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 |  موضوع: كتاب Advanced mechanics of materials and applied elasticity Fifth Edition الأربعاء 05 يوليو 2017, 1:10 am | |
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Advanced mechanics of materials and applied elasticity Fifth Edition
Ansel C. Ugural, Saul K. Fenster
ويتناول الموضوعات الأتية :
Contents
Preface xii
Acknowledgments xiv
About the Authors xv
List of Symbols xvi
Chapter 1 Analysis of Stress 1
1.1 Introduction 1
1.2 Scope of Treatment 3
1.3 Analysis and Design 5
1.4 Conditions of Equilibrium 7
1.5 Definition and Components of Stress 9
1.6 Internal Force-Resultant and Stress Relations 13
1.7 Stresses on Inclined Sections 17
1.8 Variation of Stress within a Body 19
1.9 Plane-Stress Transformation 22
1.10 Principal Stresses and Maximum In-Plane Shear Stress 26
1.11 Mohr’s Circle for Two-Dimensional Stress 28
1.12 Three-Dimensional Stress Transformation 33
1.13 Principal Stresses in Three Dimensions 36
1.14 Normal and Shear Stresses on an Oblique Plane 40
1.15 Mohr’s Circles in Three Dimensions 43
1.16 Boundary Conditions in Terms of Surface Forces 47
1.17 Indicial Notation 48
References 49
Problems 49
Chapter 2 Strain and Material Properties 65
2.1 Introduction 65
2.2 Deformation 66
2.3 Strain Defined 67
2.4 Equations of Compatibility 72
v2.5 State of Strain at a Point 73
2.6 Engineering Materials 80
2.7 Stress–Strain Diagrams 82
2.8 Elastic versus Plastic Behavior 86
2.9 Hooke’s Law and Poisson’s Ratio 88
2.10 Generalized Hooke’s Law 91
2.11 Hooke’s Law for Orthotropic Materials 94
2.12 Measurement of Strain: Strain Rosette 97
2.13 Strain Energy 101
2.14 Strain Energy in Common Structural Members 104
2.15 Components of Strain Energy 106
2.16 Saint-Venant’s Principle 108
References 110
Problems 111
Chapter 3 Problems in Elasticity 124
3.1 Introduction 124
3.2 Fundamental Principles of Analysis 125
Part A—Formulation and Methods of Solution 126
3.3 Plane Strain Problems 126
3.4 Plane Stress Problems 128
3.5 Comparison of Two-Dimensional Isotropic Problems 131
3.6 Airy’s Stress Function 132
3.7 Solution of Elasticity Problems 133
3.8 Thermal Stresses 138
3.9 Basic Relations in Polar Coordinates 142
Part B—Stress Concentrations 147
3.10 Stresses Due to Concentrated Loads 147
3.11 Stress Distribution Near Concentrated Load Acting on a Beam 151
3.12 Stress Concentration Factors 153
3.13 Contact Stresses 159
3.14 Spherical and Cylindrical Contacts 160
3.15 Contact Stress Distribution 163
3.16 General Contact 167
References 170
Problems 171
Chapter 4 Failure Criteria 181
4.1 Introduction 181
4.2 Failure 181
4.3 Failure by Yielding 182
4.4 Failure by Fracture 184
4.5 Yield and Fracture Criteria 187
4.6 Maximum Shearing Stress Theory 188
4.7 Maximum Distortion Energy Theory 189
vi Contents4.8 Octahedral Shearing Stress Theory 190
4.9 Comparison of the Yielding Theories 193
4.10 Maximum Principal Stress Theory 195
4.11 Mohr’s Theory 195
4.12 Coulomb–Mohr Theory 196
4.13 Fracture Mechanics 200
4.14 Fracture Toughness 203
4.15 Failure Criteria for Metal Fatigue 206
4.16 Impact or Dynamic Loads 212
4.17 Dynamic and Thermal Effects 215
References 217
Problems 218
Chapter 5 Bending of Beams 226
5.1 Introduction 226
Part A—Exact Solutions 227
5.2 Pure Bending of Beams of Symmetrical Cross Section 227
5.3 Pure Bending of Beams of Asymmetrical Cross Section 230
5.4 Bending of a Cantilever of Narrow Section 235
5.5 Bending of a Simply Supported Narrow Beam 238
Part B—Approximate Solutions 240
5.6 Elementary Theory of Bending 240
5.7 Normal and Shear Stresses 244
5.8 Effect of Transverse Normal Stress 249
5.9 Composite Beams 250
5.10 Shear Center 256
5.11 Statically Indeterminate Systems 262
5.12 Energy Method for Deflections 264
Part C—Curved Beams 266
5.13 Elasticity Theory 266
5.14 Curved Beam Formula 269
5.15 Comparison of the Results of Various Theories 273
5.16 Combined Tangential and Normal Stresses 276
References 280
Problems 280
Chapter 6 Torsion of Prismatic Bars 292
6.1 Introduction 292
6.2 Elementary Theory of Torsion of Circular Bars 293
6.3 Stresses on Inclined Planes 298
6.4 General Solution of the Torsion Problem 300
6.5 Prandtl’s Stress Function 302
6.6 Prandtl’s Membrane Analogy 310
6.7 Torsion of Narrow Rectangular Cross Section 315
6.8 Torsion of Multiply Connected Thin-Walled Sections 317
Contents vii6.9 Fluid Flow Analogy and Stress Concentration 321
6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section 323
6.11 Curved Circular Bars: Helical Springs 327
References 330
Problems 330
Chapter 7 Numerical Methods 337
7.1 Introduction 337
Part A—Finite Difference Method 338
7.2 Finite Differences 338
7.3 Finite Difference Equations 341
7.4 Curved Boundaries 343
7.5 Boundary Conditions 346
Part B—Finite Element Method 350
7.6 Fundamentals 350
7.7 The Bar Element 352
7.8 Arbitrarily Oriented Bar Element 354
7.9 Axial Force Equation 357
7.10 Force-Displacement Relations for a Truss 359
7.11 Beam Element 366
7.12 Properties of Two-Dimensional Elements 372
7.13 General Formulation of the Finite Element Method 374
7.14 Triangular Finite Element 379
7.15 Case Studies in Plane Stress 386
7.16 Computational Tools 394
References 395
Problems 396
Chapter 8 Axisymmetrically Loaded Members 407
8.1 Introduction 407
8.2 Thick-Walled Cylinders 408
8.3 Maximum Tangential Stress 414
8.4 Application of Failure Theories 415
8.5 Compound Cylinders: Press or Shrink Fits 416
8.6 Rotating Disks of Constant Thickness 419
8.7 Design of Disk Flywheels 422
8.8 Rotating Disks of Variable Thickness 426
8.9 Rotating Disks of Uniform Stress 429
8.10 Thermal Stresses in Thin Disks 431
8.11 Thermal Stresses in Long Circular Cylinders 432
8.12 Finite Element Solution 436
8.13 Axisymmetric Element 437
References 441
Problems 442
viii ContentsChapter 9 Beams on Elastic Foundations 448
9.1 Introduction 448
9.2 General Theory 448
9.3 Infinite Beams 449
9.4 Semi-Infinite Beams 454
9.5 Finite Beams 457
9.6 Classification of Beams 458
9.7 Beams Supported by Equally Spaced Elastic Elements 458
9.8 Simplified Solutions for Relatively Stiff Beams 460
9.9 Solution by Finite Differences 461
9.10 Applications 464
References 466
Problems 466
Chapter 10 Applications of Energy Methods 469
10.1 Introduction 469
10.2 Work Done in Deformation 470
10.3 Reciprocity Theorem 471
10.4 Castigliano’s Theorem 472
10.5 Unit- or Dummy-Load Method 479
10.6 Crotti–Engesser Theorem 481
10.7 Statically Indeterminate Systems 483
10.8 Principle of Virtual Work 486
10.9 Principle of Minimum Potential Energy 487
10.10 Deflections by Trigonometric Series 489
10.11 Rayleigh–Ritz Method 493
References 496
Problems 496
Chapter 11 Stability of Columns 505
11.1 Introduction 505
11.2 Critical Load 505
11.3 Buckling of Pinned-End Columns 507
11.4 Deflection Response of Columns 509
11.5 Columns with Different End Conditions 511
11.6 Critical Stress: Classification of Columns 513
11.7 Allowable Stress 517
11.8 Imperfections in Columns 519
11.9 Eccentrically Loaded Columns: Secant Formula 520
11.10 Energy Methods Applied to Buckling 522
11.11 Solution by Finite Differences 529
11.12 Finite Difference Solution for Unevenly Spaced Nodes 534
References 536
Problems 536
Contents ixChapter 12 Plastic Behavior of Materials 545
12.1 Introduction 545
12.2 Plastic Deformation 546
12.3 Idealized Stress–Strain Diagrams 546
12.4 Instability in Simple Tension 549
12.5 Plastic Axial Deformation and Residual Stress 551
12.6 Plastic Defection of Beams 553
12.7 Analysis of Perfectly Plastic Beams 556
12.8 Collapse Load of Structures: Limit Design 565
12.9 Elastic–Plastic Torsion of Circular Shafts 569
12.10 Plastic Torsion: Membrane Analogy 573
12.11 Elastic–Plastic Stresses in Rotating Disks 575
12.12 Plastic Stress–Strain Relations 578
12.13 Plastic Stress–Strain Increment Relations 583
12.14 Stresses in Perfectly Plastic Thick-Walled Cylinders 586
References 590
Problems 590
Chapter 13 Plates and Shells 598
13.1 Introduction 598
Part A—Bending of Thin Plates 598
13.2 Basic Assumptions 598
13.3 Strain–Curvature Relations 599
13.4 Stress, Curvature, and Moment Relations 601
13.5 Governing Equations of Plate Deflection 603
13.6 Boundary Conditions 605
13.7 Simply Supported Rectangular Plates 607
13.8 Axisymmetrically Loaded Circular Plates 610
13.9 Deflections of Rectangular Plates by the Strain-Energy Method 613
13.10 Finite Element Solution 615
Part B—Membrane Stresses in Thin Shells 618
13.11 Theories and Behavior of Shells 618
13.12 Simple Membrane Action 618
13.13 Symmetrically Loaded Shells of Revolution 620
13.14 Some Common Cases of Shells of Revolution 622
13.15 Thermal Stresses in Compound Cylinders 626
13.16 Cylindrical Shells of General Shape 628
References 631
Problems 631
Appendix A Problem Formulation and Solution 637
x ContentsAppendix B Solution of the Stress Cubic Equation 640
B.1 Principal Stresses 640
B.2 Direction Cosines 641
Appendix C Moments of Composite Areas 645
C.1 Centroid 645
C.2 Moments of Inertia 648
C.3 Parallel-Axis Theorem 649
C.4 Principal Moments of Inertia 652
Appendix D Tables and Charts 659
D.1 Average Properties of Common Engineering Materials 660
D.2 Conversion Factors: SI Units to U.S. Customary Units 662
D.3 SI Unit Prefixes 662
D.4 Deflections and Slopes of Beams 663
D.5 Reactions Deflections of Statically Indeterminate Beams 664
D.6 Stress Concentration Factors for Bars and Shafts with Fillets,
Grooves, and Holes 665
Answers to Selected Problems 669
Index 67
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