Mechanics of materials

Cover......Page 1
Principal SI Units Used in Mechanics......Page 3
U.S. Customary Units and Their SI Equivalents......Page 4
MECHANICS OF MATERIALS......Page 7
Copyright......Page 8
About the Authors......Page 9
Contents......Page 11
Preface......Page 16
List of Symbols......Page 22
1 Introduction—Concept of Stress......Page 27
1.2 A Short Review of the Methods of Statics......Page 28
1.3 Stresses in the Members of a Structure......Page 31
1.4 Analysis and Design......Page 32
1.5 Axial Loading; Normal Stress......Page 33
1.6 Shearing Stress......Page 35
1.8 Application to the Analysis and Design of Simple Structures......Page 37
1.9 Method of Problem Solution......Page 40
1.10 Numerical Accuracy......Page 41
1.11 Stress on an Oblique Plane under Axial Loading......Page 50
1.12 Stress under General Loading Conditions; Components of Stress......Page 51
1.13 Design Considerations......Page 54
Review and Summary for Chapter 1......Page 66
PROBLEMS......Page 60
REVIEW PROBLEMS......Page 69
COMPUTER PROBLEMS......Page 73
2 Stress and Strain—Axial Loading......Page 77
2.1 Introduction......Page 78
2.2 Normal Strain under Axial Loading......Page 79
2.3 Stress-Strain Diagram......Page 81
*2.4 True Stress and True Strain......Page 85
2.5 Hooke’s Law; Modulus of Elasticity......Page 86
2.6 Elastic versus Plastic Behavior of a Material......Page 88
2.7 Repeated Loadings; Fatigue......Page 90
2.8 Deformations of Members under Axial Loading......Page 91
PROBLEMS......Page 96
2.9 Statically Indeterminate Problems......Page 102
2.10 Problems Involving Temperature Changes......Page 106
PROBLEMS......Page 112
2.11 Poisson’s Ratio......Page 117
2.12 Multiaxial Loading; Generalized Hooke’s Law......Page 118
*2.13 Dilatation; Bulk Modulus......Page 120
2.14 Shearing Strain......Page 122
2.15 Further Discussion of Deformations under Axial Loading; Relation among E,ν, and G......Page 125
2.16 Stress-Strain Relationships for Fiber-Reinforced Composite Materials......Page 127
PROBLEMS......Page 132
2.17 Stress and Strain Distribution under Axial Loading; Saint-Venant’s Principle......Page 137
2.18 Stress Concentrations......Page 139
2.19 Plastic Deformations......Page 141
*2.20 Residual Stresses......Page 145
PROBLEMS......Page 148
Review and Summary for Chapter 2......Page 153
REVIEW PROBLEMS......Page 159
COMPUTER PROBLEMS......Page 162
3 Torsion......Page 165
3.1 Introduction......Page 166
3.2 Preliminary Discussion of the Stresses in a Shaft......Page 168
3.3 Deformations in a Circular Shaft......Page 169
3.4 Stresses in the Elastic Range......Page 172
PROBLEMS......Page 178
3.5 Angle of Twist in the Elastic Range......Page 183
3.6 Statically Indeterminate Shafts......Page 187
PROBLEMS......Page 192
3.7 Design of Transmission Shafts......Page 200
3.8 Stress Concentrations in Circular Shafts......Page 203
PROBLEMS......Page 205
*3.9 Plastic Deformations in Circular Shafts......Page 208
*3.10 Circular Shafts Made of an Elastoplastic Material......Page 210
*3.11 Residual Stresses in Circular Shafts......Page 213
PROBLEMS......Page 218
*3.12 Torsion of Noncircular Members......Page 221
*3.13 Thin-Walled Hollow Shafts......Page 224
PROBLEMS......Page 228
Review and Summary for Chapter 3......Page 234
REVIEW PROBLEMS......Page 239
COMPUTER PROBLEMS......Page 242
4 Pure Bending......Page 245
4.1 Introduction......Page 246
4.2 Symmetric Member in Pure Bending......Page 248
4.3 Deformations in a Symmetric Member in Pure Bending......Page 250
4.4 Stresses and Deformations in the Elastic Range......Page 253
4.5 Deformations in a Transverse Cross Section......Page 257
PROBLEMS......Page 261
4.6 Bending of Members Made of Several Materials......Page 266
4.7 Stress Concentrations......Page 270
PROBLEMS......Page 274
*4.8 Plastic Deformations......Page 279
*4.9 Members Made of an Elastoplastic Material......Page 280
*4.10 Plastic Deformations of Members with a Single Plane of Symmetry......Page 284
*4.11 Residual Stresses......Page 285
PROBLEMS......Page 290
4.12 Eccentric Axial Loading in a Plane of Symmetry......Page 294
PROBLEMS......Page 298
4.13 Unsymmetric Bending......Page 303
4.14 General Case of Eccentric Axial Loading......Page 308
PROBLEMS......Page 313
*4.15 Bending of Curved Members......Page 318
PROBLEMS......Page 325
Review and Summary for Chapter 4......Page 329
REVIEW PROBLEMS......Page 333
COMPUTER PROBLEMS......Page 336
5 Analysis and Design of Beams for Bending......Page 339
5.1 Introduction......Page 340
5.2 Shear and Bending-Moment Diagrams......Page 343
PROBLEMS......Page 348
5.3 Relations among Load, Shear, and Bending Moment......Page 353
PROBLEMS......Page 360
5.4 Design of Prismatic Beams for Bending......Page 363
PROBLEMS......Page 368
*5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam......Page 374
PROBLEMS......Page 382
*5.6 Nonprismatic Beams......Page 385
PROBLEMS......Page 389
Review and Summary for Chapter 5......Page 394
REVIEW PROBLEMS......Page 398
COMPUTER PROBLEMS......Page 402
6 Shearing Stresses in Beams and Thin-Walled Members......Page 405
6.1 Introduction......Page 406
6.2 Shear on the Horizontal Face of a Beam Element......Page 408
6.3 Determination of the Shearing Stresses in a Beam......Page 410
6.4 Shearing Stresses τ[sub(xy)] in Common Types of Beams......Page 411
*6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam......Page 414
PROBLEMS......Page 418
6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape......Page 423
6.7 Shearing Stresses in Thin-Walled Members......Page 425
*6.8 Plastic Deformations......Page 428
PROBLEMS......Page 432
*6.9 Unsymmetric Loading of Thin-Walled Members; Shear Center......Page 438
PROBLEMS......Page 447
Review and Summary for Chapter 6......Page 451
REVIEW PROBLEMS......Page 454
COMPUTER PROBLEMS......Page 458
7 Transformations of Stress and Strain......Page 461
7.1 Introduction......Page 462
7.2 Transformation of Plane Stress......Page 464
7.3 Principal Stresses: Maximum Shearing Stress......Page 467
PROBLEMS......Page 472
7.4 Mohr’s Circle for Plane Stress......Page 476
PROBLEMS......Page 483
7.5 General State of Stress......Page 486
7.6 Application of Mohr’s Circle to the Three-Dimensional Analysis of Stress......Page 488
*7.7 Yield Criteria for Ductile Materials under Plane Stress......Page 491
*7.8 Fracture Criteria for Brittle Materials under Plane Stress......Page 493
PROBLEMS......Page 497
7.9 Stresses in Thin-Walled Pressure Vessels......Page 502
PROBLEMS......Page 506
*7.10 Transformation of Plane Strain......Page 510
*7.11 Mohr’s Circle for Plane Strain......Page 513
*7.12 Three-Dimensional Analysis of Strain......Page 515
*7.13 Measurements of Strain; Strain Rosette......Page 518
PROBLEMS......Page 522
Review and Summary for Chapter 7......Page 526
REVIEW PROBLEMS......Page 531
COMPUTER PROBLEMS......Page 534
8 Principal Stresses under a Given Loading......Page 537
*8.1 Introduction......Page 538
*8.2 Principal Stresses in a Beam......Page 539
*8.3 Design of Transmission Shafts......Page 542
PROBLEMS......Page 547
*8.4 Stresses under Combined Loadings......Page 551
PROBLEMS......Page 557
Review and Summary for Chapter 8......Page 564
REVIEW PROBLEMS......Page 566
COMPUTER PROBLEMS......Page 569
9 Deflection of Beams......Page 573
9.1 Introduction......Page 574
9.2 Deformation of a Beam under Transverse Loading......Page 576
9.3 Equation of the Elastic Curve......Page 577
*9.4 Direct Determination of the Elastic Curve from the Load Distribution......Page 583
9.5 Statically Indeterminate Beams......Page 585
PROBLEMS......Page 590
*9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam......Page 595
PROBLEMS......Page 601
9.7 Method of Superposition......Page 604
9.8 Application of Superposition to Statically Indeterminate Beams......Page 606
PROBLEMS......Page 612
*9.9 Moment-Area Theorems......Page 616
*9.10 Application to Cantilever Beams and Beams with Symmetric Loadings......Page 619
*9.11 Bending-Moment Diagrams by Parts......Page 621
PROBLEMS......Page 626
*9.12 Application of Moment-Area Theorems to Beams with Unsymmetric Loadings......Page 629
*9.13 Maximum Deflection......Page 631
*9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams......Page 633
PROBLEMS......Page 638
Review and Summary for Chapter 9......Page 642
REVIEW PROBLEMS......Page 649
COMPUTER PROBLEMS......Page 651
10 Columns......Page 655
10.2 Stability of Structures......Page 656
10.3 Euler’s Formula for Pin-Ended Columns......Page 659
10.4 Extension of Euler’s Formula to Columns with Other End Conditions......Page 662
PROBLEMS......Page 668
*10.5 Eccentric Loading; the Secant Formula......Page 673
PROBLEMS......Page 679
10.6 Design of Columns under a Centric Load......Page 684
PROBLEMS......Page 694
10.7 Design of Columns under an Eccentric Load......Page 699
PROBLEMS......Page 704
Review and Summary for Chapter 10......Page 708
REVIEW PROBLEMS......Page 711
COMPUTER PROBLEMS......Page 714
11 Energy Methods......Page 717
11.2 Strain Energy......Page 718
11.3 Strain-Energy Density......Page 720
11.4 Elastic Strain Energy for Normal Stresses......Page 722
11.5 Elastic Strain Energy for Shearing Stresses......Page 725
11.6 Strain Energy for a General State of Stress......Page 728
PROBLEMS......Page 733
11.7 Impact Loading......Page 740
11.8 Design for Impact Loads......Page 742
11.9 Work and Energy under a Single Load......Page 743
11.10 Deflection under a Single Load by the Work-Energy Method......Page 746
PROBLEMS......Page 751
*11.11 Work and Energy under Several Loads......Page 756
*11.12 Castigliano’s Theorem......Page 758
*11.13 Deflections by Castigliano’s Theorem......Page 760
*11.14 Statically Indeterminate Structures......Page 764
PROBLEMS......Page 769
Review and Summary for Chapter 11......Page 774
REVIEW PROBLEMS......Page 778
COMPUTER PROBLEMS......Page 781
Appendices......Page 783
A: Moments of Areas......Page 784
B: Typical Properties of Selected Materials Used in Engineering......Page 794
C: Properties of Rolled-Steel Shapes......Page 798
D: Beam Deflections and Slopes......Page 810
E: Fundamentals of Engineering Examination......Page 811
Photo Credits......Page 813
Index......Page 815
About the Authors......Page 825