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Preface

vii

CHAPTER 1 INTRODUCTION

1

1-1. Steps in Structural Design 1 1-2. Applied Loads and Temperahtres 2 1-3. Actual Stresses and Deflections 4 1-4. Allowable Stresses or Deflections 5 1-5. Comparison of Applied and Allowable Stresses and Deflections 7 1-6. Sttmma1·y References 7 Problems 8

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CHAPTER 2 STRESS AND STRAIN

2-1. 2-2. 2-3.

10

Introduction 10 Stress: Definitions and Notations Equations of Equilibn·um 12

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2-4.

2-5. 2-6. 2-7. 2-8. 2-9.

Stress Tt·ansfonnations for Rotation of A x s 16 Principal Stresses and Maximum Shem· Stres es Dejlections and Strains 20 Strain-transfonnation Equations 24 Compatibility Equations 26 Summary 27 References 28 Problems 28

CHAPTER 3 MECHANICAL BEHAVIOR OF MATERIALS

3-1. 3-2. 3-3. 3-4. 3-5. 3-6. 3-7. 3-8. 3-9. 3-10. 3-11.

31

Introduction 31 The Tensile Test 32 Compression and Shear Tests 35 I dealizations of the Stress-Strain Curve 36 Three-parameter Representations of Stress-Strain Curves Effect of Temperature upon Short-lime Static Properties Creep 42 Fatigue 44 Allowable M echanical Properties 47 M aterial Selection 49 Three-dimensional Linearly Elastic Stress-Strain Relationships 51 References 56 Problems 57

CHAPTER 4 INTRODUCTION TO THE THEORY OF ELASTICITY

4-1. 4-2. 4-3. 4-4. 4-5. 4-6. 4-7. 4-8.

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Introduction 59 Displacement Formulation 60 61 Stress Formulation Two-dimensional Problems 62 Stress-function Formulation 64 The Inverse M ethod 70 The Semi-inverse M ethod 75 St. Venant' s Princip le 75 References 76 Problems 77

CHAPTER 5 FINITE-DIFFERENCE METHODS

5-1. 5-2. 5-3. 5-4. 5-5.

38 41

79

Introduction 79 Finite-difference Operators 80 Application to EqU?'librium Boundary-value Problems Application to Eigenvalue P1·oblems 90 Solution of M atrix Eigenvalue Equations 93 References 96 Problems 96

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R 6 INTRODUCTION TO WORK AND ENERGY PRINCIPLES

98

0- 1. 1ntroductton 9 0-2. Work and Energy 99 6-:3. Virtual Work and Equilibrium 101 6-4. Coordinates and Degrees of Freedom 104 6-5. Stability 105 6-6. Small Displacements of a Conservat1've System 107 6-7. Strain Energy and Complementary Strain Energy 110 -8. Potential and Complementary Potential of External Forces 6-9. The Principle of the Stationary Value of the Total Potential 6-10. The Principle of the Stationary Value of the Total 118 Complementary Potential 6-11. De1'ivation of Equilibrium and Compatibility Equations 120 by Va1'iational M ethods 6-12. The Rayleigh-Ritz M ethod 122 6-13. The Recip1'ocal Theorems of Betti and Maxwell 127 6-1 4. The Use of Virtual Work to Compute Dejlections 128 Refe?"ences 131 Problems 131

1 A TER 7 BENDING AND EXTENSION OF BEAMS 7-1. 7-2. 7-3. 7-4. 7-5. 7-6. 7-7. 7-8. 7-9. 7-10.

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I ntroducUon 133 St1·ess Resultants 133 Stresses Due to Extension and Bending 135 M odulus-weighted Section Propertt'es 139 Accuracy of Beam-stress Equation 141 I dealization of Stiffened-shell St1·uctures 143 Equilibrium Equations 152 Beam Dejlections 157 The Dijferential Equations of Beams, Ba1's, and Gables 168 Energy Expressions for Beams References 173 P1·oblems 174

UAPTER 8 THE TORSION OF SLENDER BODIES

115 117

178

8-1. l nlroduction 178 8-2. Prandtl Stress-}unction Formulation 179 8-3. The M embrar/e Analogy 185 8-4. W arping-.function Formulation 188 8-5. Analytical Methods for Approximate Solutions 8-6. Thin-walled Open Sections 198 8-7. Thin-walled Closed Sections 202 8-8. Accuracy of Torsion Theory 213

192

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Differ ntial JJiqHa.tiontJ fm· References 220 Problems 220

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CHAPTER 9 STRESSES DUE TO SHEAR IN THIN-WALLED SLENDER BEAMS

9-1. 9-2. 9-3. 9-4. 9-5. 9-6. 9-7.

CHAPTER 10

224 Introduction 225 Open Sections Fluid-flow Analogy 236 Shear Center 239 240 Closed Sections Effects of Taper 247 Transverse M ember Loads References 254 255 Problems

11-3. 11-4. 11-5. 11-6.

286

Introduction 286 Application of the Principle of the Stationary Value of the Total Potential 287 Application of the Princip le of the Stationary Value of the Total Complementary Potential 290 Equations for ôU' of Simple Elements 294 Notes on Bas~·c and Redundant-force Systems 295 Elastic-center and Column-analogy M ethods 304 References 313 Problems 313

INTRODUCTION TO MATRIX METHODS OF STRUCTURAL ANALYSIS

12-1. 12-2. 12-3.

258

Introduction 258 The Method of Virtual Work 258 Equations for ôU of Simple Elements 263 Relative Displacements 273 Flexibility and Stiffness Matrices 275 Distributed Loads and Weighting Matrices 280 References 282 Problems 283

STATICALLY INDETERMINATE STRUCTURES

11-1. 11-2.

CHAPTER 12

253

DEFLECTION ANALYSIS OF STRUCTURES

10-1. 10-2. 10-3. 10-4. 10-5. 10-6.

CHAPTER 11

224

317

Introductwn 317 The Force M ethod 318 Discussion of the Force Method

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:l2 M thod a:3:~ /)iM'IIt~sion of the D1's pla em nt M ethod Conrludin(l Jle·m arks 344 Nef •r nee.~ 34 5 J>robl ms 346 A Jlplil·ntwn lo SlijJmNl 'h ll11

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12-7.

n;.~ pla cl'lltIt ·' raft, etc. Such information can be found in Refs. 1 to 1 1 1l11 i nd of the chapter. In sorne cases, the applied loads which the llltc •Ltm lllllHt withstand are specified by the procuring or certifying ' '1111 , lmH cl upon statistical data obtained from operating experience lit tn1ilr~t· •raft. In other cases, especially if the design and its environlill rd nl't Ill\ onventional, it is part of the contractor's responsibility to tl d 11111 l'nt.ionn.l loads and thermal criteria. l't•w d •finitions of terms relating to loads should be mentioned at lit 1111i '' t, 1>