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1 Introduction—Concept of Stress 2

1.1 Introduction 4

1.2 A Short Review of the Methods of Statics 4

1.3 Stresses in the Members of a Structure 7

1.4 Analysis and Design 8

1.5 Axial Loading； Normal Stress 9

1.6 Shearing Stress 11

1.7 Bearing Stress in Connections 13

1.8 Application to the Analysis and Design of Simple Structures 13

1.9 Method of Problem Solution 16

1.10 Numerical Accuracy 17

1.11 Stress on an Oblique Plane under Axial Loading 26

1.12 Stress under General Loading Conditions；Components of Stress 27

1.13 Design Considerations 30

Review and Summary for Chapter 1 42

2 Stress and Strain—Axial Loading 52

2.1 Introduction 54

2.2 Normal Strain under Axial Loading 55

2.3 Stress-Strain Diagram 57

2.4 True Stress and True Strain 61

2.5 Hooke’s Law； Modulus of Elasticity 62

2.6 Elastic versus Plastic Behavior of a Material 64

2.7 Repeated Loadings； Fatigue 66

2.8 Deformations of Members under Axial Loading 67

2.9 Statically Indeterminate Problems 78

2.10 Problems Involving Temperature Changes 82

2.11 Poisson’s Ratio 93

2.12 Multiaxial Loading； Generalized Hooke’s Law 94

2.13 Dilatation； Bulk Modulus 96

2.14 Shearing Strain 98

2.15 Further Discussion of Deformations under Axial Loading； Relation among E，v，and G 101

2.16 Stress-Strain Relationships for Fiber-Reinforced Composite Materials 103

2.17 Stress and Strain Distribution under Axial Loading； Saint-Venant’s Principle 113

2.18 Stress Concentrations 115

2.19 Plastic Deformations 117

2.20 Residual Stresses 121

Review and Summary for Chapter 2 129

3 Torsion 140

3.1 Introduction 142

3.2 Preliminary Discussion of the Stresses in a Shaft 144

3.3 Deformations in a Circular Shaft 145

3.4 Stresses in the Elastic Range 148

3.5 Angle of Twist in the Elastic Range 159

3.6 Statically Indeterminate Shafts 163

3.7 Design of Transmission Shafts 176

3.8 Stress Concentrations in Circular Shafts 179

3.9 Plastic Deformations in Circular Shafts 184

3.10 Circular Shafts Made of an Elastoplastic Material 186

3.11 Residual Stresses in Circular Shafts 189

3.12 Torsion of Noncircular Members 197

3.13 Thin-Walled Hollow Shafts 200

Review and Summary for Chapter 3 210

4 Pure Bending 220

4.1 Introduction 222

4.2 Symmetric Member in Pure Bending 224

4.3 Deformations in a Symmetric Member in Pure Bending 226

4.4 Stresses and Deformations in the Elastic Range 229

4.5 Deformations in a Transverse Cross Section 233

4.6 Bending of Members Made of Several Materials 242

4.7 Stress Concentrations 246

4.8 Plastic Deformations 255

4.9 Members Made of an Elastoplastic Material 256

4.10 Plastic Deformations of Members with a Single Plane of Symmetry 260

4.11 Residual Stresses 261

4.12 Eccentric Axial Loading in a Plane of Symmetry 270

4.13 Unsymmetric Bending 279

4.14 General Case of Eccentric Axial Loading 284

4.15 Bending of Curved Members 294

Review and Summary for Chapter 4 305

5 Analysis and Design of Beams for Bending 314

5.1 Introduction 316

5.2 Shear and Bending-Moment Diagrams 319

5.3 Relations among Load，Shear，and Bending Moment 329

5.4 Design of Prismatic Beams for Bending 339

5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam 350

5.6 Nonprismatic Beams 361

Review and Summary for Chapter 5 370

6 Shearing Stresses in Beams and Thin-Walled Members 380

6.1 Introduction 382

6.2 Shear on the Horizontal Face of a Beam Element 384

6.3 Determination of the Shearing Stresses in a Beam 386

6.4 Shearing Stresses T xy in Common Types of Beams 387

6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam 390

6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape 399

6.7 Shearing Stresses in Thin-Walled Members 401

6.8 Plastic Deformations 404

6.9 Unsymmetric Loading of Thin-Walled Members；Shear Center 414

Review and Summary for Chapter 6 427

7 Transformations of Stress and Strain 436

7.1 Introduction 438

7.2 Transformation of Plane Stress 440

7.3 Principal Stresses：Maximum Shearing Stress 443

7.4 Mohr’s Circle for Plane Stress 452

7.5 General State of Stress 462

7.6 Application of Mohr’s Circle to the Three-Dimensional Analysis of Stress 464

7.7 Yield Criteria for Ductile Materials under Plane Stress 467

7.8 Fracture Criteria for Brittle Materials under Plane Stress 469

7.9 Stresses in Thin-Walled Pressure Vessels 478

7.10 Transformation of Plane Strain 486

7.11 Mohr’s Circle for Plane Strain 489

7.12 Three-Dimensional Analysis of Strain 491

7.13 Measurements of Strain； Strain Rosette 494

Review and Summary for Chapter 7 502

8 Principal Stresses under a Given Loading 512

8.1 Introduction 514

8.2 Principal Stresses in a Beam 515

8.3 Design of Transmission Shafts 518

8.4 Stresses under Combined Loadings 527

Review and Summary for Chapter 8 540

9 Deflection of Beams 548

9.1 Introduction 550

9.2 Deformation of a Beam under Transverse Loading 552

9.3 Equation of the Elastic Curve 553

9.4 Direct Determination of the Elastic Curve from the Load Distribution 559

9.5 Statically Indeterminate Beams 561

9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam 571

9.7 Method of Superposition 580

9.8 Application of Superposition to Statically Indeterminate Beams 582

9.9 Moment-Area Theorems 592

9.10 Application to Cantilever Beams and Beams with Symmetric Loadings 595

9.11 Bending-Moment Diagrams by Parts 597

9.12 Application of Moment-Area Theorems to Beams with Unsymmetric Loadings 605

9.13 Maximum Deflection 607

9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams 609

Review and Summary for Chapter 9 618

10 Columns 630

10.1 Introduction 632

10.2 Stability of Structures 632

10.3 Euler’s Formula for Pin-Ended Columns 635

10.4 Extension of Euler’s Formula to Columns with Other End Conditions 638

10.5 Eccentric Loading； the Secant Formula 649

10.6 Design of Columns under a Centric Load 660

10.7 Design of Columns under an Eccentric Load 675

Review and Summary for Chapter 10 684

11 Energy Methods 692

11.1 Introduction 694

11.2 Strain Energy 694

11.3 Strain-Energy Density 696

11.4 Elastic Strain Energy for Normal Stresses 698

11.5 Elastic Strain Energy for Shearing Stresses 701

11.6 Strain Energy for a General State of Stress 704

11.7 Impact Loading 716

11.8 Design for Impact Loads 718

11.9 Work and Energy under a Single Load 719

11.10 Deflection under a Single Load by the Work-Energy Method 722

11.11 Work and Energy under Several Loads 732

11.12 Castigliano’s Theorem 734

11.13 Deflections by Castigliano’s Theorem 736

11.14 Statically Indeterminate Structures 740

Review and Summary for Chapter 11 750

Appendices 759

A Moments of Areas 760

B Typical Properties of Selected Materials Used in Engineering 770

C Properties of Rolled-Steel Shapes 774

D Beam Deflections and Slopes 786

E Fundamentals of Engineering Examination 787

Photo Credits 789

Index 791

Answers to Problems 801