PREFACE ....................................................... vii
LIST OF SYMBOLS ............................................... xix
Chapter 1 INTRODUCTION ......................................... 1
1.1 Mechanics of Materials .................................. 2
1.2 Scope of the Book ....................................... 4
1.4 Engineering Design ...................................... 5
1.5 Review of Static Equilibrium ............................ 6
1.6 Internal Force Resultants .............................. 10
1.7 Problem Formulation and Solution ....................... 13
1.8 Application to Simple Structures ....................... 15
Chapter Summary ........................................ 26
References ............................................. 27
Chapter 2 CONCEPT OF STRESS ................................... 28
2.1 Introduction ........................................... 29
2.2 Internal Axial Forces .................................. 29
2.3 Normal Stress .......................................... 31
2.4 Bearing Stress in Connections .......................... 37
2.5 Shearing Stress ........................................ 38
2.6 Stresses in Simple Structures .......................... 43
2.7 Allowable Stress and Factor of Safety .................. 52
2.8 Design of Bars for Axial Loading ....................... 56
2.9 Case Studies ........................................... 60
2.10 Stress under General Loading ........................... 68
Chapter Summary ........................................ 77
References ............................................. 78
Chapter 3 STRAIN AND MATERIAL PROPERTIES ...................... 79
3.1 Introduction ........................................... 80
3.2 Deformation ............................................ 80
3.3 Strain ................................................. 81
3.4 Components of Strain ................................... 84
3.5 Materials .............................................. 89
3.6 Stress-Strain Diagrams ................................. 90
3.7 True Stress and True Strain ............................ 97
3.8 Elastic versus Plastic Behavior ........................ 98
3.9 Hooke's Law ............................................ 99
3.10 Poisson's Ratio ....................................... 102
3.11 Generalized Hooke's Law ............................... 108
3.12 Strain Energy ......................................... 113
3.13 Impact Strength ....................................... 115
3.14 Fatigue ............................................... 116
3.15 Permanent Deformation ................................. 119
3.16 General Properties of Materials ....................... 121
3.17 Selecting Materials ................................... 122
Chapter Summary ....................................... 127
References ............................................ 129
Chapter 4 AXIALLY LOADED MEMBERS ............................. 130
4.1 Introduction .......................................... 131
4.2 Deformation of Axially Loaded Members ................. 131
4.3 Statically Indeterminate Structures ................... 143
4.4 Method of Superposition ............................... 147
4.5 Thermal Deformation and Stress ........................ 148
4.6 Stresses on Inclined Planes ........................... 156
4.7 Saint-Venant's Principle .............................. 159
4.8 Stress Concentrations ................................. 160
4.9 Ductility and Design .................................. 164
4.10 Plastic Deformation and Residual Stress ............... 165
Chapter Summary ....................................... 172
References ............................................ 173
Chapter 5 TORSION ............................................ 174
5.1 Introduction .......................................... 175
5.2 Deformation of a Circular Shaft ....................... 175
5.3 The Torsion Formula ................................... 178
5.4 Axial and Transverse Shear Stresses ................... 180
5.5 Stresses on Inclined Planes ........................... 183
5.6 Angle of Twist ........................................ 188
5.7 Statically Indeterminate Shafts ....................... 196
5.8 Design of Circular Shafts ............................. 202
5.9 Stress Concentrations ................................. 206
5.10 Inelastic Torsion of Circular Shafts .................. 211
5.11 Torsion of Noncircular Solid Bars ..................... 215
5.12 Thin-Walled Hollow Members ............................ 218
Chapter Summary ....................................... 228
References ............................................ 230
Chapter 6 SHEAR AND MOMENT IN BEAMS .......................... 231
6.1 Introduction .......................................... 232
6.2 Classification of Beams ............................... 232
6.3 Calculation of Beam Reactions ......................... 233
6.4 Shear Force and Bending Moment ........................ 238
6.5 Load, Shear, and Moment Relationships ................. 243
6.6 Shear and Moment Diagrams ............................. 245
6.7 Discontinuity Functions ............................... 259
Chapter Summary ....................................... 268
References ............................................ 270
Chapter 7 STRESSES IN BEAMS .................................. 271
7.1 Introduction .......................................... 272
PART A Pure Bending .................................. 273
7.2 Beam Deformation in Pure Bending ...................... 273
7.3 Assumptions of Beam Theory ............................ 275
7.4 Normal Strain in Beams ................................ 276
7.5 Normal Stress in Beams ................................ 280
7.6 Stress Concentrations in Bending ...................... 285
PART В Shear and Bending ............................. 292
7.7 Shear Stresses in Beams ............................... 292
7.8 Shear Stress Distribution in Rectangular Beams ........ 297
7.9 Shear Stresses in Beams of Circular Cross Section ..... 299
7.10 Shear Stress Distribution in Flanged Beams ............ 300
7.11 Comparison of Shear and Bending Stresses .............. 304
7.12 Design of Prismatic Beams ............................. 308
7.13 Design of Beams of Constant Strength .................. 311
PART С Special Topics ................................ 321
7.14 Composite Beams ....................................... 321
7.15 Reinforced Concrete Beams ............................. 325
7.16 Unsymmetric Bending ................................... 327
7.17 Shear Center .......................................... 332
7.18 Inelastic Bending ..................................... 334
7.19 Curved Beams .......................................... 341
Chapter Summary ....................................... 356
References ............................................ 359
Chapter 8 TRANSFORMATION OF STRESS AND STRAIN ................ 360
8.1 Introduction .......................................... 361
8.2 Plane Stress .......................................... 361
8.3 Principal Stresses .................................... 367
8.4 Maximum Shear Stress .................................. 368
8.5 Mohr's Circle for Plane Stress ........................ 370
8.6 Absolute Maximum Shear Stress ......................... 383
8.7 Principal Stresses for a General State of Stress ...... 384
8.8 Thin-Walled Pressure Vessels .......................... 385
8.9 Thick-Walled Pressure Vessels ......................... 393
8.10 Plane Strain .......................................... 402
8.11 Mohr's Circle for Plane Strain ........................ 405
8.12 Measurement of Strain; Strain Rosette ................. 409
8.13 Relation Involving E, v, and G ........................ 412
Chapter Summary ....................................... 416
References ............................................ 418
Chapter 9 COMBINED LOADINGS AND FAILURE CRITERIA ............. 419
9.1 Introduction .......................................... 420
PART A Combined Stresses ............................. 421
9.2 Axial and Torsional Loads ............................. 421
9.3 Direct Shear and Torsional Loads: Helical Springs ..... 427
9.4 Axial, Transverse, and Torsional Loads ................ 431
9.5 Transverse Shear and Bending Moment Loads: Principal
Stresses in Beams ..................................... 437
9.6 Eccentric Axial Loads ................................. 440
PART B Failure Theories in Design .................... 450
9.7 Material Failure ...................................... 450
9.8 Yield Criteria for Ductile Materials .................. 451
9.9 Fracture Criteria for Brittle Materials ............... 454
9.10 Design of Transmission Shafts ......................... 460
Chapter Summary ....................................... 468
References ............................................ 470
Chapter 10 DEFLECTIONS OF BEAMS .............................. 471
10.1 Introduction .......................................... 472
10.2 The Elastic Curve ..................................... 472
10.3 Boundary Conditions ................................... 473
10.4 Method of Integration ................................. 476
10.5 Use of Discontinuity Functions ........................ 487
10.6 Method of Superposition ............................... 493
10.7 Statically Indeterminate Beams ........................ 496
10.8 Statically Indeterminate Beams — Method of
Integration ........................................... 497
10.9 Statically Indeterminate Beams — Method of
Superposition ......................................... 507
10.10 Moment-Area Method .................................... 514
10.11 Statically Indeterminate Beams — Moment-Area Method ... 525
10.12 Continuous Beams ...................................... 527
Chapter Summary ....................................... 535
References ............................................ 536
Chapter 11 BUCKLING OF COLUMNS ............................... 537
11.1 Introduction .......................................... 538
11.2 Stability of Structures ............................... 538
11.3 Pin-Ended Columns ..................................... 540
11.4 Columns with Other End Conditions ..................... 542
11.5 Critical Stress: Classification of Columns ............ 547
11.6 Eccentric Loaded Columns and the Secant Formula ....... 558
11.7 Design of Columns for Centric Loading ................. 564
11.8 Design of Columns for Eccentric Loading ............... 569
Chapter Summary ....................................... 574
References ............................................ 575
Chapter 12 ENERGY METHODS AND IMPACT ......................... 576
12.1 Introduction .......................................... 577
12.2 Strain Energy under Axial Loading ..................... 577
12.3 Strain Energy in Circular Shafts ...................... 580
12.4 Strain Energy in Beams ................................ 581
12.5 Strain Energy for a General State of Stress ........... 584
12.6 Conservation of Energy ................................ 589
12.7 Displacement under a Single Load by the Work-Energy
Method ................................................ 590
12.8 Displacements by Castigliano's Theorem ................ 593
12.9 Unit-Load Method ...................................... 599
12.10 Statically Indeterminate Structures ................... 602
12.11 Impact Loading ........................................ 609
12.12 Longitudinal and Bending Impact ....................... 610
Chapter Summary ....................................... 621
References ............................................ 623
Chapter 13 FINITE ELEMENT ANALYSIS ........................... 624
13.1 Introduction .......................................... 625
13.2 The Bar Element ....................................... 626
13.3 Two-Dimensional Bar Element ........................... 627
13.4 Axial Force in the Bar Element ........................ 630
13.5 Formulation of the Finite Element Method .............. 631
13.6 Beam Elements ......................................... 644
Chapter Summary ....................................... 652
References ............................................ 653
Appendix A PROPERTIES OF AREAS ............................... 655
A.1 Centroid of an Area ................................... 655
A.2 Moments of Inertia and Radius of Gyration ............. 658
А.3 Parallel-Axis Theorem ................................. 660
A.4 Principal Moments of Inertia .......................... 662
Appendix В TABLES ............................................ 667
B.1 Principal SI Units Used in Mechanics .................. 668
B.2 SI Prefixes ........................................... 668
B.3 Conversion Factors between U.S. Customary and
SI Units .............................................. 669
B.4 Properties of Selected Engineering Materials .......... 670
B.5 Materials and Selected Members of Each Class .......... 672
B.6 Properties of Areas ................................... 674
B.7 Properties of Selected Steel Pipe and Tubing .......... 675
B.8 Properties of Steel W Shapes, Wide-Flange Sections .... 676
B.9 Properties of Steel S Shapes, American Standard
I-Beams ............................................... 678
B.10 Properties of Steel С Shapes, American Standard
Channels .............................................. 680
B.11 Properties of Steel L Shapes, Angles with Equal
Legs .................................................. 682
B.12 Properties of Steel L Shapes, Angles with Unequal
Legs .................................................. 684
B.13 Properties of Structural Lumber ....................... 686
B.14 Deflections and Slopes of Beams ....................... 687
B.15 Reactions and Deflections of Statically
Indeterminate Beams ................................... 689
Appendix С MATRIX ALGEBRA .................................... 690
C.1 Definition of a Matrix ................................ 690
C.2 Determinant of a Matrix ............................... 691
C.3 Matrix Operations ..................................... 693
C.4 Simultaneous Linear Equations ......................... 695
Appendix D FUNDAMENTALS OF ENGINEERING EXAMINATION ........... 697
ANSWERS TO SELECTED EVEN-NUMBERED PROBLEMS .................... 698
INDEX ......................................................... 711
|
