateral Pressure taken by rock Shear Capacity of Rock

Su 455,526 ksf σh 4.10E+07 k/ft Vr 4.10E+08 kips

Area of Concrete Concrete Density

= 0.05f'c if qu>f'c ; Ref. 5 = π*bs*L*f ; Ref. 6

Shear Check

Vmax

Maximum Shear Factor of Safety Design Shear Vr>V?

FS V

References 1 Mechanics of Material, James M Gere (1997) 2 Coduto, "Geotechnical Engineering Principles and Practices"(1999) 3 Kulhawy, Phoon, and Akbas (1993) "Drilled Shaft Side Resisitance in Clau Soil to Rock" Geotech Spec Publications No. 38 4 Geotechnical Report 5 Kulhawy, Phoon, and Akbas (2005) "Evaluation of Capacity of Rock Foundation Sockets" Proceddings, 40th US Symposium on Rock Mechanics, Anchoarage Alaska, June.

= 67*kh*sqrt(d*1ft) ; Ref. 4 = k*d*Su = σh*d

40000 kips 4 160000 kips Yes

from Midas Gen = Vmax*FS

P

P

Tmax

6 Geotechnical Design of Deep Foundations 20.6.4.1 Vs

6.3.2 Mega-Column Caisson Design

C-254

6.3.3 Ring Beam Design A ring beam will be used to connect the core walls to the caissons. This is designed to even distribute the axial load to the caissons and to resist that shear forces from the core.

Ring Beam Proper es hring := 8ft

Height of Ring Beam

router := 47ft

Outer Radius of Ring Beam

rinner := 33ft

Inner Radius of Ring Beam

rcaissons := 5ft

Radius of Caissons

Aring :=  π⋅ router 

2

2 2   −  π rinner  = 3518.6 ⋅ ft

Acaissons := 20 ⋅  π ⋅ rcaissons 

2

2

2  = 1570.8 ⋅ ft

Aslab := π ⋅ rinner = 3421.2 ⋅ ft

2

A := Aring + Aslab − Acaissons = 5369 ⋅ ft

2

Effec+ve Area for Fric+on

Soil Proper es lbf Su := 9000 2 ft lbf ρclay := 70 3 ft ρw := 62.4

Undrained Shear Strength ; Geotechnical Report

Denisty of Clay

lbf ft

Denisty of Water

3

Le := 49.2ft

ρe := ρclay + ρw

Effec+ve Density

Le := 49.2ft

Effec+ve Length for Earth Pressure on a Curved Surface

(

)

Pp := Le ⋅ hring ⋅ 4 ⋅ Su − ρe ⋅ hring = 13752.7 ⋅ kip V := Pp + Su ⋅ A = 62073.5 ⋅ kip

C-255

Passive Earth Pressure ; CEE 6410

Shear Resistance from Soil

Design Base Shear: 49030 kip (from Midas Gen) Vcore := 49030kip V = 62073.5 ⋅ kip V > Vcore

Yes

V

= 1.3

FS :=

Vcore

C-256

6.3.4 Core Caisson Design

Created by: KLS 5/9/2012

Design tool for rock-socketed caissons supporting the core See bottom of calculation for diagram.

Overall Check Acceptible? % Overdesigned

YES 29.70%

Material Properties Concrete Compressive Strength

f'c

14

ksi

Steel Yield Strength Young's Modulus Bedrock Poisson's Ratio Bedrock Emperical Constant

Fy

35 3,500 0.28 0.5

ksi ksi

492 102 120 114

in in in in in

dc dd

102 20 0.9 1

in in

0.0625

in

Core Reaction at Elevation=0 Core Wall Weight Below Elevation=0 Core Caisson Total Base Reaction Allowable Stress in Concrete

kips kips kips ksi

from Midas Gen

P σc

378,016 21,970 400,489 4.61

Allowable Stress in rock

σr

4.16

ksi

Ref. 4

Allowable Stress

σall

4.16

ksi

Minimum of σc,σr

Actual Stress per Caisson Factor of Safety

σact

1.77 2

ksi

= P/(πd2/4)

E ν n

Chicago Building Code Ref. 1 Ref. 2 Ref. 3

Dimensions Depth to Bedrock Depth in Bedrock Diameter of Caisson Diameter of Caisson socket Length of Socket Number of Caisson Minimum Steel Casing Actual Steel Casing Diameter Deduct steel thickness for durability

L Lo d ds Ls

= 0.0075*d

Forces and Stresses

FS

includes self-weight = 0.3f'c+(Fy1.5(dc-dd))/d

= σall/σact

0.57

Settlements Settlement in Rock Settlement in Shaft

0.088 0.156

= (π/2*σact(1-ν2)(d/2))/(n*Ebedrock) = (σact(Lb+Lo))/(57*f'c)

in in 0.30

C-257

6.3.4 Core Caisson Design

Uplift Check Tmax

2,100

kip

Area of Steel Weight of Steel Area of Concrete Concrete Density

As

256 35.7 11,054 160

in2 kip kip pcf

Weight of Caisson Unconfined Compressive Strength

wc f

503.6 0.7

kip ksi

Socket Shear

Vs

25,571

kips

Resistance Against Uplift Ru>Tmax?

Ru

26,075

kips

Maximum Tension Reaction

ρc

Yes

Ref. 4 13.6 lb/ft for #18 bars

= 0.05f'c if qu>f'c ; Ref. 5 = π*bs*L*qu ; Ref. 6 = Vs+Wc

0.92

References 1 Mechanics of Material, James M Gere (1997) 2 Coduto, "Geotechnical Engineering Principles and Practices"(1999) 3 Kulhawy, Phoon, and Akbas (1993) "Drilled Shaft Side Resisitance in Clau Soil to Rock" Geotech Spec Publications No. 38 4 Geotechnical Report 5 Kulhawy, Phoon, and Akbas (2005) "Evaluation of Capacity of Rock Foundation Sockets" Proceddings, 40th US Symposium on Rock Mechanics, Anchoarage Alaska, June. 6 Geotechnical Design of Deep Foundations 20.6.4.1

P

P

Tmax

Vs

6.3.4 Core Caisson Design

C-258

6.3.5 Caisson Rebar

Created by: KLS

5/9/2012

This spreadsheet calculates the amount of rebar needed inside the caissons

Caisson Properties Radius

r

Color Key User Input

ft 2 A 11,310 in Fy 60 ksi

Area Steel Yield Strength

5

Top of Mega-column Caissons Stress at Top Maximum Tension Force Area of Steel

σ 4.9 ksi T 55,418 kip 2 As 924 in 272

in

Area of Rebar Needed Bar Size Area of Rebar Number of Bars Actual Area of Steel Asactual>As

652 18 4 168 944

in2

Abar As-actual

Yes No Abaqus Model = σ*A = T/Fy

2

Area of Embedded Steel Shape #

Constant/Previous Calc. Calc/Lookup

in2 in2

Yes

Bottom of Mega-column Caissons Stress at Bottom Maximum Tension Force Area of Steel Bar Size Area of Rebar Number of Bars Actual Area of Steel Asactual>As

σ 1.9 ksi T 21,488 kip 2 As 358 in # 18 in2 Abar 4 90 2 As-actual 360 in

Abaqus Model = σ*A = T/Fy

Yes

Core Caissons Stress in Core Caisson Maximum Tension Force Area of Steel Bar Size Area of Rebar Number of Bars Actual Area of Steel Asactual>As

C-259

σ 1.2 ksi T 13,572 kip 2 As 226 in # 18 in2 Abar 4 As-actual

64 256

Abaqus Model = σ*A = T/Fy

in2

Yes

6.3.5 Caisson Rebar

Passes Check Fails Check

7.0 Creep and Shrinkage 7.1 Steel Column Deformation

261

7.1.1 Steel Column Properties and Loads

262

7.1.2 Steel Column Deformation Calculations

263

7.2 Concrete Core Deformation

265

7.2.1 Concrete Core Properties and Loads

266

7.2.2 Concrete Core Deformation Calculations

267

Displacement Over 20 Years Core Displacement (inches)

25 20 15 CONSTRUCTION ENDS

Concrete Core Summary

10

STEEL COLUMNS

5 0 0

5

10

15

20

Time (years)

C-260

7.1 Steel Column Deformation This chart reflects the deformation of the steel columns for each floor group and the overall steel deformation at a time of 2 years. t = 2 years 730

Calculated Days

Floors Lobby 5-16 17-28 29-39 40-51 52-63 64-73 74-86 87-99 100-110 111-122 123-133 134-145

Deflection per floor 0.979 0.077 0.067 0.057 0.049 0.041 0.034 0.054 0.042 0.031 0.021 0.012 0.004

Local Def per floor group 0.979 0.921 0.805 0.631 0.590 0.492 0.335 0.702 0.546 0.340 0.251 0.131 0.045

Ultimate Steel Deformation:

Global Deformation Sum 0.98 1.90 2.71 3.34 3.93 4.42 4.75 5.46 6.00 6.34 6.59 6.72 6.77

inches inches inches inches inches inches inches inches inches inches inches inches inches

6.77

inches

C-261

7.1 Steel Column Deformation

7.1.1 Steel Column Properties and Loads Summary of column and core dimensions and the loads applied on each Column Properties Column dimensions depth base concrete Strength conc. modulus 57000*sqrt(f'c) Total Area Concrete Area

Lobby

17-28

29-39

40-51

52-63

64-73

74-86

87-99

100-110

111-122

123-133

134-145

40 40 14,000 6,744 928 0

40 40 14,000 6,744 928 0

40 40 14,000 6,744 928 0

40 40 14,000 6,744 928 0

40 40 14,000 6,744 928 0

40 40 14,000 6,744 928 0

36 36 14,000 6,744 688 0

36 36 14,000 6,744 688 0

36 36 14,000 6,744 688 0

36 36 14,000 6,744 688 0

36 36 14,000 6,744 688 0

36 36 14,000 6,744 688 0

in in psi ksi in2 2 in

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-1 928 36 36 0 0

BU-2 688 28 36 0 0

BU-2 688 28 36 0 0

BU-2 688 28 36 0 0

BU-2 688 28 36 0 0

BU-2 688 28 36 0 0

BU-2 688 28 36 0 0

in2 in in in in

1.000 187.5 188

1.000 41.3 41

1.000 41.3 41

1.000 41.3 41

1.000 41.3 41

1.000 41.3 41

1.000 41.3 41

1.000 30.6 31

1.000 30.6 31

1.000 30.6 31

1.000 30.6 31

1.000 30.6 31

1.000 30.6 31

kips kips

d 40 b 40 f'c 14,000 Ec 6,744 At 928 Ac 0

Steel Shape: Area depth width of flange thickness of flange thickness of web

W A

Steel Ratio Steel Shape Self Weight TOTAL COLUMN SELF WEIGHT

ϱg

Core Properties Bank Radius thickness Total Volume / Floor Total Weight/Floor Total Area/Floor # of Columns Area per core "column" SW per core "column"

5-16

d bf tf tw

1 40 8 26,527 4,244 2,010 21 96 202

2 38 6 18,900 3,024 1,432 21 68 144

3 36 4 11,937 1,910 904 14 65 136

DL (kips) 35.6 96.2 32.7 74.6 36.0 86.0 35.6 63.7

LL (kips) 34.9 35.3 30.1 27.2 28.2 31.0 34.9 22.8

SUS LL (psf) 6 6 6 6 6 6 6 6

4 26 3.33 7,177 1,148 544 14 39 82

ft ft ft3 kips ft2 ft2 kips

Unfactored Nodal Loads

Bank 1 (Core) Bank 1 (Ext. Column) Bank 2 (Core) Bank 2 (Ext. Column) Bank 3 (Core) Bank 3 (Ext. Column) Bank 4 (Core) Bank 4 (Ext. Column)

SDL (psf) 20 20 20 20 20 20 20 20

SDL (kips) 44.6 20.8 37.6 16.0 28.1 18.4 22.9 12.4

Trib. Area (ft^2) 2,229 1,038 1,881 800 1,407 922 1,146 620

7.1.1 Steel Column Properties and Loads

C-262

7.1.2 Steel Column Deformation Calculations This is a representative calculation, performed in the same manner for all floor sets. Creep and Shrinkage calculations per GL2000 Method from ACI 209.2R-27 Bank Floor Group

1 5 - 16

Column Properties fc (28) [psi]= 14000 psi fcm28 (A-94) 16100 psi

d b

in in

s k

0.13

from table A.14

1.15

from table A.14

538

microstrain ; (A-99)

level

10

f'c

14000 psi

εshu

first level

5

Ec

6744

h

0.714

relative humidity from National Climatic Data Center average

last level

16.0

At

928

βh

0.694

(A-100)

total def (t = 3yr)

0.9

inches

total def (t = 20yr)

0.9

inches

Ac

1

when t0=tc

in

Ac

0.0 158 0.0

in2

in2

d bf

in in in in

ϱg

36 36 0 0 1

1.7 1.9 2.0 2.1 2.2 2.2

34.4 68.7 103.1 137.5 171.8 206.2 240.6 274.9 309.3 343.6

62.3 62.3 62.3 62.3 124.5 124.5 124.5 124.5 186.8 186.8

97 131 165 200 296 331 365 399 496 530

0.01972 0.02931 0.03854 0.04771 0.07198 0.08133 0.09065 0.09996 0.12494 0.13433

0.00000 0.00000 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00002 0.00002

1 1 1 1 1 1 1 1 1 1

tf tw

in in

5492 6021 6273 6429 6537 6619 6683 6735 6778 6816

1.00 1.00 1.00 1.00 1.00 1.00

373.23 373.23 373.23 373.23 373.23 373.23

7.1.2 Steel Column Deformation Calculations

3 3 3 3 3 3 3 3 3 3

0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 0.003 0.003

deformation

Ec (ksi) (A-95)

9216 11273 12325 12999 13480 13846 14137 14377 14578 14751

Steel Deformation (PL/AE)

fcmt(t) (A-96)

1 1 1 1 1 1 1 1 1 1

Number of Columns/Column

βe (A-97)

1 2 3 4 5 6 7 8 9 10

β(t-tc) (A-101)

tlocal

tglobal

928

Bank

φ(tc)

As

elastic strain unreinforced

time load is applied

fc (ksi)

4

Ps total (kip)

time drying begins

Ps SDL (kip)

928

25 26 27 28 29 30 31 32 33 34

120 256 404 540

4

2

As height v/s

30 34 37 34

day ended

tc (days) t0 (days)

Ps DL (kip)

kips kips kips kips ksi

in

Creep Coefficient (A103)

137.5 115.9 77.7 62.9 29000

2

Corrected Shrinkage (A-98)

Bank 1 Load Bank 2 Load Bank 3 Load Bank 4 Load Es

0

ksi in2

BU-1 floors

C-263

40 40

Values for Creep and Shrinkage analysis

0.0006 0.0008 0.0010 0.0012 0.0017 0.0019 0.0021 0.0023 0.0029 0.0031

fcmt(t) (A-96)

Ec (ksi) (A-95)

β(t-tc) (A-101)

Corrected Shrinkage (A-98)

Creep Coefficient (A103)

Ps DL (kip)

Ps SDL (kip)

Ps total (kip)

fc (ksi)

elastic strain unreinforced

Bank

14901 15033 15150 15256 15351 15438 15518 15591 15658 15721 15779 15834 15885 15933 15978 16021 16062 16100 16509 16752 16917 17039 17134 17219 17232 17359 17449 17519 17564 17574 17619 17657 17687 17718 17800 17867 17954 18127 18188

6848 6876 6901 6923 6943 6961 6978 6993 7007 7020 7032 7043 7054 7064 7073 7082 7090 7098 7181 7230 7263 7288 7307 7324 7326 7351 7369 7383 7391 7393 7402 7410 7416 7422 7438 7451 7468 7501 7513

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23 373.23

2.3 2.3 2.4 2.4 2.4 2.4 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.7 2.8 2.8 2.8 2.9 2.9 2.9 2.9 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.1 3.1 3.2 3.3 3.5

378.0 412.4 446.7 481.1 515.5 549.8 584.2 618.6 652.9 687.3 721.7 756.0 790.4 824.7 859.1 893.5 927.8 962.2 1477.7 1993.1 2508.6 3024.1 3539.5 4123.7 4210.6 5224.4 6238.1 7251.9 8062.9 8198.9 8879.0 9559.1 10180.9 10938.7 13075.9 13075.9 13075.9 13075.9 13075.9

186.8 186.8 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 249.0 192.0 192.0 192.0 192.0 192.0 147.6 147.6 147.6 147.6 147.6 0.0 0.0 0.0 0.0 0.0

565 599 696 730 764 799 833 868 902 936 971 1005 1039 1074 1108 1142 1177 1211 1727 2242 2758 3273 3789 4373 4403 5416 6430 7444 8255 8346 9027 9707 10328 11086 13076 13076 13076 13076 13076

0.14370 0.15307 0.17840 0.18782 0.19723 0.20663 0.21603 0.22543 0.23484 0.24424 0.25364 0.26304 0.27244 0.28184 0.29124 0.30065 0.31005 0.31946 0.46076 0.60238 0.74426 0.88634 1.02858 1.18995 1.19850 1.47949 1.76067 2.04202 2.26720 2.29299 2.48280 2.67254 2.84599 3.05734 3.61381 3.62007 3.62830 3.64459 3.65030

0.00002 0.00002 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00005 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016 0.00016 0.00020 0.00024 0.00028 0.00031 0.00031 0.00034 0.00036 0.00038 0.00041 0.00049 0.00049 0.00049 0.00049 0.00049

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4

7.1.2 Steel Column Deformation Calculations

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2

Switch to Bank 2 Load

Switch to Bank 3 Load

Switch to Bank 4 Load Stop Applying Bank 4 Load

0.003 0.004 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.005 0.006 0.006 0.006 0.006 0.007 0.007 0.007 0.007 0.010 0.013 0.016 0.019 0.022 0.026 0.026 0.032 0.038 0.044 0.048 0.049 0.053 0.057 0.061 0.065 0.077 0.077 0.077 0.077 0.077

deformation

βe (A-97) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Steel Deformation (PL/AE)

tlocal 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 43 58 73 88 103 120 123 158 193 228 256 263 298 333 365 404 540 706 1071 3626 7276

Number of Columns/Column

tglobal 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 67 82 97 112 127 144 147 182 217 252 280 287 322 357 389 428 564 730 1095 3650 7300

0.0033 0.0035 0.0041 0.0043 0.0045 0.0047 0.0049 0.0051 0.0053 0.0055 0.0057 0.0059 0.0061 0.0063 0.0065 0.0067 0.0069 0.0071 0.0101 0.0132 0.0162 0.0192 0.0222 0.0257 0.0258 0.0318 0.0378 0.0437 0.0485 0.0490 0.0530 0.0570 0.0606 0.0651 0.0768 0.0768 0.0768 0.0768 0.0768

C-264

7.2 Concrete Core Deformation

Created by: ADV, JDM, SJR, DSF

4/28/2012

This sheet summarizes values from the calculation pages in an easy to read format and calculates the total deformations of the core.

t = 2 years

Floors Lobby 5-16 17-28 29-39 40-51 52-63 64-73 74-86 87-99 100-110 111-122 123-133 134-145

Deformation per Floor (in) 0.309 0.073 0.065 0.056 0.004 0.003 0.003 0.171 0.134 0.100 0.539 0.309 0.100

Concrete Core Summary Total Deformation Time (yr) Def (in) 0 0 2 18.8 3 20.0 10 23.0 20 24.8

Deformation per Floor Segment (in) 0.31 0.88 0.77 0.62 0.04 0.04 0.03 2.22 1.74 1.10 6.47 3.39 1.20

t = 3 years Sum of Floor Segment Deformations (in) 0.3 1.2 2.0 2.6 2.6 2.7 2.7 4.9 6.6 7.7 14.2 17.6 18.8

Deformation per Floor (in) 0.319 0.075 0.067 0.058 0.004 0.003 0.003 0.180 0.142 0.107 0.576 0.333 0.110

t = 10 years

Deformation per Floor Segment (in) 0.32 0.90 0.80 0.64 0.05 0.04 0.03 2.34 1.84 1.18 6.91 3.67 1.33

Sum of Floor Segment Deformations (in) 0.3 1.2 2.0 2.7 2.7 2.7 2.8 5.1 7.0 8.1 15.0 18.7 20.0

Deformation per Floor (in) 0.350 0.083 0.074 0.064 0.004 0.004 0.003 0.204 0.162 0.123 0.664 0.388 0.132

20-Year Deformation Comparisons Core Deformation: 24.8 Steel Deformation: 6.77 Difference: 18.0 Compensation / floor 0.12 Add around 20% to account for error % Total Deformation at 2 yr

Deformation per Floor Segment (in) 0.35 0.99 0.88 0.71 0.05 0.05 0.03 2.66 2.11 1.36 7.97 4.26 1.58

t = 20 years Sum of Floor Segment Deformations (in) 0.3 1.3 2.2 2.9 3.0 3.0 3.1 5.7 7.8 9.2 17.2 21.4 23.0

Deformation per Floor (in) 0.371 0.088 0.078 0.068 0.005 0.004 0.004 0.220 0.175 0.133 0.715 0.419 0.145

Construction Line in in in in

Time (yr)

Def (in) 1.64 1.64

75.9%

= def(2yr)/def(20yr)

C-265 7.2 Concrete Core Deformation

0 26

Deformation per Floor Segment (in) 0.37 1.05 0.94 0.75 0.06 0.05 0.04 2.86 2.27 1.47 8.59 4.61 1.74

Sum of Floor Segment Deformations (in) 0.4 1.4 2.4 3.1 3.2 3.2 3.3 6.1 8.4 9.9 18.4 23.1 24.8

7.2.1 Concrete Core Properties and Loads This sheet displays the properties for the core used in the creep and shrinkage analysis.

Core Properties Bank

1

2

3

4 26 3.33

Radius Thickness Total Volume / Floor

Ro t Vc

40 8

38 6

36 4

23,886

17,417

11,280

Total Weight/Floor

Wc

3,822

2,787

1,805

At

1,810 21

1,319 21

855 14

509 14

ft2

As

2,873 86 182

10,187 63 133

715 61 129

123 36 77

in2

LL (kips) 34.9 35.3 30.1 27.2 28.2 31 34.9 22.8

SUS LL (psf) 6 6 6 6 6 6 6 6

SDL (psf) 20 20 20 20 20 20 20 20

SDL (kips) 44.6 20.8 37.6 16.0 28.1 18.4 22.9 12.4

Total Area/Floor # of Columns Steel Area Area per core "column" Self Weight per core "column"

ft ft

3 6,721 ft 1,075 kips

ft2 kips

Unfactored Nodal Loads Taken from Finite Element Model Bank 1 (Core) Bank 1 (Ext. Column) Bank 2 (Core) Bank 2 (Ext. Column) Bank 3 (Core) Bank 3 (Ext. Column) Bank 4 (Core) Bank 4 (Ext. Column)

DL (kips) 747.6 96.2 686.7 74.6 504 86 498.4 63.7

Reinforcing Steel Areas Bank

Trib. Area (ft2) 2,229 1,038 1,881 800 1,407 922 1,146 620

1

2

3

4

Core Radius

Ro

40

38

36

26

ft

Core Thickness Core Circumference Rebar Spacing (in) Rebar Spacing (ft) Bar Size Number of Bars per Row

tc

6 239 9 0.75 18 318

4 226 12 1 8 226

3.33 163 14 1.17 6 140

ft ft in ft

nb

8 251 12 1 10 251

Stee Area per Bar

Asb

1.27

4

0.79

0.44

in2

Steel Area per Row

Asr

319

1,273

179

62

in2

Number of Rows of Bars

nr

9

8

4

2

Total Steel Area

As ρg

2,873

10,187

715

123

0.011

0.054

0.006

0.002

Percent Steel

s

in2

C-266

7.2.1 Concrete Core Properties and Loads

7.2.2 Concrete Core Deformation Calculations This sheet performs creep and shrinkage calculations per the GL2000 model from ACI 209.2R-27. This sheet calculates the deformations for floor 10, which is mid-level in the 5-16 floor segment. Bank Floor Group

1 5 - 16

Bank Information

Core Properties

Specified 28-day Compressive Strength

f'c

14000

psi

Mean Concrete Compressive Strength

fcm28

16100

psi

Floor # Mid-level

Core Radius

Ro

40

ft

Core Thickness

tc

8

10

Column Area

Ag

1810

ft ft2

= 1.1f'c + 700; ACI209R (A-94)

2

First Floor in Segment

f0

5

Concrete Area

Ac

1790

ft

Last Floor in Segment

ff

16

Steel Area

As

2873

in2

Steel Ratio

ρg

0.0110

Ultimate Deformation in Segment

1.05

= (ff - f0 + 1)*d20yr

in

Loading

= As/Ag

Values for Creep and Shrinkage Analysis

Bank Load

1 930

2 819

3 633

4 575

kips

Strength Development Parameter Cement Type Correction Factor

s k

0.335 1

from table A.14 from table A.14

microstrain # Floors of Load

30

34

37

34

Day Loading Ended

120

256

404

540

day

Material Properties Es 29000 ksi

Steel Elastic Modulus

As

2873

in

Concrete Area

Ac

1790

h V/S

158 42.7

ft2 in in

Floor Height Volume/Surface Ratio

εshu

468

Relative Humidity Humidity Correction Factor Curing Days

0.714 0.694 4

days

time drying begins

Age of Loading

h β(h) tc to

4

days

time load is applied

Drying Correction Factor

φ(tc)

1

2

Steel Area

= Vc/(2*Ro)

Deformation Summary 2 years 3 years 10 years 20 years

C-267

Per Floor 0.073 0.075 0.083 0.088

Group 0.876 0.904 0.994 1.054

= 900*k*(4350/fcm28)0.5; ACI 209R (A-99)

Ultimate Shrinkage

units in in in in

7..2.2 Concrete Core Deformation Calculations

National Climatic Data Center average = (1 - 1.18*h4); ACI 209R (A-100)

ACI 209R (A-104)

Steel Load, Ps DL

Steel Load, Ps SDL

Ps total

Concrete Stress, fc

Elastic Strain Unreinforced

Creep Strain Unreinforced

Shrinkage Strain

Pc(fc)

Elastic Deformation Reinforced

Eleastic Deformation Unreinforced

Ratio of Reinforced to Unreinforced

Rcfi

Bank

# Columns/Column

(in)

(in)

3,715

215

124

339

0.015

0.00000

0.00000

0.00000

27

0.00000

0.00006

0.074

0.920

1

3

4,668 5,177 5,508 5,748 5,933

422 627 831 1,034 1,237

122 120 120 238 237

544 748 951 1,272 1,474

0.030 0.046 0.063 0.088 0.105

0.00001 0.00001 0.00001 0.00002 0.00002

0.00000 0.00000 0.00000 0.00001 0.00001

0.00000 0.00000 0.00000 0.00000 0.00000

55 83 113 157 188

0.00001 0.00001 0.00001 0.00002 0.00002

0.00008 0.00010 0.00012 0.00015 0.00017

0.091 0.100 0.106 0.110 0.113

0.935 0.941 0.945 0.947 0.948

1 1 1 1 1

3 3 3 3 3

3,823

0.632 0.709 0.759 0.795 0.823

6,426 8,088 9,277 10,187 10,915

Creep Coefficient (A-103)

kips

Corrected Shrinkage (A-98)

in

β(t-tc) (A-101)

in

Ec (ksi) (A-95)

in

fcmt(t) (A-96)

ksi

microstrain

…

…

…

…

…

…

…

…

…

…

…

…

19,144

7,695

0.0287

9.32

1.78

23,932

459

24,391

2.253

0.00029

0.00052

0.00001

4,032

0.00032

0.00226

0.142

0.960

1

3

280

256

1.119

20,146

7,881

0.0423

13.73

1.90

47,758

386

48,144

4.554

0.00058

0.00110

0.00001

8,151

0.00063

0.00438

0.145

0.961

2

3

428

404

1.131

20,607

7,965

0.0533

17.29

1.97

67,754

192

67,946

6.496

0.00082

0.00161

0.00002

11,625

0.00089

0.00613

0.146

0.961

3

2

564

540

1.138

20,854

8,009

0.0616

20.00

2.02

84,440

0.0

84,440

8.118

0.00101

0.00205

0.00002

14,528

0.00111

0.00758

0.147

0.961

4

2

730

706

1.144

21,054

8,045

0.0705

22.88

2.07

84,440

0.0

84,440

8.155

0.00101

0.00210

0.00002

14,594

0.00111

0.00755

0.147

0.961

4

2

1,095 3,650 7,300

1,071 3,626 7,276

1.151 1.165 1.170

21,320 21,854 22,044

8,093 8,187 8,221

0.0868 0.1585 0.2218

28.17 51.44 71.98

2.15 2.41 2.58

84,440 84,440 84,440

0.0 0.0 0.0

84,440 84,440 84,440

8.203 8.299 8.332

0.00101 0.00101 0.00101

0.00218 0.00244 0.00262

0.00003 0.00005 0.00007

14,680 14,851 14,912

0.00111 0.00111 0.00111

0.00751 0.00744 0.00741

0.148 0.150 0.150

0.962 0.962 0.962

4 4 4

2 2 2

Elastic Strain

Creep Strain

Shrinkage Strain

Total Deformation

in

in

in

in

0.00000 0.00000

0.00000 0.00000

0.000000 0.000000

0.00005 0.00009

0.00000

0.00000

0.000000

0.00014

0.00000

0.00000

0.000000

0.00019

0.00000

0.00000

0.000000

0.00044

0.00000

0.00000

0.000000

0.00059 …

…

1.090

…

…

120

…

…

144

…

…

0.00 0.60 0.79

…

0.000 0.866 1.22

…

0.0000 0.0027 0.0038

…

2 3 4 5 6

kips

0.487

βe (A-97)

26 27 28 29 30

kips

ksi

…

tlocal 1

kips

psi

…

tglobal

days

…

days 25

0.00004 0.00008 0.00012 0.00015 0.00015 0.00015 0.00015 0.00015

0.00007 0.00016 0.00024 0.00030 0.00031 0.00032 0.00037 0.00039

0.000001 0.000002 0.000003 0.000003 0.000003 0.000004 0.000008 0.000011

0.01842 0.03862 0.05638 0.07154 0.07300 0.07534 0.08286 0.08786

7..2.2 Concrete Core Deformation Calculations

Switch to Bank 2 Load Switch to Bank 3 Load Switch to Bank 4 Load Stop Applying Bank 4 Load

C-268

8.0 References 8.1 Energy-Based Design of Lateral Systems by W.F. Baker

270

8.2 Geotechnical Report for the Chicago Spire

274

8.0 References C-269

8.1 Energy-Based Design of Lateral Systems

Abstract The sizing of the members of the lateral resistance system for multi-story buildings

is often controlled by stiffness requirements. In order to achieve economical buildings, it is important that these members be appropriately sized and that the structural materials be efficiently distributed among the various components. This paper presents a sizing technique utilizing energy methods that is currently in use by several firms involved in the design of high-rise buildings.

William 1. Baker

Theoretical Basis —

By moving the material from one

Axial Members

member to another, it is possible for all members of the structure to have equal energy densities.

Frequently in the design of high-rise

Assoc. Partner Skidmore, Owings & Merrill Chicago, IL, USA \Villiam F. Baker is an Associate Partner and Senior Structural Engineer of Skidmore, Owings & Merrill, Chicago, Illinois, USA. As Adjunct Professor of Architecture he also works at the Illinois Institute of Technology. He was involved in a number of significant projects, amongst them the Sears Tower Revitalization, Chicago (1985), the 63 story AT&T Corporate Center, Chicago (1990), and more recently, in 1992, the USG Building, a 35 story office building in Chicago.

buildings, the structural designer wants to use the minimum material to resist a prescribed wind load without exceeding a deflection criteria (such as tip deflection). In essence, the external work done by the wind load has been predefined. The task then is to proportion the structure so that the internal work is attained with a minimum volume structure. We know from virtual work methods that

nFL

structure (Fig. 1) is given by

constraint can be formulated as (1)

A

member, and n

is

the force in the

member due to a unit virtual lateral load applied at the top.

Equation (1) contains some very useful information for sizing of members. The FL/EA term gives the actual elongation

of the individual member. The n is a weighting function which gives the relative influence of the individual members on the total deflection.

Since the goal is to use the least volume

of material, it is useful to divide the deflection contribution of each member (given by the Eq. [1] by the volume of the

member). This creates a term which is essentially a virtual work or energy density, e, and can be viewed as a measure of efficiency. The energy density is given by the following equation:

2/92

ture as given by

subject to the constraint that it has a constant volume of material (V). This

the lateral (wind) loads, L/EA are the geometric and material properties of a

Structural Engineering International

sulting structure is a minimum volume structure. This can be investigated using LaGrange Iultipliers. The approach is to minimize the deflection of the struc-

the deflection at the top of a braced

where F is the force in a member due to

peer reviewed by international experts and accepted by IABSE Publications Committee

Now the question is whether the re-

g=EAL- v=O

A constrained deflection equation may then be written as A=f+Ag

Substituting for fan g from Equations (3) and (4) respectively:

A =E !'f_+A(L4L-) where X is a constant called the LaGrange Multiplier. Given that the geometry of the structure is set, the independent variables are the areas of the individual elements (A1). The next step is to differentiate the constrained deflection equation with respect to the areas, in order to find a local extremum.

-(y

)+x-c14L-)=o

Noting that the terms f and g are continuously differentiable and the g has a nonzero gradient, it can be shown that ? exists and is unique at a local extremum.

e = [(nF4L1)/(EA1)] I [L1A

(2)

=

E4 Science and C-270 Technology

99

//

>1kb

£ YL

Fig. 1

—' Unit Load

for a statically determinate structure,

structure, then the deflection is a minimum for a given volume of structure or, conversely, the volume of structure is a minimum for a given deflection.

will lead to

By comparing Equations (2) and (9), it

This can be shown by using the

can be seen that for a system of axial

LaGrange Multiplier approach. Paralleling the equations for axial members produces —

members, the energy density e, is in fact the LaGrange Multiplier for a statically determinate structure.

J.

If a structure is statically determinate, n, and F1 are constant for a given structure and loading. Equation (7) then reduces to:

-nFL.

When X is equal for all members in a

It can be derived from the above, that the optimum cross-sectional areas for a statically determinant truss can be determined from the following equation: ]O.5))

(8)

(Ai)req= 1:eqE 1F1)°5 (E(L1 F n F1

(9)

Where A q is the target deflection and n, and F, are the virtual and real forces in member i, obtained from either hand

or n .F.

F4

(10)

calculations or computer calculations

using a model with arbitrary crosssectional areas. Cross-sectional area of

Theoretical Basis —

member i

Flexural Members

a, b = Linear regression constants E = Modulus of elasticity e

= Energy density

= Axial force in member i due to lateral load case H = Story height = Depth of member i = Moment of inertia of member i L, = Length of member i I = Bay size = Moment in member i due to lateral load case m1 = Moment in member i due to unit load case = Axial force in member i due to unit load case P = Horizontal shear in beam and column assemblage r1 = Radius of gyration of member i u = Non-dimension length, equals 0 at x = 0, equals 1 at x = L V = Volume of structure = Width of member i a = Correction factor for flexural members A = Tip deflection = LaGrange Multiplier v = Virtual work of beam element i times A1 F1

100

Science and Technology C-271

LM , =—__+A(EAL-v)

(14)

The local extremum is found by differentiation.

a —=

-L.M. dl. '

El12

'__!-+AL.=O dA1

(15)

or M. dl. ,.L. _..L

2-'

(16)

El, "

For a rectangular shape of constant depth (h) and variable width (w):

_i-wh3=ih2A

I=

Nomenclature

A=

for other cross sections.

0A1

EA

an optimum material

distribution for certain types of cross sections and is approximately minimal

=r2A

(17)

Therefore,

4-L=2 dA

A parallel approach can be applied to flexural systems. The deflection contribution of flexural deformations is given by

(18)

and =

(19)

A

E i A.

which matches the energy density (11)

El

For rolled US steel shapes, the moment of inertia can be expressed as a linear function of A.

where NI =

Mmdu

M=

Moment in a member due to lateral load case,

m=

Moment in a member due to unit load case

and u

(Eq. 13).

I=a+bA

(20)

therefore,

= Non-dimensional length.

The integral is well known for elements

with the moment applied at the s and!

(21)

dA

end nodes (as is usually the case of

and

lateral analysis of multistory buildings) and is given by:

Mb. A =_!

(22)

El,

M = IMmdu +

= [M3

(2m-m)

Which is somewhat different from the

M1(2m1—m3)]/6

(12)

As was done with the axial members, a

virtual work density can be calculated by

e=

-

M.

ii (13)

energy density (Eq. 13).

For automated resizing, it is useful to define . in terms of areas, radii of gyration and correction factors. Equation (16) can be rewritten as: =

(23)

As will be shown below, making the

where a is a correction factor defined

energy densities equal for all members

as: Structural Engineering International

2/92

d11

1

(24)

and for rolled shapes, a is given in Table I (a = 1.3 is a reasonable value for the design of

For rectangular shapes, a =

I=

Series

1

W 14 x 61—82

a

+ bA

a

b

(in4)

(in2)

Range of a

Average a

—59

39.1

1.07 to 1.09

1.08

commonly used shapes in strong axis

W14x90—132

—146

43.2

l.lOtol.l5

1.12

bending).

W14 x 145—426

—937

58.7

l.llto 1.47

1.30

Wl4x455—730 W18 W21 W24 W27

-4640

87.4

l.3ltol.63

1.47

—208

68.2

l.O9to 1.38

1.21

—385

92.8

l.lOto 1.43

1.23

—626

121

l.l2tol.45

1.25

—946

152

l.l4to 1.32

1.22

W30 W33 W36

—1674 —2075 —2445

193

1.l6to 1.41

1.29

229 257

l.l4to 1.35

1.24

l.l2to 1.31

1.20

As was done for axial members, the optimal cross-sectional area for a statically

determinant flexural member can be determined from: — 0.5

(A ' i/req

=

M.

1

req

E

0.5

— 0.5

L.M.

a.

ri

0.5

IX,

T1

(25) The

Table

I

above assumes that the radius of

gyration (r) is constant for a member as the members change size (this is a

reasonable assumption as long as the member stays in the same series).

.'1uuu 20000

W36 +

19000 18000

—

17000

16000

VALUES FROM STEEL TABLES LEAST SQUARES FIT FOR I

= a + bA

15000

Theoretical Basis — General Beam Element

14000

For a general beam element, the pertinent deformations are axial, major axis flexural, minor axis flexural, major axis shear, minor axis shear and torsional. The above sizing techniques can be extended to include all of these deforma-

10000

tions. Although it is clear that axial deformations are a direct function of the cross-sectional area, the other de-

3000

W33

13000

W14

12000 11000

9000

8000 7000 6000 5000

4000 2000 1000 1

In rectangular cross sections of constant

depth, the major and minor axis shear section properties are linear functions of cross-sectional area and these functions approach zero as the cross-sectional area approaches zero. Therefore,

a procedure similar to those above shows that a uniform energy density (element virtual work divided by element volume) will produce a minimum volume structure.

The minor axis moment of inertia and torsional properties are non-linear functions of area. Uniform energy density is not equal to the LaGrange Multiplier and will not produce a minimum volume structure (Table 2). However, these deformations are often unimportant in many structural systems.

0

20

40

60

80

100

duced from the same roller, the major and minor axis moment of inertias and the major and minor axis shear areas are approximately linear functions of area. The sizing techniques previously descri-

bed can be used for the corresponding deformations. The remaining section property, the torsional constant, is not a linear function of area and, therefore, the energy density is not closely related to minimum volume sizing. Fortunately,

torsional rotation is often an unimportant deformation. In design, it is often sufficiently accurate to assume that all the properties are linear functions of cross-sectional

area which intersect the origin. This leads to the following resizing algorithm:

functions of area for

of the changes in the rollers used.

(L. v '26' / req L where v is equal to the total virtual

However, for those weights that are pro-

work of beam elementjtimes A.

weights of a given series depth because

Structural Engineering International 2/92

A. =

120

140

100

180

200

220

Area (in2)

Fig. 2

Rolled steel shapes generally do not have section properties that are linear all available

in = .54 cm

0

formations merit some discussion.

v 0.5

Design A key part of the above discussion is that

this method provides the minimum volume of material for statically deter-

minate structures (since the member forces do not change as the member sizes are changed). This may seem to limit the usefulness of this method but a closer look shows that it can be applied to many problems.

An important concept to start with is that all high-rise buildings are statically determinate in a global sense (Fig. 3). The building is simply a cantilever beam

and, therefore, at each story the shear and overturning moment are known. Since the global shear and moment are known, the next question is how these

forces are shared among the lateral systems present.

Fig. 4 shows lateral bracing systems which are normally used in a building. C-272 Science and Technology

101

_____

-3.'' -3 -3 -3 -3 -3

-3

-3 -3 -3

ly considered to be indeterminate, is determinate for lateral loads when the designer makes both diagonals in a

-3

I

Fig. 3

h.

. I I. a.

Fig.

All of these bracing systems can be considered statically determinate for lateral loads. Even X-bracing, which is normal-

c.

b.

e.

f.

4

Bracing (Typ.)

Floor Plan

members should be removed from the system. If the interactions converge on a

cent to core elements such as elevator shafts and stairwells. Although these elements share the lateral shears and moments in a story, they often are proportioned on a basis of tributary wind load. Therefore, as they are simultaneously resized, the forces in the mdividual members do not change significantly and behave as though they were statically determinate.

problematic, is where there are parallel

•1

systems of different types such as parallel trusses of different depths or combinations of parallel trusses and

Column: I, r, b Girder: 'g' rg, bg

Il

4I:-

moment frames. For these systems the force levels in the individual members

will change as the member sizes are

---A.-

changed. Therefore, the method no longer can be assured of giving minimum

volume structure. Although the technique no longer has a clear theoretical

Fig. 6

reasonable structure, it usually much less redundant than the initial structure. The LaGrange \ I u It iplier methodology can also be applied to subsystems such as a beam and column assemblage (Fig. 6).

mation is as follows:

H2IH ii Pj[+j+

Axial

f(A)

d dA

A

1

Elongation

LaGrange Multiplier

Energy Density

Fn

Fn

EA2

(A)

Major Axis Flexure

EA2

,

Ah2

h2

M

M

12

12

EIA

EJA

A3

A2

3M EIA

EIA

Vv

Vv

,

(I)

Minor Axis Flexure

/2

4k2

f

i

A

f

M

(I)

Major Axis Shear (As,)

Minor Axis Shear

A

(As) Torsional Rotation (J)

1

1

A3

A

3k2

h2

GAVA

I

Which reduces to:

Vv

GAVA I 3T1

C-273 Science and Technology

l2Ej2dA g

12E12dA C

(28)

or

1

dI

2 dA

—

—

1

2

dIg

(29)

ciAg

For rectangular cross sections this becomes: (30)

r

Where r and r are the radii of gyration for the girder and column, respectively.

For rolled shapes, Equation 29 becomes: b I .1= _(

I

0.5

b

(31)

b can be taken from Table 1 for the girder and columns

Where bg and

respectively.

It is interesting to note that the beam and column subsystem result is independent of the story height or bay size.

GAVA

Conclusion Vv

GAVA

j, Tt 1

Table 2: Comparison of LaGrange Multiplier and Energy Density for Rectangular Cross Section of Constant Depth (h) 102

(27)

(AH+A6l-v)

1 Displacement (Property)

For this system, the constrained

deflection equation for flexural defor-

Another system type which is more

Fig. 5

IC

is common to have negative energy densities. This often indicates that the

the case).

when there are multiple parallel lines of bracing in a building (Fig. 5). This is the typical case for bracing which is adja-

d.

the technique to this type of structure. As the material and loads are transferred from one lateral system to another it

story the same size (which is normally

. The next condition to be examined is

I .1.

basis, it may still be very useful to apply

A method has been presented which is useful for the sizing of lateral bracing in multi-story buildings where building drift is the controlling factor. It has been shown that the method will provide the minimum volume structure for a statically determinate structure and the ap-

plication to indeterminate structures has been discussed. Structural Engineering International

2/92

8.2 Geotechnical Report for the Chicago Spire

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