Advanced Mechanics of Materials and Applied

Long the leading text for students and practitioners in advanced materials mechanics, this new edition has been thoroughly revised to reflect the newest techniques, supporting more advanced study and professional design and analysis for the coming decade. More complete and current than ever, this edition systematically explores real-world stress analysis, and introduces state-of-the-art methods and applications used throughout aeronautical, civil, and mechanical engineering and engineering mechanics. Distinguished by exceptional visual interpretations of the solutions, it carefully balances thorough treatments of solid mechanics, elasticity, and computer-oriented numerical methods. This edition adds many new fully worked illustrative examples and extensive problem sets, many taken directly from practice. Other major changes and improvements include: " A new first chapter reviewing key fundamentals " New coverage of the computer oriented Finite Element Method " Rewritten coverage of plastic behavior, the three-dimensional Mohr's circle, and energy methods " Expanded, more contemporary coverage of stress concentration factors and contact stress developments " New coverage of engineering design, materials, beams, compound cylinders, shrink fits, buckling, and shells

Ansel C. Ugural, Ph.D., is a visiting professor at the New Jersey Institute of Technology. He has held various faculty and administrative positions at Fairleigh Dickinson University, and previously taught at the University of Wisconsin. Ugural has extensive industrial experience, is a member of several professional societies, and is author of Mechanics of Materials (Wiley, 2007), Stresses in Beams, Plates and Shells (CRC Press, 2009), and Mechanical Design: An Integrated Approach (McGraw-Hill, 2004).

Saul K. Fenster, Ph.D., was a professor at the New Jersey Institute of Technology, where he served as president for over twenty years. He is a fellow of the American Society of Mechanical Engineers and the American Society for Engineering Education.

Preface         xii
Acknowledgments         xiv

About the Authors         xv

List of Symbols         xvi

Chapter 1: Analysis of Stress 1

1.1 Introduction 1

1.2 Scope of Treatment 3

1.3 Analysis and Design 5

1.4 Conditions of Equilibrium 7

1.5 Definition and Components of Stress 9

1.6 Internal Force-Resultant and Stress Relations 13

1.7 Stresses on Inclined Sections 17

1.8 Variation of Stress within a Body 19

1.9 Plane-Stress Transformation 22

1.10 Principal Stresses and Maximum In-Plane Shear Stress 26

1.11 Mohr’s Circle for Two-Dimensional Stress 28

1.12 Three-Dimensional Stress Transformation 33

1.13 Principal Stresses in Three Dimensions 36

1.14 Normal and Shear Stresses on an Oblique Plane 40

1.15 Mohr’s Circles in Three Dimensions 43

1.16 Boundary Conditions in Terms of Surface Forces 47

1.17 Indicial Notation 48

References 49

Problems 49

Chapter 2: Strain and Material Properties 65

2.1 Introduction 65

2.2 Deformation 66

2.3 Strain Defined 67

2.4 Equations of Compatibility 72

2.5 State of Strain at a Point 73

2.6 Engineering Materials 80

2.7 Stress—Strain Diagrams 82

2.8 Elastic versus Plastic Behavior 86

2.9 Hooke’s Law and Poisson’s Ratio 88

2.10 Generalized Hooke’s Law 91

2.11 Hooke’s Law for Orthotropic Materials 94

2.12 Measurement of Strain: Strain Rosette 97

2.13 Strain Energy 101

2.14 Strain Energy in Common Structural Members 104

2.15 Components of Strain Energy 106

2.16 Saint-Venant’s Principle 108

References 110

Problems 111

Chapter 3: Problems in Elasticity 124

3.1 Introduction 124

3.2 Fundamental Principles of Analysis 125

Part A–Formulation and Methods of Solution 126

3.3 Plane Strain Problems 126

3.4 Plane Stress Problems 128

3.5 Comparison of Two-Dimensional Isotropic Problems 131

3.6 Airy’s Stress Function 132

3.7 Solution of Elasticity Problems 133

3.8 Thermal Stresses 138

3.9 Basic Relations in Polar Coordinates 142

Part B–Stress Concentrations 147

3.10 Stresses Due to Concentrated Loads 147

3.11 Stress Distribution Near Concentrated Load Acting on a Beam 151

3.12 Stress Concentration Factors 153

3.13 Contact Stresses 159

3.14 Spherical and Cylindrical Contacts 160

3.15 Contact Stress Distribution 163

3.16 General Contact 167

References 170

Problems 171

Chapter 4: Failure Criteria 181

4.1 Introduction 181

4.2 Failure 181

4.3 Failure by Yielding 182

4.4 Failure by Fracture 184

4.5 Yield and Fracture Criteria 187

4.6 Maximum Shearing Stress Theory 188

4.7 Maximum Distortion Energy Theory 189

4.8 Octahedral Shearing Stress Theory 190

4.9 Comparison of the Yielding Theories 193

4.10 Maximum Principal Stress Theory 195

4.11 Mohr’s Theory 195

4.12 Coulomb—Mohr Theory 196

4.13 Fracture Mechanics 200

4.14 Fracture Toughness 203

4.15 Failure Criteria for Metal Fatigue 206

4.16 Impact or Dynamic Loads 212

4.17 Dynamic and Thermal Effects 215

References 217

Problems 218

Chapter 5: Bending of Beams 226

5.1 Introduction 226

Part A–Exact Solutions 227

5.2 Pure Bending of Beams of Symmetrical Cross Section 227

5.3 Pure Bending of Beams of Asymmetrical Cross Section 230

5.4 Bending of a Cantilever of Narrow Section 235

5.5 Bending of a Simply Supported Narrow Beam 238

Part B–Approximate Solutions 240

5.6 Elementary Theory of Bending 240

5.7 Normal and Shear Stresses 244

5.8 Effect of Transverse Normal Stress 249

5.9 Composite Beams 250

5.10 Shear Center 256

5.11 Statically Indeterminate Systems 262

5.12 Energy Method for Deflections 264

Part C–Curved Beams 266

5.13 Elasticity Theory 266

5.14 Curved Beam Formula 269

5.15 Comparison of the Results of Various Theories 273

5.16 Combined Tangential and Normal Stresses 276

References 280

Problems 280

Chapter 6: Torsion of Prismatic Bars 292

6.1 Introduction 292

6.2 Elementary Theory of Torsion of Circular Bars 293

6.3 Stresses on Inclined Planes 298

6.4 General Solution of the Torsion Problem 300

6.5 Prandtl’s Stress Function 302

6.6 Prandtl’s Membrane Analogy 310

6.7 Torsion of Narrow Rectangular Cross Section 315

6.8 Torsion of Multiply Connected Thin-Walled Sections 317

6.9 Fluid Flow Analogy and Stress Concentration 321

6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section 323

6.11 Curved Circular Bars: Helical Springs 327

References 330

Problems 330

Chapter 7: Numerical Methods 337

7.1 Introduction 337

Part A–Finite Difference Method 338

7.2 Finite Differences 338

7.3 Finite Difference Equations 341

7.4 Curved Boundaries 343

7.5 Boundary Conditions 346

Part B–Finite Element Method 350

7.6 Fundamentals 350

7.7 The Bar Element 352

7.8 Arbitrarily Oriented Bar Element 354

7.9 Axial Force Equation 357

7.10 Force-Displacement Relations for a Truss 359

7.11 Beam Element 366

7.12 Properties of Two-Dimensional Elements 372

7.13 General Formulation of the Finite Element Method 374

7.14 Triangular Finite Element 379

7.15 Case Studies in Plane Stress 386

7.16 Computational Tools 394

References 395

Problems 396

Chapter 8: Axisymmetrically Loaded Members 407

8.1 Introduction 407

8.2 Thick-Walled Cylinders 408

8.3 Maximum Tangential Stress 414

8.4 Application of Failure Theories 415

8.5 Compound Cylinders: Press or Shrink Fits 416

8.6 Rotating Disks of Constant Thickness 419

8.7 Design of Disk Flywheels 422

8.8 Rotating Disks of Variable Thickness 426

8.9 Rotating Disks of Uniform Stress 429

8.10 Thermal Stresses in Thin Disks 431

8.11 Thermal Stresses in Long Circular Cylinders 432

8.12 Finite Element Solution 436

8.13 Axisymmetric Element 437

References 441

Problems 442

Chapter 9: Beams on Elastic Foundations 448

9.1 Introduction 448

9.2 General Theory 448

9.3 Infinite Beams 449

9.4 Semi-Infinite Beams 454

9.5 Finite Beams 457

9.6 Classification of Beams 458

9.7 Beams Supported by Equally Spaced Elastic Elements 458

9.8 Simplified Solutions for Relatively Stiff Beams 460

9.9 Solution by Finite Differences 461

9.10 Applications 464

References 466

Problems 466

Chapter 10: Applications of Energy Methods 469

10.1 Introduction 469

10.2 Work Done in Deformation 470

10.3 Reciprocity Theorem 471

10.4 Castigliano’s Theorem 472

10.5 Unit- or Dummy-Load Method 479

10.6 Crotti—Engesser Theorem 481

10.7 Statically Indeterminate Systems 483

10.8 Principle of Virtual Work 486

10.9 Principle of Minimum Potential Energy 487

10.10 Deflections by Trigonometric Series 489

10.11 Rayleigh—Ritz Method 493

References 496

Problems 496

Chapter 11: Stability of Columns 505

11.1 Introduction 505

11.2 Critical Load 505

11.3 Buckling of Pinned-End Columns 507

11.4 Deflection Response of Columns 509

11.5 Columns with Different End Conditions 511

11.6 Critical Stress: Classification of Columns 513

11.7 Allowable Stress 517

11.8 Imperfections in Columns 519

11.9 Eccentrically Loaded Columns: Secant Formula 520

11.10 Energy Methods Applied to Buckling 522

11.11 Solution by Finite Differences 529

11.12 Finite Difference Solution for Unevenly Spaced Nodes 534

References 536

Problems 536

Chapter 12: Plastic Behavior of Materials 545

12.1 Introduction 545

12.2 Plastic Deformation 546

12.3 Idealized Stress—Strain Diagrams 546

12.4 Instability in Simple Tension 549

12.5 Plastic Axial Deformation and Residual Stress 551

12.6 Plastic Defection of Beams 553

12.7 Analysis of Perfectly Plastic Beams 556

12.8 Collapse Load of Structures: Limit Design 565

12.9 Elastic—Plastic Torsion of Circular Shafts 569

12.10 Plastic Torsion: Membrane Analogy 573

12.11 Elastic—Plastic Stresses in Rotating Disks 575

12.12 Plastic Stress—Strain Relations 578

12.13 Plastic Stress—Strain Increment Relations 583

12.14 Stresses in Perfectly Plastic Thick-Walled Cylinders 586

References 590

Problems 590

Chapter 13: Plates and Shells 598

13.1 Introduction 598

Part A–Bending of Thin Plates 598

13.2 Basic Assumptions 598

13.3 Strain—Curvature Relations 599

13.4 Stress, Curvature, and Moment Relations 601

13.5 Governing Equations of Plate Deflection 603

13.6 Boundary Conditions 605

13.7 Simply Supported Rectangular Plates 607

13.8 Axisymmetrically Loaded Circular Plates 610

13.9 Deflections of Rectangular Plates by the Strain-Energy Method 613

13.10 Finite Element Solution 615

Part B–Membrane Stresses in Thin Shells 618

13.11 Theories and Behavior of Shells 618

13.12 Simple Membrane Action 618

13.13 Symmetrically Loaded Shells of Revolution 620

13.14 Some Common Cases of Shells of Revolution 622

13.15 Thermal Stresses in Compound Cylinders 626

13.16 Cylindrical Shells of General Shape 628

References 631

Problems 631

Appendix A: Problem Formulation and Solution 637

Appendix B: Solution of the Stress Cubic Equation 640

B.1 Principal Stresses 640

B.2 Direction Cosines 641

Appendix C: Moments of Composite Areas 645

C.1 Centroid 645

C.2 Moments of Inertia 648

C.3 Parallel-Axis Theorem 649

C.4 Principal Moments of Inertia 652

Appendix D: Tables and Charts 659

D.1 Average Properties of Common Engineering Materials 660

D.2 Conversion Factors: SI Units to U.S. Customary Units 662

D.3 SI Unit Prefixes 662

D.4 Deflections and Slopes of Beams 663

D.5 Reactions Deflections of Statically Indeterminate Beams 664

D.6 Stress Concentration Factors for Bars and Shafts with Fillets, Grooves, and Holes 665

Answers to Selected Problems 669

Index 677

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Advanced Mechanics of Materials and Applied Elasticity

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