Strength of Materials: A Unified Theory

Surya Patnaik, Dale Hopkins9780750674027, 0750674024

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 3
Title Page……Page 5
Copyright……Page 6
Contents……Page 7
Preface……Page 11
Strength of Materials……Page 14
Determinate Analysis……Page 15
Indeterminate Analysis……Page 16
Stiffness Method……Page 17
Other Methods……Page 18
Unified Theory of Strength of Materials……Page 20
Historical Sketch……Page 21
References……Page 23
1. Introduction……Page 25
1.1 Systems of Units……Page 28
1.2 Response Variables……Page 31
1.3 Sign Conventions……Page 39
1.4 Load-Carrying Capacity of Members……Page 40
1.5 Material Properties……Page 52
1.6 Stress-Strain Law……Page 54
1.7 Assumptions of Strength of Materials……Page 61
1.8 Equilibrium Equations……Page 66
Three-Legged Table Problem……Page 68
Navier’s Table Problem……Page 71
Problems……Page 74
2.1 Bar Member……Page 79
2.2 Stress in a Bar Member……Page 92
2.3 Displacement in a Bar Member……Page 96
2.5 Strain in a Bar Member……Page 98
2.6 Definition of a Truss Problem……Page 100
2.7 Nodal Displacement……Page 109
2.8 Initial Deformation in a Determinate Truss……Page 120
2.9 Thermal Effect in a Truss……Page 123
2.10 Settling of Support……Page 125
2.11 Theory of Determinate Analysis……Page 128
2.12 Definition of Determinate Truss……Page 137
Problems……Page 146
3. Simple Beam……Page 153
3.1 Analysis for Internal Forces……Page 155
3.2 Relationship between Bending Moment, Shear Force, and Load……Page 173
3.3 Flexure Formula……Page 177
3.4 Shear Stress Formula……Page 183
3.5 Displacement in a Beam……Page 188
3.6 Thermal Displacement in a Beam……Page 203
3.7 Settling of Supports……Page 207
3.8 Shear Center……Page 208
3.9 Built-up Beam an Interface Shear Force……Page 221
3.10 Composite Beams……Page 226
Problems……Page 233
4. Determinate Shaft……Page 241
4.1 Analysis of Internal Torque……Page 242
4.2 Torsion Formula……Page 246
4.3 Deformation Analysis……Page 248
4.4 Power Transmission through a Circular Shaft……Page 257
Problems……Page 260
5. Simple Frames……Page 263
Problems……Page 283
6. Indeterminate Truss……Page 287
6.1 Equilibrium Equations……Page 290
6.2 Deformation Displacement Relations……Page 292
6.4 Compatibility Conditions……Page 293
6.5 Initial Deformation and Support Settling……Page 294
6.7 Response Variables of Analysis……Page 297
6.9 Method of Displacements or the Displacement Method……Page 298
6.10 Integrated Force Method……Page 299
Procedures for Analysis……Page 300
Theory of Dual Integrated Force Method……Page 313
Theory of Stiffness Method……Page 320
Stiffness Method for Thermal Load……Page 324
First Thermal Load……Page 325
Second Thermal Load……Page 326
Stiffness Method for Support Settling……Page 327
Problems……Page 329
7. Indeterminate Beam……Page 335
7.1 Internal Forces in a Beam……Page 339
7.2 IFM Analysis for Indeterminate Beam……Page 341
7.3 Flexibility Matrix……Page 353
7.4 Stiffness Method Analysis for Indeterminate Beam……Page 361
7.5 Stiffness Method for Mechanical Load……Page 363
7.6 Stiffness Solution for Thermal Load……Page 365
7.7 Stiffness Solution for Support Settling……Page 367
7.8 Stiffness Method Solution to the Propped Beam……Page 374
7.9 IFM Solution to Example 7-5……Page 379
7.10 Stiffness Method Solution to Example 7-5……Page 384
Problems……Page 390
8. Indeterminate Shaft……Page 395
8.1 Equilibrium Equations……Page 396
8.3 Force Deformation Relations……Page 397
8.4 Compatibility Conditions……Page 399
8.5 Integrated Force Method for Shaft……Page 400
8.6 Stiffness Method Analysis for Shaft……Page 403
Problems……Page 425
9. Indeterminate Frame……Page 429
9.1 Integrated Force Method for Frame Analysis……Page 431
9.2 Stiffness Method Solution for the Frame……Page 445
9.3 Portal Frame—Thermal Load……Page 449
9.4 Thermal Analysis of the Frame by IFM……Page 451
9.5 Thermal Analysis of a Frame by the Stiffness Method……Page 453
9.6 Support Settling Analysis for Frame……Page 455
Problems……Page 460
10.1 Stress State in a Plate……Page 465
10.2 Plane Stress State……Page 466
10.3 Stress Transformation Rule……Page 469
10.4 Principal Stresses……Page 472
10.5 Moh’s Circle for Plane Stress……Page 477
10.6 Properties of Principal Stress……Page 480
10.8 Stress in a Spherical Pressure Vessel……Page 487
10.9 Stress in a Cylindrical Pressure Vessel……Page 490
Problems……Page 494
11.1 The Buckling Concept……Page 499
11.2 State of Equilibrium……Page 502
11.3 Perturbation Equation for Column Buckling……Page 503
11.4 Solution of the Buckling Equation……Page 505
11.5 Effective Length of a Column……Page 511
11.6 Secant Formula……Page 512
Interpretation of the Secant Formulas……Page 515
Problems……Page 516
12. Energy Theorems……Page 521
12.1 Basic Engergy Concepts……Page 522
Energy Theorems……Page 533
Problems……Page 574
13. Finite Element Method……Page 579
13.1 Finite Element Model……Page 581
Equations of Integrated Force Method……Page 583
Equations of the Stiffness Method……Page 585
13.2 Matrices of the Finite Element Methods……Page 586
Problems……Page 616
14.1 Method of Redundant Force……Page 619
14.2 Method of Redundant Force for a Beam……Page 629
14.3 Method of Redundant Force for a Shaft……Page 637
14.4 Analysis of a Beam Supported by a Tie Rod……Page 639
14.5 IFM Solution to the Beam Supported by a Tie Rod Problem……Page 642
14.6 Conjugate Beam Concept……Page 646
14.7 Principle of Superposition……Page 650
14.8 Navier’s Table Problem……Page 653
14.9 A Ring Problem……Page 657
14.10 Variables and Analysis Methods……Page 661
Problems……Page 664
Introduction……Page 669
Types of Matrices……Page 671
Matrix Operation……Page 673
Choleski Method……Page 676
Eigenvalue Problem……Page 679
Introduction……Page 683
Base Units……Page 701
Sign Conventions for Equilibrium Equations……Page 705
Appendix 5: Mechanical Properties of Structural Materials……Page 709
Axial Force……Page 711
Shear Force……Page 712
Bending Moment……Page 713
Beam Formulas……Page 714
Appendix 7: Strength of Materials Computer Code……Page 727
Appendix 8: Answers……Page 741
Index……Page 765