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1 INTRODUCTION—CONCEPT OF STRESS2

1.1 Introduction2

1.2 A Short Review of the Methods of Statics2

1.3 Stresses in the Members of a Structure5

1.4 Analysis and Design6

1.5 Axial Loading;Normal Stress7

1.6 Shearing Stress9

1.7 Bearing Stress in Connections11

1.8 Application to the Analysis and Design of Simple Structures12

1.9 Method of Problem Solution14

1.10 Numerical Accuracy15

1.11 Stress on an Oblique Plane under Axial Loading23

1.12 Stress under General Loading Conditions;Components of Stress24

1.13 Design Considerations27

Review and Summary for Chapter 138

2 STRESS AND STRAIN—AXIAL LOADING47

2.1 Introduction47

2.2 Normal Strain under Axial Loading48

2.3 Stress-Strain Diagram50

2.4 True Stress and True Strain55

2.5 Hooke's Law;Modulus of Elasticity56

2.6 Elastic versus Plastic Behavior of a Material57

2.7 Repeated Loadings;Fatigue59

2.8 Deformations of Members under Axial Loading61

2.9 Statically Indeterminate Problems70

2.10 Problems Involving Temperature Changes74

2.11 Poisson's Ratio84

2.12 Multiaxial Loading;Generalized Hooke's Law85

2.13 Dilatation;Bulk Modulus87

2.14 Shearing Strain89

2.15 Further Discussion of Deformations under Axial Loading;Relation among E,v,and G92

2.16 Stress-Strain Relationships for Fiber-Reinforced Composite Materials95

2.17 Stress and Strain Distribution under Axial Loading;Saint-Venant's Principle104

2.18 Stress Concentrations107

2.19 Plastic Deformations109

2.20 Residual Stresses113

Review and Summary for Chapter 2121

3 TORSION132

3.1 Introduction132

3.2 Preliminary Discussion of the Stresses in a Shaft134

3.3 Deformations in a Circular Shaft136

3.4 Stresses in the Elastic Range139

3.5 Angle of Twist in the Elastic Range150

3.6 Statically Indeterminate Shafts153

3.7 Design of Transmission Shafts165

3.8 Stress Concentrations in Circular Shafts167

3.9 Plastic Deformations in Circular Shafts172

3.10 Circular Shafts Made of an Elastoplastic Material174

3.11 Residual Stresses in Circular Shafts177

3.12 Torsion of Noncircular Members186

3.13 Thin-Walled Hollow Shafts189

Review and Summary for Chapter 3198

4 PURE BENDING209

4.1 Introduction209

4.2 Symmetric Member in Pure Bending211

4.3 Deformations in a Symmetric Member in Pure Bending213

4.4 Stresses and Deformations in the Elastic Range216

4.5 Deformations in a Transverse Cross Section220

4.6 Bending of Members Made of Several Materials230

4.7 Stress Concentrations234

4.8 Plastic Deformations243

4.9 Members Made of an Elastoplastic Material246

4.10 Plastic Deformations of Members with a Single Plane of Symmetry250

4.11 Residual Stresses250

4.12 Eccentric Axial Loading in a Plane of Symmetry260

4.13 Unsymmetric Bending270

4.14 General Case of Eccentric Axial Loading276

4.15 Bending of Curved Members285

Review and Summary for Chapter 4298

5 ANALYSIS AND DESIGN OF BEAMS FOR BENDING308

5.1 Introduction308

5.2 Shear and Bending-Moment Diagrams311

5.3 Relations among Load,Shear,and Bending Moment322

5.4 Design of Prismatic Beams for Bending332

5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam343

5.6 Nonprismatic Beams354

Review and Summary for Chapter 5363

6 SHEARING STRESSES IN BEAMS AND THIN-WALLED MEMBERS372

6.1 Introduction372

6.2 Shear on the Horizontal Face of a Beam Element374

6.3 Determination of the Shearing Stresses in a Beam376

6.4 Shearing Stresses ？xy in Common Types of Beams377

6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam380

6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape388

6.7 Shearing Stresses in Thin-Walled Members390

6.8 Plastic Deformations392

6.9 Unsymmetric Loading of Thin-Walled Members;Shear Center402

Review and Summary for Chapter 6414

7 TRANSFORMATIONS OF STRESS AND STRAIN423

7.1 Introduction423

7.2 Transformation of Plane Stress425

7.3 Principal Stresses:Maximum Shearing Stress428

7.4 Mohr's Circle for Plane Stress436

7.5 General State of Stress446

7.6 Application of Mohr's Circle to the Three-Dimensional Analysis of Stress448

7.7 Yield Criteria for Ductile Materials under Plane Stress451

7.8 Fracture Criteria for Brittle Materials under Plane Stress453

7.9 Stresses in Thin-Walled Pressure Vessels462

7.10 Transformation of Plane Stress470

7.11 Mohr's Circle for Plane Strain473

7.12 Three-Dimensional Analysis of Strain475

7.13 Measurements of Strain;Strain Rosette478

Review and Summary for Chapter 7486

8 PRINCIPAL STRESSES UNDER A GIVEN LOADING496

8.1 Introduction496

8.2 Principal Stresses in a Beam497

8.3 Design of Transmission Shafts500

8.4 Stresses under Combined Loadings508

Review and Summary for Chapter 8521

9 DEFLECTION OF BEAMS530

9.1 Introduction530

9.2 Deformation of a Beam under Transverse Loading532

9.3 Equation of the Elastic Curve533

9.4 Direct Determination of the Elastic Curve from the Load Distribution538

9.5 Statically Indeterminate Beams540

9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam549

9.7 Method of Superposition558

9.8 Application of Superposition to Statically Indeterminate Beams560

9.9 Moment-Area Theorems569

9.10 Application to Cantilever Beams and Beams with Symmetric Loading571

9.11 Bending-Moment Diagrams by Parts573

9.12 Application of Moment-Area Theorems to Beams with Unsymmetric Loadings582

9.13 Maximum Deflection584

9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams586

Review and Summary for Chapter 9594

10 COLUMNS607

10.1 Introduction607

10.2 Stability of Structures608

10.3 Euler's Formula for Pin-Ended Columns610

10.4 Extension of Euler's Formula to Columns with Other End Conditions614

10.5 Eccentric Loading;the Secant Formula625

10.6 Design of Columns under a Centric Load636

10.7 Design of Columns under an Eccentric Load652

Review and Summary for Chapter 10662

11 ENERGY METHODS670

11.1 Introduction670

11.2 Strain Energy670

11.3 Strain-Energy Density672

11.4 Elastic Strain Energy for Normal Stresses674

11.5 Elastic Strain Energy for Shearing Stresses677

11.6 Strain Energy for a General State of Stress680

11.7 Impact Loading693

11.8 Design for Impact Loads695

11.9 Work and Energy under a Single Load696

11.10 Deflection under a Single Load by the Work-Energy Method698

11.11 Work and Energy under Several Loads709

11.12 Castigliano's Theorem711

11.13 Deflections by Castigliano's Theorem712

11.14 Statically Indeterminate Structures716

Review and Summary for Chapter 11726

APPENDICES735

A Moments of Areas736

B Typical Properties of Selected Materials Used in Engineering746

C Properties of Rolled-Steel Shapes750

D Beam Deflections and Slopes762

E Fundamentals of Engineering Examination763

Photo Credits765

Index766

Answers to Problems775