**Chapter 1: Stress**

1.1 Introduction 1

1.2 Normal Stress Under Axial Loading 2

1.3 Direct Shear Stress 7

1.4 Bearing Stress 12

1.5 Stresses on Inclined Sections 22

1.6 Equality of Shear Stresses on Perpendicular Planes 24

**Chapter 2: Strain**

2.1 Displacement, Deformation, and the Concept of Strain 31

2.2 Normal Strain 32

2.3 Shear Strain 39

2.4 Thermal Strain 43

**Chapter 3: Mechanical Properties of Materials**

3.1 The Tension Test 47

3.2 The Stress–Strain Diagram 50

3.3 Hooke’s Law 58

3.4 Poisson’s Ratio 58

**Chapter 4: Design Concepts**

4.1 Introduction 69

4.2 Types of Loads 70

4.3 Safety 71

4.4 Allowable Stress Design 72

4.5 Load and Resistance Factor Design 83

**Chapter 5: Axial Deformation**

5.1 Introduction 89

5.2 Saint-Venant’s Principle 90

5.3 Deformations in Axially Loaded Bars 92

5.4 Deformations in a System of Axially Loaded Bars 101

5.5 Statically Indeterminate Axially Loaded Members 109

5.6 Thermal Effects on Axial Deformation 128

5.7 Stress Concentrations 140

**Chapter 6: Torsion**

6.1 Introduction 147

6.2 Torsional Shear Strain 149

6.3 Torsional Shear Stress 150

6.4 Stresses on Oblique Planes 152

6.5 Torsional Deformations 154

6.6 Torsion Sign Conventions 155

6.7 Gears in Torsion Assemblies 168

6.8 Power Transmission 175

6.9 Statically Indeterminate Torsion Members 182

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 201

6.11 Torsion of Noncircular Sections 204

6.12 Torsion of Thin-Walled Tubes:

Shear Flow 207

**Chapter 7: Equilibrium of Beams**

7.1 Introduction 213

7.2 Shear and Moment in Beams 215

7.3 Graphical Method for Constructing Shear and Moment Diagrams 227

7.4 Discontinuity Functions to Represent Load, Shear, and Moment 248

**Chapter 8: Bending **

8.1 Introduction 261

8.2 Flexural Strains 263

8.3 Normal Stresses in Beams 264

8.4 Analysis of Bending Stresses in Beams 279

8.5 Introductory Beam Design for Strength 292

8.6 Flexural Stresses in Beams of Two Materials 297

8.7 Bending Due to Eccentric Axial Load 310

8.8 Unsymmetric Bending 322

8.9 Stress Concentrations Under Flexural Loadings 332

**Chapter 9: Shear Stress in Beams**

9.1 Introduction 337

9.2 Resultant Forces Produced by Bending Stresses 337

9.3 The Shear Stress Formula 345

9.4 The First Moment of Area *Q *349

9.5 Shear Stresses in Beams of Rectangular Cross Section 351

9.6 Shear Stresses in Beams of Circular Cross Section 358

9.7 Shear Stresses in Webs of Flanged Beams 358

9.8 Shear Flow in Built-Up Members 369

9.9 Shear Stress and Shear Flow in Thin-Walled Members 382

9.10 Shear Centers of Thin-Walled Open Sections 393

**Chapter 10: Beam Deflections**

10.1 Introduction 409

10.2 Moment-Curvature Relationship 410

10.3 The Differential Equation of the Elastic Curve 410

10.4 Deflections by Integration of a Moment Equation 414

10.5 Deflections by Integration of Shear-Force or Load Equations 429

10.6 Deflections Using Discontinuity Functions 433

10.7 Method of Superposition 443

**Chapter 11: Statically Indeterminate Beams**

11.1 Introduction 469

11.2 Types of Statically Indeterminate Beams 469

11.3 The Integration Method 471

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 478

11.5 The Superposition Method 486

**Chapter 12: Stress Transformations**

12.1 Introduction 507

12.2 Stress at a General Point in an Arbitrarily Loaded Body 508

12.3 Equilibrium of the Stress Element 510

12.4 Plane Stress 511

12.5 Generating the Stress Element 511

12.6 Equilibrium Method for Plane Stress Transformations 517

12.7 General Equations of Plane Stress Transformation 520

12.8 Principal Stresses and Maximum Shear Stress 528

12.9 Presentation of Stress Transformation Results 535

12.10 Mohr’s Circle for Plane Stress 543

12.11 General State of Stress at a Point 562

**Chapter 13: Strain Transformations**

13.1 Introduction 569

13.2 Two-Dimensional or Plane Strain 570

13.3 Transformation Equations for Plane Strain 571

13.4 Principal Strains and Maximum Shearing Strain 576

13.5 Presentation of Strain Transformation Results 578

13.6 Mohr’s Circle for Plane Strain 581

13.7 Strain Measurement and Strain Rosettes 585

13.8 Generalized Hooke’s Law for Isotropic Materials 591

**Chapter 14: Thin-Walled Pressure Vessels**

14.1 Introduction 607

14.2 Spherical Pressure Vessels 608

14.3 Cylindrical Pressure Vessels 610

14.4 Strains in Pressure Vessels 613

**Chapter 15: Combined Loads**

15.1 Introduction 623

15.2 Combined Axial and Torsional Loads 623

15.3 Principal Stresses in a Flexural Member 629

15.4 General Combined Loadings 643

15.5 Theories of Failure 668

**Chapter 16: Columns**

16.1 Introduction 681

16.2 Buckling of Pin-Ended Columns 684

16.3 The Effect of End Conditions on Column Buckling 696

16.4 The Secant Formula 707

16.5 Empirical Column Formulas—Centric Loading 714

16.6 Eccentrically Loaded Columns 726

**Chapter 17: Energy Methods**

17.1 Introduction 737

17.2 Work and Strain Energy 738

17.3 Elastic Strain Energy for Axial Deformation 742

17.4 Elastic Strain Energy for Torsional Deformation 744

17.5 Elastic Strain Energy for Flexural Deformation 746

17.6 Impact Loading 751

17.7 Work-Energy Method for Single Loads 769

17.8 Method of Virtual Work 774

17.9 Defl ections of Trusses by the Virtual-Work Method 779

17.10 Defl ections of Beams by the Virtual-Work Method 786

17.11 Castigliano’s Second Theorem 800

17.12 Calculating Defl ections of Trusses by Castigliano’s Theorem 802

17.13 Calculating Defl ections of Beams by Castigliano’s Theorem 807

Appendix A Geometric Properties of an Area 819

A.1 Centroid of an Area 819

A.2 Moment of Inertia for an Area 823

A.3 Product of Inertia for an Area 828

A.4 Principal Moments of Inertia 831

A.5 Mohr’s Circle for Principal Moments of Inertia 835

Appendix B Geometric Properties of Structural Steel Shapes 839

Appendix C Table of Beam Slopes and Deflections 853

Appendix D Average Properties of Selected Materials 857

Answers to Odd Numbered Problems 861

Index 885