Mechanics of Materials An Integrated Learning System

The well-regarded materials science textbook, updated for enhanced learning and current content

Mechanics of Materials: An Integrated Learning System, 5th Edition helps engineering students visualize how materials move and change better than any other course available. This text focuses on helping learners develop practical skills, encouraging them to recognize fundamental concepts relevant to specific situations, identify equations needed to solve problems, and engage critically with literature in the field. In this new edition, hundreds of new problems—including over 200 problems with video solutions—have been added to enhance the flexibility and robustness of the course.

With WileyPLUS, this course contains a rich selection of online content and interactive materials, including animations, tutorial videos, and worked problems—many of which are new and expanded in this 5th Edition. An emphasis on critical thinking forms the foundation of Mechanics of Materials in this revised edition. From basic concepts of stress and strain to more advanced topics like beam deflections and combined loads, this book provides students with everything they need to embark on successful careers in materials and mechanical engineering.

• Introduces students to the core concepts of material mechanics and presents the latest methods and current problems in the field
• Adds hundreds of new and revised problems, 200+ new video solutions, and over 400 new EQAT coded algorithmic problems
• Emphasizes practical skills and critical thinking, encouraging learners to devise effective methods of solving example problems
• Contains updates and revisions to reflect the current state of the discipline and to enhance the breadth of course content
• Includes access to interactive animations, demonstration videos, and step-by-step problem solutions with WileyPLUS online environment

With added flexibility and opportunities for course customization, Mechanics of Materials provides excellent value for instructors and students alike. Learners will stay engaged and on track, gaining a solid and lasting understanding of the subject matter.

1 Stress 1

1.1 Introduction 1

1.2 Normal Stress Under Axial Loading 2

1.3 Direct Shear Stress 8

1.4 Bearing Stress 13

1.5 Stresses on Inclined Sections 17

1.6 Equality of Shear Stresses on Perpendicular Planes 20

2 Strain 25

2.1 Displacement, Deformation, and the Concept of Strain 25

2.2 Normal Strain 27

2.3 Shear Strain 32

2.4 Thermal Strain 35

3 Mechanical Properties of Materials 37

3.1 The Tension Test 37

3.2 The Stress–Strain Diagram 40

3.3 Hooke’s Law 48

3.4 Poisson’s Ratio 49

4 Design Concepts 55

4.1 Introduction 55

4.2 Types of Loads 56

4.3 Safety 58

4.4 Allowable Stress Design 58

4.5 Load and Resistance Factor Design 65

5 Axial Deformation 71

5.1 Introduction 71

5.2 Saint-Venant’s Principle 72

5.3 Deformations in Axially Loaded Bars 74

5.4 Deformations in a System of Axially Loaded Bars 81

5.5 Statically Indeterminate Axially Loaded Members 88

5.6 Thermal Effects on Axial Deformation 101

5.7 Stress Concentrations 110

6 Torsion 115

6.1 Introduction 115

6.2 Torsional Shear Strain 117

6.3 Torsional Shear Stress 118

6.4 Stresses on Oblique Planes 120

6.5 Torsional Deformations 122

6.6 Torsion Sign Conventions 124

6.7 Gears in Torsion Assemblies 133

6.8 Power Transmission 138

6.9 Statically Indeterminate Torsion Members 142

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 155

6.11 Torsion of Noncircular Sections 158

6.12 Torsion of Thin-Walled Tubes: Shear Flow 161

7 Equilibrium of Beams 165

7.1 Introduction 165

7.2 Shear and Moment in Beams 167

7.3 Graphical Method for Constructing Shear and Moment Diagrams 176

7.4 Discontinuity Functions to Represent Load, Shear, and Moment 194

8 Bending 205

8.1 Introduction 205

8.2 Flexural Strains 207

8.3 Normal Stresses in Beams 208

8.4 Analysis of Bending Stresses in Beams 220

8.5 Introductory Beam Design for Strength 230

8.6 Flexural Stresses in Beams of Two Materials 234

8.7 Bending Due to an Eccentric Axial Load 244

8.8 Unsymmetric Bending 251

8.9 Stress Concentrations Under Flexural Loadings 259

8.10 Bending of Curved Bars 263

9 Shear Stress in Beams 271

9.1 Introduction 271

9.2 Resultant Forces Produced by Bending Stresses 272

9.3 The Shear Stress Formula 277

9.4 The First Moment of Area, Q 282

9.5 Shear Stresses in Beams of Rectangular Cross Section 284

9.6 Shear Stresses in Beams of Circular Cross Section 288

9.7 Shear Stresses in Webs of Flanged Beams 289

9.8 Shear Flow in Built-Up Members 294

9.9 Shear Stress and Shear Flow in Thin-Walled Members 302

9.10 Shear Centers of Thin-Walled Open Sections 319

10 Beam Deflections 331

10.1 Introduction 331

10.2 Moment–Curvature Relationship 332

10.3 The Differential Equation of the Elastic Curve 332

10.4 Determining Deflections by Integration of a Moment Equation 336

10.5 Determining Deflections by Integration of Shear-Force or Load Equations 348

10.6 Determining Deflections by Using Discontinuity Functions 350

10.7 Determining Deflections by the Method of Superposition 357

11 Statically Indeterminate Beams 377

11.1 Introduction 377

11.2 Types of Statically Indeterminate Beams 378

11.3 The Integration Method 379

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 384

11.5 The Superposition Method 390

12 Stress Transformations 405

12.1 Introduction 405

12.2 Stress at a General Point in an Arbitrarily Loaded Body 406

12.3 Equilibrium of the Stress Element 408

12.4 Plane Stress 410

12.5 Generating the Stress Element 410

12.6 Equilibrium Method for Plane Stress Transformations 413

12.7 General Equations of Plane Stress Transformation 415

12.8 Principal Stresses and Maximum Shear Stress 422

12.9 Presentation of Stress Transformation Results 429

12.10 Mohr’s Circle for Plane Stress 435

12.11 General State of Stress at a Point 452

13 Strain Transformations 459

13.1 Introduction 459

13.2 Plane Strain 460

13.3 Transformation Equations for Plane Strain 461

13.4 Principal Strains and Maximum Shearing Strain 466

13.5 Presentation of Strain Transformation Results 468

13.6 Mohr’s Circle for Plane Strain 470

13.7 Strain Measurement and Strain Rosettes 473

13.8 Generalized Hooke’s Law for Isotropic Materials 478

13.9 Generalized Hooke’s Law for Orthotropic Materials 494

14 Pressure Vessels 499

14.1 Introduction 499

14.2 Thin-Walled Spherical Pressure Vessels 500

14.3 Thin-Walled Cylindrical Pressure Vessels 502

14.4 Strains in Thin-Walled Pressure Vessels 505

14.5 Stresses in Thick-Walled Cylinders 509

14.6 Deformations in Thick-Walled Cylinders 517

14.7 Interference Fits 520

15 Combined Loads 527

15.1 Introduction 527

15.2 Combined Axial and Torsional Loads 528

15.3 Principal Stresses in a Flexural Member 530

15.4 General Combined Loadings 540

15.5 Theories of Failure 557

16 Columns 567

16.1 Introduction 567

16.2 Buckling of Pin-Ended Columns 570

16.3 The Effect of End Conditions on Column Buckling 578

16.4 The Secant Formula 587

16.5 Empirical Column Formulas—Centric Loading 592

16.6 Eccentrically Loaded Columns 600

17 Energy Methods 607

17.1 Introduction 607

17.2 Work and Strain Energy 608

17.3 Elastic Strain Energy for Axial Deformation 613

17.4 Elastic Strain Energy for Torsional Deformation 614

17.5 Elastic Strain Energy for Flexural Deformation 616

17.6 Impact Loading 620

17.7 Work–Energy Method for Single Loads 633

17.8 Method of Virtual Work 636

17.9 Deflections of Trusses by the Virtual-Work Method 641

17.10 Deflections of Beams by the Virtual-Work Method 649

17.11 Castigliano’s Second Theorem 658

17.12 Calculating Deflections of Trusses by Castigliano’s Theorem 660

17.13 Calculating Deflections of Beams by Castigliano’s Theorem 665

Appendix A Geometric Properties Of An Area 671

A.1 Centroid of an Area 671

A.2 Moment of Inertia for an Area 675

A.3 Product of Inertia for an Area 680

A.4 Principal Moments of Inertia 682

A.5 Mohr’s Circle for Principal Moments of Inertia 686

Appendix B Geometric Properties Of Structural Steel Shapes 691

Appendix C Table Of Beam Slopes And Deflections 703

Appendix D Average Properties Of Selected Materials 707

Appendix E Fundamental Mechanics Of Materials Equations 711

Problems P-1

Chapter 1 Problems P-1

Chapter 2 Problems P-7

Chapter 3 Problems P-11

Chapter 4 Problems P-14

Chapter 5 Problems P-18

Chapter 6 Problems P-29

Chapter 7 Problems P-39

Chapter 8 Problems P-46

Chapter 9 Problems P-63

Chapter 10 Problems P-76

Chapter 11 Problems P-87

Chapter 12 Problems P-95

Chapter 13 Problems P-108

Chapter 14 Problems P-115

Chapter 15 Problems P-119

Chapter 16 Problems P-129

Chapter 17 Problems P-138

Answers to Odd Numbered Problems A-1

Index I-1

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