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1 INTRODUCTION—CONCEPT OF STRESS 2

1.1 Introduction 2

1.2 A Short Review of the Methods of Statics 2

1.3 Stresses in the Members of a Structure 5

1.4 Analysis and Design 6

1.5 Axial Loading;Normal Stress 7

1.6 Shearing Stress 9

1.7 Bearing Stress in Connections 11

1.8 Application to the Analysis and Design of Simple Structures 12

1.9 Method of Problem Solution 14

1.10 Numerical Accuracy 15

1.11 Stress on an Oblique Plane under Axial Loading 23

1.12 Stress under General Loading Conditions;Components of Stress 24

1.13 Design Considerations 27

Review and Summary for Chapter 1 38

2 STRESS AND STRAIN—AXIAL LOADING 47

2.1 Introduction 47

2.2 Normal Strain under Axial Loading 48

2.3 Stress-Strain Diagram 50

2.4 True Stress and True Strain 55

2.5 Hooke's Law;Modulus of Elasticity 56

2.6 Elastic versus Plastic Behavior of a Material 57

2.7 Repeated Loadings;Fatigue 59

2.8 Deformations of Members under Axial Loading 61

2.9 Statically Indeterminate Problems 70

2.10 Problems Involving Temperature Changes 74

2.11 Poisson's Ratio 84

2.12 Multiaxial Loading;Generalized Hooke's Law 85

2.13 Dilatation;Bulk Modulus 87

2.14 Shearing Strain 89

2.15 Further Discussion of Deformations under Axial Loading;Relation among E,v,and G 92

2.16 Stress-Strain Relationships for Fiber-Reinforced Composite Materials 95

2.17 Stress and Strain Distribution under Axial Loading;Saint-Venant's Principle 104

2.18 Stress Concentrations 107

2.19 Plastic Deformations 109

2.20 Residual Stresses 113

Review and Summary for Chapter 2 121

3 TORSION 132

3.1 Introduction 132

3.2 Preliminary Discussion of the Stresses in a Shaft 134

3.3 Deformations in a Circular Shaft 136

3.4 Stresses in the Elastic Range 139

3.5 Angle of Twist in the Elastic Range 150

3.6 Statically Indeterminate Shafts 153

3.7 Design of Transmission Shafts 165

3.8 Stress Concentrations in Circular Shafts 167

3.9 Plastic Deformations in Circular Shafts 172

3.10 Circular Shafts Made of an Elastoplastic Material 174

3.11 Residual Stresses in Circular Shafts 177

3.12 Torsion of Noncircular Members 186

3.13 Thin-Walled Hollow Shafts 189

Review and Summary for Chapter 3 198

4 PURE BENDING 209

4.1 Introduction 209

4.2 Symmetric Member in Pure Bending 211

4.3 Deformations in a Symmetric Member in Pure Bending 213

4.4 Stresses and Deformations in the Elastic Range 216

4.5 Deformations in a Transverse Cross Section 220

4.6 Bending of Members Made of Several Materials 230

4.7 Stress Concentrations 234

4.8 Plastic Deformations 243

4.9 Members Made of an Elastoplastic Material 246

4.10 Plastic Deformations of Members with a Single Plane of Symmetry 250

4.11 Residual Stresses 250

4.12 Eccentric Axial Loading in a Plane of Symmetry 260

4.13 Unsymmetric Bending 270

4.14 General Case of Eccentric Axial Loading 276

4.15 Bending of Curved Members 285

Review and Summary for Chapter 4 298

5 ANALYSIS AND DESIGN OF BEAMS FOR BENDING 308

5.1 Introduction 308

5.2 Shear and Bending-Moment Diagrams 311

5.3 Relations among Load,Shear,and Bending Moment 322

5.4 Design of Prismatic Beams for Bending 332

5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam 343

5.6 Nonprismatic Beams 354

Review and Summary for Chapter 5 363

6 SHEARING STRESSES IN BEAMS AND THIN-WALLED MEMBERS 372

6.1 Introduction 372

6.2 Shear on the Horizontal Face of a Beam Element 374

6.3 Determination of the Shearing Stresses in a Beam 376

6.4 Shearing Stresses ？xy in Common Types of Beams 377

6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam 380

6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape 388

6.7 Shearing Stresses in Thin-Walled Members 390

6.8 Plastic Deformations 392

6.9 Unsymmetric Loading of Thin-Walled Members;Shear Center 402

Review and Summary for Chapter 6 414

7 TRANSFORMATIONS OF STRESS AND STRAIN 423

7.1 Introduction 423

7.2 Transformation of Plane Stress 425

7.3 Principal Stresses:Maximum Shearing Stress 428

7.4 Mohr's Circle for Plane Stress 436

7.5 General State of Stress 446

7.6 Application of Mohr's Circle to the Three-Dimensional Analysis of Stress 448

7.7 Yield Criteria for Ductile Materials under Plane Stress 451

7.8 Fracture Criteria for Brittle Materials under Plane Stress 453

7.9 Stresses in Thin-Walled Pressure Vessels 462

7.10 Transformation of Plane Stress 470

7.11 Mohr's Circle for Plane Strain 473

7.12 Three-Dimensional Analysis of Strain 475

7.13 Measurements of Strain;Strain Rosette 478

Review and Summary for Chapter 7 486

8 PRINCIPAL STRESSES UNDER A GIVEN LOADING 496

8.1 Introduction 496

8.2 Principal Stresses in a Beam 497

8.3 Design of Transmission Shafts 500

8.4 Stresses under Combined Loadings 508

Review and Summary for Chapter 8 521

9 DEFLECTION OF BEAMS 530

9.1 Introduction 530

9.2 Deformation of a Beam under Transverse Loading 532

9.3 Equation of the Elastic Curve 533

9.4 Direct Determination of the Elastic Curve from the Load Distribution 538

9.5 Statically Indeterminate Beams 540

9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam 549

9.7 Method of Superposition 558

9.8 Application of Superposition to Statically Indeterminate Beams 560

9.9 Moment-Area Theorems 569

9.10 Application to Cantilever Beams and Beams with Symmetric Loading 571

9.11 Bending-Moment Diagrams by Parts 573

9.12 Application of Moment-Area Theorems to Beams with Unsymmetric Loadings 582

9.13 Maximum Deflection 584

9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams 586

Review and Summary for Chapter 9 594

10 COLUMNS 607

10.1 Introduction 607

10.2 Stability of Structures 608

10.3 Euler's Formula for Pin-Ended Columns 610

10.4 Extension of Euler's Formula to Columns with Other End Conditions 614

10.5 Eccentric Loading;the Secant Formula 625

10.6 Design of Columns under a Centric Load 636

10.7 Design of Columns under an Eccentric Load 652

Review and Summary for Chapter 10 662

11 ENERGY METHODS 670

11.1 Introduction 670

11.2 Strain Energy 670

11.3 Strain-Energy Density 672

11.4 Elastic Strain Energy for Normal Stresses 674

11.5 Elastic Strain Energy for Shearing Stresses 677

11.6 Strain Energy for a General State of Stress 680

11.7 Impact Loading 693

11.8 Design for Impact Loads 695

11.9 Work and Energy under a Single Load 696

11.10 Deflection under a Single Load by the Work-Energy Method 698

11.11 Work and Energy under Several Loads 709

11.12 Castigliano's Theorem 711

11.13 Deflections by Castigliano's Theorem 712

11.14 Statically Indeterminate Structures 716

Review and Summary for Chapter 11 726

APPENDICES 735

A Moments of Areas 736

B Typical Properties of Selected Materials Used in Engineering 746

C Properties of Rolled-Steel Shapes 750

D Beam Deflections and Slopes 762

E Fundamentals of Engineering Examination 763

Photo Credits 765

Index 766

Answers to Problems 775