Engineering Mechanics of Solids

Cover......Page 1
Noted Errata in 1st Printing......Page 3
Abbreviations and Symbols......Page 5
Title Page......Page 10
Contents......Page 12
Preface......Page 22
1-1. Introduction......Page 28
1-2. Method of Sections......Page 30
1-3. Definition of Stress......Page 31
1-4. stress Tensor......Page 32
1-5. Differential Equations of Equilibrium......Page 38
1-6. Stresses on Inclined Sections in Axialiy Loaded Bars......Page 39
1-7. Maximum Normal stress in Axially Loaded Bars......Page 43
1-8. Shear Stresses......Page 46
1-9. Analysis for Normal and Shear Stresses......Page 49
1-10. Member Strength as a Design Criterion......Page 58
1-11. Deterministic Design of Members: Axially Loaded Bars......Page 61
1-12. Probabilistic Basis for Structural Design......Page 65
1-13. Bolted and Riveted Connections......Page 74
1-14. Welded Joints......Page 77
Problems......Page 79
2-2. Normal Strain......Page 87
2-3. Stress-Strain Relationships......Page 89
2-4. Hooke's Law......Page 92
2-5. Further Remarks on Stress-Strain Relationships......Page 94
2-6. Other Idealizations of Constitutive Relations......Page 95
2-7. Deformation of Axially Loaded Bars......Page 98
2-8. Poisson's Ratio......Page 109
2-9. Thermal Strain and Deformation......Page 111
2-10. Saint-Venant's Principle and Stress Concentrations......Page 113
2-11. Elastic Strain Energy for Uniaxial Stress......Page 118
2-12. Deflections by the Energy Method......Page 121
2-13. Dynamic and Impact Loads......Page 123
2-14. General Considerations......Page 126
2-15. Force Method of Analysis......Page 127
2-16. Introduction to the Displacement Method......Page 133
2-17. Displacement Method with Several Degrees of Freedom......Page 135
2-18. Introduction to Statically Indeterminate Nonlinear Probiems......Page 139
2-19. Alternative Differential Equation Approach for Deflections......Page 152
Problems......Page 154
3-2. Stress-Strain Relationships for Shear......Page 166
3-3. Elastic Strain Energy for Shear Stresses......Page 168
3-4. Mathematical Definition of Strain......Page 170
3-5. Strain Tensor......Page 172
3-6. Generalized Hooke's Law for Isotropic Materials......Page 173
3-7. E, G and Nu Relationships......Page 177
3-8. Dilatation and Bulk Modulus......Page 178
3-9. Cylindrical and Spherical Pressure Vessels......Page 179
3-10. Remarks on Thin-Walled Pressure Vessels......Page 184
3-11. Introduction......Page 186
3-12. Solution of the General Problem......Page 187
3-13. Special Cases......Page 192
3-14. Behavior of Ideally Plastic Thick-Walled Cylinders......Page 194
Problems......Page 198
4-2. Application of the Method of Sections......Page 202
4-3. Basic Assumptions for Circular Members......Page 204
4-4. The Torsion Formula......Page 205
4-5. Remarks on the Torsion Formula......Page 209
4-6. Design of Circular Members in Torsion......Page 212
4-7. Stress Concentrations......Page 214
4-8. Angle-of-Twist of Circular Members......Page 216
4-9. Statically Indeterminate Problems......Page 221
4-10. Alternative Differential Equation Approach for Torsion Problems......Page 224
4-11. Energy and Impact Loads......Page 226
4-12. Shaft Couplings......Page 228
4-13. Shear Stresses and Deformations in Circular Shafts in the Inelastic Range......Page 229
4-14. Solid Bars of Any Cross Section......Page 234
4-15. Warpage of Thin-Walled Open Sections......Page 238
4-16. Thin-Walled Hollow Members......Page 240
Problems......Page 244
5-1. Introduction......Page 251
5-2. Diagrammatic Conventions for Supports......Page 252
5-3. Diagrammatic Conventions for Loading......Page 253
5-4. Classification of Beams......Page 255
5-5. Calculation of Beam Reactions......Page 257
5-6. Application of the Method of Sections......Page 261
5-7. Axial Force in Beams......Page 262
5-8. Shear in Beams......Page 263
5-9. Bending Moment in Beams......Page 264
5-10. Axial-Force, Shear, and Bending-Moment Diagrams......Page 267
5-11. Differential Equations of Equilibrium for a Beam Element......Page 275
5-12. Shear Diagrams by Integration of the Load......Page 277
5-13. Moment Diagrams by Integration of the Shear......Page 279
5-14. Effect of Concentrated Moment on Moment Diagrams......Page 285
5-15. Moment Diagram and the Elastic Curve......Page 288
Problems......Page 296
6-1. Introduction......Page 307
6-2. The Basic Kinematic Assumption......Page 308
6-3. The Elastic Flexure Formula......Page 310
6-4. Computation of the Moment of Inertia......Page 316
6-5. Applications of the Flexure Formula......Page 320
6-6. Stress Concentrations......Page 324
6-7. Elastic Strain Energy in Pure Bending......Page 326
6-8. Beams of Composite Cross Section......Page 328
6-9. Curved Bars......Page 333
6-10. Inelastic Bending of Beams......Page 338
6-11. Bending About Both Principal Axes......Page 346
6-12. Elastic Bending with Axial Loads......Page 351
6-13. Inelastic Bending with Axial Loads......Page 360
6-14. Bending of Beams with Unsymmetric (Arbitrary) Cross Section......Page 363
6-15. Area Moments and Products of Inertia......Page 367
6-16. Principal Axes of Inertia......Page 368
Problems......Page 370
7-2. Preliminary Remarks......Page 384
7-3. Shear Flow......Page 388
7-4. The Shear-Stress Formula for Beams......Page 394
7-5. Warpage of Plane Sections Due to Shear......Page 400
7-6. Some Limitations of the Shear-Stress Formula......Page 405
7-7. Shear Stresses in Beam Flanges......Page 407
7-8. Shear Center......Page 409
7-9. Combined Direct and Torsional Shear Stresses......Page 413
7-10. Stresses in Closely Coiled Helical Springs......Page 416
7-11. Deflection of Closely Coiled Helical Springs......Page 418
Problems......Page 420
8-2. The Basic Problem......Page 430
8-3. Transformation of Stresses in Two-Dimensional Problems......Page 434
8-4. Principal Stresses in Two-Dimensional Problems......Page 436
8-5. Maximum Shear Stresses in Two-Dimensional Problems......Page 437
8-6. Mohr's Circle of Stress for Two-Dimensional Problems......Page 441
8-7. Construction of Mohr's Circles for Stress Transformation......Page 444
8-8. Principal Stresses for a General State of Stress......Page 451
8-9. Mohr's Circle for a General State of Stress......Page 453
8-11. Transformation of Strain in Two Dimensions......Page 457
8-12. Alternative Derivation for Strain Transformation in Two-Dimensions......Page 460
8-13. Mohr's Circle for Two-Dimensional Strain......Page 462
8-14. Strain Rosettes......Page 465
8-15. Introductory Remarks......Page 468
8-16. Maximum Shear-Stress Theory......Page 469
8-17. Maximum Distortion-Energy Theory......Page 471
8-18. Comparison of Maximum-Shear and Distortion-Energy Theories for Plane Stress......Page 475
8-20. Comparison of Yield and Fracture Criteria......Page 476
Problems......Page 480
9-1. Introduction......Page 486
9-2. State of Stress for Some Basic Cases......Page 488
9-3. Comparative Accuracy of Beam Solutions......Page 493
9-4. Experimental Methods of Stress Analysis......Page 496
9-5. Design of Axially Loaded Members......Page 497
9-6. Design of Torsion Members......Page 498
9-7. Design Criteria for Prismatic Beams......Page 499
9-8. Design of Prismatic Beams......Page 502
9-9. Design of Nonprismatic Beams......Page 507
9-10. Design of Complex Members......Page 509
Problems......Page 512
10-1. Introduction......Page 525
10-2. Moment-Curvature Relation......Page 526
10-3. Governing Differential Equation......Page 528
10-4. Alternative Derivation of the Governing Equation......Page 531
10-6. Boundary Conditions......Page 532
10-7. Direct Integration Solutions......Page 534
10-8. Singularity Functions for Beams......Page 550
10-9. Deflections by Superposition......Page 552
10-10. Deflections in Unsymmetrical Bending......Page 556
10-11. Energy Method for Deflections and Impact......Page 558
10-12. Inelastic Deflection of Beams......Page 561
10-13. Introduction to the Moment-Area Method......Page 564
10-14. Moment-Area Theorems......Page 565
10-15. Statically Indeterminate Beams......Page 578
Problems......Page 586
11-1. Introduction......Page 601
11-2. Examples of Instability......Page 603
11-3. Criteria for Stability of Equilibrium......Page 605
11-4. Euler Load for Columns with Pinned Ends......Page 610
11-5. Euler Loads for Columns with Different end Restraints......Page 612
11-6. Limitations of the Euler Formulas......Page 615
11-7. Generalized Euler Buckling-Load Formulas......Page 617
11-8. Eccentric Loads and the Secant Formula......Page 619
11-9. Beam-Columns......Page 623
11-10. Alternative Differential Equations for Beam-Columns......Page 627
11-11. General Considerations......Page 632
11-12. Concentrically Loaded Columns......Page 635
11-13. Eccentrically Loaded Columns......Page 643
Problems......Page 650
12-1. Introduction......Page 661
12-2. Elastic Strain Energy......Page 662
12-3. Displacements by Conservation of Energy......Page 664
12-4. Virtual Work Principle......Page 665
12-5. Virtual Forces for Deflections......Page 669
12-6. Virtual Force Equations for Elastic Systems......Page 671
12-7. Virtual Forces for Indeterminate Problems......Page 677
12-8. Virtual Displacements for Equilibrium......Page 680
12-9. Virtual Work for Discrete Systems......Page 684
12-11. Strain Energy and Complementary Strain Energy Theorems......Page 688
12-12. Castigliano's Theorems......Page 692
12-13. Statically Indeterminate Systems......Page 697
12-14. Elastic Energy for Buckling Loads......Page 701
Problems......Page 703
13-1 Introduction......Page 713
13-3. Force Method......Page 714
13-4. Flexibility Coefficients Reciprocity......Page 717
13-5. Introduction to the Displacement Method......Page 724
13-6. Further Remarks on the Displacement Method......Page 727
13-7. Stiffness Coefficients Reciprocity......Page 730
13-8. Plastic Limit Analysis of Beams......Page 735
13-9. Continuous Beams and Frames......Page 748
Problems......Page 750
Appendices: Tables......Page 756
Answers to Odd-numbered Problems......Page 770
Index......Page 776
SI Units......Page 783
Conversion Factors......Page 784
Backcover......Page 786