CHAPTER 1 INTRODUCTION 1
1.1 Review of Elementary Mechanics of Materials 1
1.2 Methods of Analysis 5
1.3 Stressâ"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 STRESSâ"STRAINâ"TEMPERATURE RELATIONS 79
3.1 First Law of Thermodynamics, Internal-Energy Density, and Complementary Internal-Energy Density 79
3.2 Hookeâs Law: Anisotropic Elasticity 84
3.3 Hookeâs Law: Isotropic Elasticity 85
3.4 Equations of Thermoelasticity for Isotropic Materials 91
3.5 Hookeâs Law: Orthotropic Materials 93
Problems 101
References 103
CHAPTER 4 INELASTIC MATERIAL BEHAVIOR 104
4.1 Limitations on the Use of Uniaxial Stressâ"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 Castiglianoâs Theorem on Deflections 152
5.3 Castiglianoâs Theorem on Deflections for Linear Loadâ"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-Venantâs 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: Strainâ"Displacement Relations for Plates 461
13.4 Equilibrium Equations for Small-Displacement Theory of Flat Plates 466
13.5 Stressâ"Strainâ"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 _â"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
