Mechanics of Materials, Global Edition

Chapter 1 Stress 1

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 31

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 47

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 69

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 89

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 129

5.7 Stress Concentrations 141

Chapter 6 Torsion 147

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 213

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 261

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 337

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 368

9.9 Shear Stress and Shear Flow in Thin-Walled Members 381

9.10 Shear Centers of Thin-Walled Open Sections 392

Chapter 10 Beam Defl ections 409

10.1 Introduction 409

10.2 Moment-Curvature Relationship 410

10.3 The Differential Equation of the Elastic Curve 410

10.4 Defl ections by Integration of a Moment Equation 414

10.5 Defl ections by Integration of Shear-Force or Load Equations 429

10.6 Defl ections Using Discontinuity Functions 433

10.7 Method of Superposition 443

Chapter 11 Statically Indeterminate Beams 469

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 507

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 561

Chapter 13 Strain Transformations 569

13.1 Introduction 569

13.2 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 607

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 623

15.1 Introduction 623

15.2 Combined Axial and Torsional Loads 623

15.3 Principal Stresses in a Flexural Member 628

15.4 General Combined Loadings 643

15.5 Theories of Failure 668

Chapter 16 Columns 681

16.1 Introduction 681

16.2 Buckling of Pin-Ended Columns 684

16.3 The Effect of End Conditions on Column Buckling 695

16.4 The Secant Formula 706

16.5 Empirical Column Formulas—Centric Loading 712

16.6 Eccentrically Loaded Columns 723

Chapter 17 Energy Methods 733

17.1 Introduction 733

17.2 Work and Strain Energy 734

17.3 Elastic Strain Energy for Axial Deformation 738

17.4 Elastic Strain Energy for Torsional Deformation 740

17.5 Elastic Strain Energy for Flexural Deformation 742

17.6 Impact Loading 747

17.7 Work-Energy Method for Single Loads 765

17.8 Method of Virtual Work 770

17.9 Deflections of Trusses by the Virtual-Work Method 775

17.10 Deflections of Beams by the Virtual-Work Method 782

17.11 Castigliano’s Second Theorem 796

17.12 Calculating Deflections of Trusses by Castigliano’s Theorem 798

17.13 Calculating Deflections of Beams by Castigliano’s Theorem 803

Appendix A Geometric Properties of an Area 813

A.1 Centroid of an Area 813

A.2 Moment of Inertia for an Area 817

A.3 Product of Inertia for an Area 822

A.4 Principal Moments of Inertia 825

A.5 Mohr’s Circle for Principal Moments of Inertia 829

Appendix B Geometric Properties of Structural Steel Shapes 833

Appendix C Table of Beam Slopes and Deflections 841

Appendix D Average Properties of Selected Materials 845

Answers to Odd Numbered Problems 849

Index 871