Advanced Mechanics of Materials

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