Strength of materials: a unified theory

Surya Patnaik, Dale Hopkins0750674024, 9780750674027

Strength of Materials provides a comprehensive overview of the latest theory of strength of materials. The unified theory presented in this book is developed around three concepts: Hooke’s Law, Equilibrium Equations, and Compatibility conditions. The first two of these methods have been fully understood, but clearly are indirect methods with limitations. Through research, the authors have come to understand compatibility conditions, which, until now, had remained in an immature state of development. This method, the Integrated Force Method (IFM) couples equilibrium and compatibility conditions to determine forces directly. The combination of these methods allows engineering students from a variety of disciplines to comprehend and compare the attributes of each. The concept that IFM strength of materials theory is problem independent, and can be easily generalized for solving difficult problems in linear, nonlinear, and dynamic regimes is focused upon. Discussion of the theory is limited to simple linear analysis problems suitable for an undergraduate course in strength of materials. To support the teaching application of the book there are problems and an instructor’s manual. ·Provides a novel approach integrating two popular indirect solution methods with newly researched, more direct conditions ·Completes the previously partial theory of strength of materials ·A new frontier in solid mechanics

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Table of contents :
Cover……Page 1
Half Title Page……Page 2
Title Page……Page 4
Copyright……Page 5
Contents……Page 6
Preface……Page 10
Strength of Materials……Page 13
Determinate Analysis……Page 14
Indeterminate Analysis……Page 15
Stiffness Method……Page 16
Other Methods……Page 17
Unified Theory of Strength of Materials……Page 19
Historical Sketch……Page 20
References……Page 22
1. Introduction……Page 24
1.1 Systems of Units……Page 27
1.2 Response Variables……Page 30
1.3 Sign Conventions……Page 38
1.4 Load-Carrying Capacity of Members……Page 39
1.5 Material Properties……Page 51
1.6 Stress-Strain Law……Page 53
1.7 Assumptions of Strength of Materials……Page 60
1.8 Equilibrium Equations……Page 65
Three-Legged Table Problem……Page 67
Navier’s Table Problem……Page 70
Problems……Page 73
2.1 Bar Member……Page 78
2.2 Stress in a Bar Member……Page 91
2.3 Displacement in a Bar Member……Page 95
2.5 Strain in a Bar Member……Page 97
2.6 Definition of a Truss Problem……Page 99
2.7 Nodal Displacement……Page 108
2.8 Initial Deformation in a Determinate Truss……Page 119
2.9 Thermal Effect in a Truss……Page 122
2.10 Settling of Support……Page 124
2.11 Theory of Determinate Analysis……Page 127
2.12 Definition of Determinate Truss……Page 136
Problems……Page 145
3. Simple Beam……Page 152
3.1 Analysis for Internal Forces……Page 154
3.2 Relationship between Bending Moment, Shear Force, and Load……Page 172
3.3 Flexure Formula……Page 176
3.4 Shear Stress Formula……Page 182
3.5 Displacement in a Beam……Page 187
3.6 Thermal Displacement in a Beam……Page 202
3.7 Settling of Supports……Page 206
3.8 Shear Center……Page 207
3.9 Built-up Beam an Interface Shear Force……Page 220
3.10 Composite Beams……Page 225
Problems……Page 232
4. Determinate Shaft……Page 240
4.1 Analysis of Internal Torque……Page 241
4.2 Torsion Formula……Page 245
4.3 Deformation Analysis……Page 247
4.4 Power Transmission through a Circular Shaft……Page 256
Problems……Page 259
5. Simple Frames……Page 262
Problems……Page 282
6. Indeterminate Truss……Page 286
6.1 Equilibrium Equations……Page 289
6.2 Deformation Displacement Relations……Page 291
6.4 Compatibility Conditions……Page 292
6.5 Initial Deformation and Support Settling……Page 293
6.7 Response Variables of Analysis……Page 296
6.9 Method of Displacements or the Displacement Method……Page 297
6.10 Integrated Force Method……Page 298
Procedures for Analysis……Page 299
Theory of Dual Integrated Force Method……Page 312
Theory of Stiffness Method……Page 319
Stiffness Method for Thermal Load……Page 323
First Thermal Load……Page 324
Second Thermal Load……Page 325
Stiffness Method for Support Settling……Page 326
Problems……Page 328
7. Indeterminate Beam……Page 334
7.1 Internal Forces in a Beam……Page 338
7.2 IFM Analysis for Indeterminate Beam……Page 340
7.3 Flexibility Matrix……Page 352
7.4 Stiffness Method Analysis for Indeterminate Beam……Page 360
7.5 Stiffness Method for Mechanical Load……Page 362
7.6 Stiffness Solution for Thermal Load……Page 364
7.7 Stiffness Solution for Support Settling……Page 366
7.8 Stiffness Method Solution to the Propped Beam……Page 373
7.9 IFM Solution to Example 7-5……Page 378
7.10 Stiffness Method Solution to Example 7-5……Page 383
Problems……Page 389
8. Indeterminate Shaft……Page 394
8.1 Equilibrium Equations……Page 395
8.3 Force Deformation Relations……Page 396
8.4 Compatibility Conditions……Page 398
8.5 Integrated Force Method for Shaft……Page 399
8.6 Stiffness Method Analysis for Shaft……Page 402
Problems……Page 424
9. Indeterminate Frame……Page 428
9.1 Integrated Force Method for Frame Analysis……Page 430
9.2 Stiffness Method Solution for the Frame……Page 444
9.3 Portal Frame—Thermal Load……Page 448
9.4 Thermal Analysis of the Frame by IFM……Page 450
9.5 Thermal Analysis of a Frame by the Stiffness Method……Page 452
9.6 Support Settling Analysis for Frame……Page 454
Problems……Page 459
10.1 Stress State in a Plate……Page 464
10.2 Plane Stress State……Page 465
10.3 Stress Transformation Rule……Page 468
10.4 Principal Stresses……Page 471
10.5 Moh’s Circle for Plane Stress……Page 476
10.6 Properties of Principal Stress……Page 479
10.8 Stress in a Spherical Pressure Vessel……Page 486
10.9 Stress in a Cylindrical Pressure Vessel……Page 489
Problems……Page 493
11.1 The Buckling Concept……Page 498
11.2 State of Equilibrium……Page 501
11.3 Perturbation Equation for Column Buckling……Page 502
11.4 Solution of the Buckling Equation……Page 504
11.5 Effective Length of a Column……Page 510
11.6 Secant Formula……Page 511
Interpretation of the Secant Formulas……Page 514
Problems……Page 515
12. Energy Theorems……Page 520
12.1 Basic Engergy Concepts……Page 521
Energy Theorems……Page 532
Problems……Page 573
13. Finite Element Method……Page 578
13.1 Finite Element Model……Page 580
Equations of Integrated Force Method……Page 582
Equations of the Stiffness Method……Page 584
13.2 Matrices of the Finite Element Methods……Page 585
Problems……Page 615
14.1 Method of Redundant Force……Page 618
14.2 Method of Redundant Force for a Beam……Page 628
14.3 Method of Redundant Force for a Shaft……Page 636
14.4 Analysis of a Beam Supported by a Tie Rod……Page 638
14.5 IFM Solution to the Beam Supported by a Tie Rod Problem……Page 641
14.6 Conjugate Beam Concept……Page 645
14.7 Principle of Superposition……Page 649
14.8 Navier’s Table Problem……Page 652
14.9 A Ring Problem……Page 656
14.10 Variables and Analysis Methods……Page 660
Problems……Page 663
Introduction……Page 668
Types of Matrices……Page 670
Matrix Operation……Page 672
Choleski Method……Page 675
Eigenvalue Problem……Page 678
Introduction……Page 682
Base Units……Page 700
Sign Conventions for Equilibrium Equations……Page 704
Appendix 5: Mechanical Properties of Structural Materials……Page 708
Axial Force……Page 710
Shear Force……Page 711
Bending Moment……Page 712
Beam Formulas……Page 713
Appendix 7: Strength of Materials Computer Code……Page 726
Appendix 8: Answers……Page 740
Index……Page 764