Advanced Mechanics of Materials, 6th Edition

CHAPTER 1 INTRODUCTION 1

1.1 Review of Elementary Mechanics of Materials 1

1.2 Methods of Analysis 5

1.3 Stress–Strain Relations 8

1.4 Failure and Limits on Design 16

Problems 22

References 24

CHAPTER 2 THEORIES OF STRESS AND STRAIN 25

2.1 Definition of Stress at a Point 25

2.2 Stress Notation 26

2.3 Symmetry of the Stress Array and Stress on an Arbitrarily Oriented Plane 28

2.4 Transformation of Stress, Principal Stresses, and Other Properties 31

2.5 Differential Equations of Motion of a Deformable Body 50

2.6 Deformation of a Deformable Body 54

2.7 Strain Theory, Transformation of Strain, and Principal Strains 55

2.8 Small-Displacement Theory 61

2.9 Strain Measurement and Strain Rosettes 70

Problems 72

References 78

CHAPTER 3 LINEAR STRESS–STRAIN–TEMPERATURE RELATIONS 79

3.1 First Law of Thermodynamics, Internal-Energy Density, and Complementary Internal-Energy Density 79

3.2 Hooke’s Law: Anisotropic Elasticity 84

3.3 Hooke’s Law: Isotropic Elasticity 85

3.4 Equations of Thermoelasticity for Isotropic Materials 91

3.5 Hooke’s Law: Orthotropic Materials 93

Problems 101

References 103

CHAPTER 4 INELASTIC MATERIAL BEHAVIOR 104

4.1 Limitations on the Use of Uniaxial Stress–Strain Data 104

4.2 Nonlinear Material Response 107

4.3 Yield Criteria: General Concepts 113

4.4 Yielding of Ductile Metals 117

4.5 Alternative Yield Criteria 126

4.6 General Yielding 129

Problems 142

References 146

CHAPTER 5 APPLICATIONS OF ENERGY METHODS 147

5.1 Principle of Stationary Potential Energy 147

5.2 Castigliano’s Theorem on Deflections 152

5.3 Castigliano’s Theorem on Deflections for Linear Load–Deflection Relations 155

5.4 Deflections of Statically Determinate Structures 163

5.5 Statically Indeterminate Structures 177

Problems 187

References 199

CHAPTER 6 TORSION 200

6.1 Torsion of a Prismatic Bar of Circular Cross Section 200

6.2 Saint-Venant’s Semiinverse Method 209

6.3 Linear Elastic Solution 213

6.4 The Prandtl Elastic-Membrane (Soap-Film) Analogy 216

6.5 Narrow Rectangular Cross Section 219

6.6 Torsion of Rectangular Cross Section Members 222

6.7 Hollow Thin-Wall Torsion Members and Multiply Connected Cross Sections 228

6.8 Thin-Wall Torsion Members with Restrained Ends 234

6.9 Numerical Solution of the Torsion Problem 239

6.10 Inelastic Torsion: Circular Cross Sections 243

6.11 Fully Plastic Torsion: General Cross Sections 250

Problems 254

References 262

CHAPTER 7 BENDING OF STRAIGHT BEAMS 263

7.1 Fundamentals of Beam Bending 263

7.2 Bending Stresses in Beams Subjected to Nonsymmetrical Bending 272

7.3 Deflections of Straight Beams Subjected to Nonsymmetrical Bending 280

7.4 Effect of Inclined Loads 284

7.5 Fully Plastic Load for Nonsymmetrical Bending 285

Problems 287

References 294

CHAPTER 8 SHEAR CENTER FOR THIN-WALL BEAM CROSS SECTIONS 295

8.1 Approximations for Shear in Thin-Wall Beam Cross Sections 295

8.2 Shear Flow in Thin-Wall Beam Cross Sections 296

8.3 Shear Center for a Channel Section 298

8.4 Shear Center of Composite Beams Formed from Stringers and Thin Webs 303

8.5 Shear Center of Box Beams 306

Problems 312

References 318

CHAPTER 9 CURVED BEAMS 319

9.1 Introduction 319

9.2 Circumferential Stresses in a Curved Beam 320

9.3 Radial Stresses in Curved Beams 333

9.4 Correction of Circumferential Stresses in Curved Beams Having I, T, or Similar Cross Sections 338

9.5 Deflections of Curved Beams 343

9.6 Statically Indeterminate Curved Beams: Closed Ring Subjected to a Concentrated Load 348

9.7 Fully Plastic Loads for Curved Beams 350

Problems 352

References 356

CHAPTER 10 BEAMS ON ELASTIC FOUNDATIONS 357

10.1 General Theory 357

10.2 Infinite Beam Subjected to a Concentrated Load: Boundary Conditions 360

10.3 Infinite Beam Subjected to a Distributed Load Segment 369

10.4 Semiinfinite Beam Subjected to Loads at Its End 374

10.5 Semiinfinite Beam with Concentrated Load Near Its End 376

10.6 Short Beams 377

10.7 Thin-Wall Circular Cylinders 378

Problems 384

References 388

CHAPTER 11 THE THICK-WALL CYLINDER 389

11.1 Basic Relations 389

11.2 Stress Components at Sections Far from Ends for a Cylinder with Closed Ends 392

11.3 Stress Components and Radial Displacement for Constant Temperature 395

11.4 Criteria of Failure 399

11.5 Fully Plastic Pressure and Autofrettage 405

11.6 Cylinder Solution for Temperature Change Only 409

11.7 Rotating Disks of Constant Thickness 411

Problems 419

References 422

CHAPTER 12 ELASTIC AND INELASTIC STABILITY OF COLUMNS 423

12.1 Introduction to the Concept of Column Buckling 424

12.2 Deflection Response of Columns to Compressive Loads 425

12.3 The Euler Formula for Columns with Pinned Ends 428

12.4 Euler Buckling of Columns with Linearly Elastic End Constraints 436

12.5 Local Buckling of Columns 440

12.6 Inelastic Buckling of Columns 442

Problems 450

References 455

CHAPTER 13 FLAT PLATES 457

13.1 Introduction 457

13.2 Stress Resultants in a Flat Plate 458

13.3 Kinematics: Strain–Displacement Relations for Plates 461

13.4 Equilibrium Equations for Small-Displacement Theory of Flat Plates 466

13.5 Stress–Strain–Temperature Relations for Isotropic Elastic Plates 469

13.6 Strain Energy of a Plate 472

13.7 Boundary Conditions for Plates 473

13.8 Solution of Rectangular Plate Problems 476

13.9 Solution of Circular Plate Problems 486

Problems 500

References 501

CHAPTER 14 STRESS CONCENTRATIONS 502

14.1 Nature of a Stress Concentration Problem and the Stress Concentration Factor 504

14.2 Stress Concentration Factors: Theory of Elasticity 507

14.3 Stress Concentration Factors: Combined Loads 515

14.4 Stress Concentration Factors: Experimental Techniques 522

14.5 Effective Stress Concentration Factors 530

14.6 Effective Stress Concentration Factors: Inelastic Strains 536

Problems 539

References 541

CHAPTER 15 FRACTURE MECHANICS 543

15.1 Failure Criteria and Fracture 544

15.2 The Stationary Crack 551

15.3 Crack Propagation and the Stress Intensity Factor 555

15.4 Fracture: Other Factors 561

Problems 564

References 565

CHAPTER 16 FATIGUE: PROGRESSIVE FRACTURE 567

16.1 Fracture Resulting from Cyclic Loading 568

16.2 Effective Stress Concentration Factors: Repeated Loads 575

16.3 Effective Stress Concentration Factors: Other Influences 575

16.4 Low Cycle Fatigue and the _–N Relation 580

Problems 585

References 588

CHAPTER 17 CONTACT STRESSES 589

17.1 Introduction 589

17.2 The Problem of Determining Contact Stresses 590

17.3 Geometry of the Contact Surface 591

17.4 Notation and Meaning of Terms 596

17.5 Expressions for Principal Stresses 597

17.6 Method of Computing Contact Stresses 598

17.7 Deflection of Bodies in Point Contact 607

17.8 Stress for Two Bodies in Line Contact: Loads Normal to Contact Area 611

17.9 Stresses for Two Bodies in Line Contact: Loads Normal and Tangent to Contact Area 613

Problems 622

References 623

CHAPTER 18 CREEP: TIME-DEPENDENT DEFORMATION 624

18.1 Definition of Creep and the Creep Curve 624

18.2 The Tension Creep Test for Metals 626

18.3 One-Dimensional Creep Formulas for Metals Subjected to Constant Stress and Elevated Temperature 626

18.4 One-Dimensional Creep of Metals Subjected to Variable Stress and Temperature 631

18.5 Creep Under Multiaxial States of Stress 640

18.6 Flow Rule for Creep of Metals Subjected to Multiaxial States of Stress 643

18.7 An Application of Creep of Metals 649

18.8 Creep of Nonmetals 650

References 654

APPENDIX A AVERAGE MECHANICAL PROPERTIES OF SELECTED MATERIALS 657

APPENDIX B SECOND MOMENT (MOMENT OF INERTIA) OF A PLANE AREA 660

B.1 Moments of Inertia of a Plane Area 660

B.2 Parallel Axis Theorem 661

B.3 Transformation Equations for Moments and Products of Inertia 664

Problems 666

APPENDIX C PROPERTIES OF STEEL CROSS SECTIONS 668

AUTHOR INDEX 673

SUBJECT INDEX 676