1 Introduction 2
1-1 Engineering and the Mechanics of Materials 4
1-2 Units and Numbers 5
International System of Units 5
U.S.Customary Units 5
Use of Numbers 6
1-3 Review of Statics 6
Free-Body Diagrams 6
Equilibrium 8
Structures 10
CONTENTS 11
About the Authors 11
Preface 13
Centroids 15
Distributcd Forces 17
Problems 21
2 Measures of Stress and Strain 28
2-1 Stresses 30
Traction,Normal Stress,and Shear Stress 30
Average Stresses 31
2-2 Strains 39
Extensional Strain 39
Shear Strain 41
Chapter Summary 45
Problems 46
3 Axially Loaded Bars 60
3-1 Stresses in Prismatic Bars 62
Stresses on Perpendicular Planes 62
Stresses on Oblique Planes 68
3-2 Strains in Prismatic Bars 72
Axial Strain andModulus ofElasticity 72
Lateral Strain and Poisson s Ratio 73
3-3 Statically Indeterminate Problems 81
Example 82
Flexibility and Stiffness Methods 83
3-4 Nonprismatic Bars and Distributed Loads 91
Bars with Gradually Varying Cross Sections 91
Distributed Axial Loads 93
3-5 Thermal Strains 100
3-6 Material Behavior 105
Axial Force Tests 105
Other Aspects of Material Behavior 110
3-7 Design Issues 112
Allowable Stress 113
Other Design Considerations 113
Chapter Summary 114
Problems 117
4 Torsion 136
4-1 Pure Shear Stress 138
State of Stress 138
Shear Modulus 138
Stresses on Oblique Planes 139
4-2 Torsion of Prismatic Circular Bars 141
Stresses and Strains 141
Polar Moment of Inertia 144
Positive Directions of the Torque and Angle of Twist 146
4-3 Statically Indeterminate Problems 149
4-4 Nonprismatic Bars and Distributed Loads 150
Bars with Gradually Varying Cross Sections 150
Distributed Torsional Loads 153
4-5 Torsiotn of an Elastic-Perfectly Plastic Circular Bar 156
4-6 Torsion of Thin-Walled Tubes 160
Stress 160
Angle of Twist 163
Cross Sections 167
4-7 Design Issues 167
Allowable Stress 168
Chapter Summary 171
Problems 174
5 States of Stress 186
5-1 Components of Stress 188
5-2 Transformations of Plane Stress 191
Coordinate Transformations 192
Maximum and Minimum Stresses 197
Constructing the Circle 206
5-3 Mohr s Circle for Plane Stress 206
Why Mohr s Circle Works 207
Determining Principal Stresses and the Maximum In-PlaneShear Stress 208
5-4 Principal Stresses in Three Dimensions 217
General State of Stress 218
Triaxial Stress 219
5-5 Design IssuesPressure Vessels 221
Spherical Vessels 221
Cylindrical Vessels 223
Allowable Stress 227
5-6 Tetrahedron Argument 228
Determining the Traction 228
Determining the Normal and Shear Stresses 230
Chapter Summary 233
Problems 236
6 States of Strain 248
6-1 Components of Strain 250
6-2 Transformations of Plane Strain 252
Strain Gauge Rosette 254
Maximum and Minimum Strains 257
6-3 Mohr s Circle for Plane Strain 264
Constructing the Circle 265
Determining Principal Strains and the Maximum In-Plane Shear Strain 266
6-4 Stress-Strain Relations 270
Linearly Elastic Materials 270
lsotropic Materials 271
Chapter Summary 279
Problems 284
7 Internal Forces and Moments in Beams 292
7-1 Axial Force,Shear Force,and Bending Moment 294
7-2 Shear Force and Bending Moment Diagrams 298
7-3 Equations Relating Distributed Load,Shear Force,and Bending Moment305 Chapter Summary 314
Problems 315
8 Stresses in Beams 322
8-1 Distribution of the Stress 324
Normal Stress 324
Geometry ofDeformation 325
Relation between Normal Stress and Bending Moment 328
Beams Subiected to ArbitraryLoads 330
8-2 Design Issues 338
Cross Sections 338
Allowable Stress 340
8-3 Composite Beams 343
8-4 Elastic-Perfectly Plastic Beams 347
8-5 Unsymmetric Cross Sections 355
Moment Exerted about a Principal Axis 355
Moment Exerted about an Arbitrary Axis 358
Shear Stress 362
8-6 Distribution of the Average Stress 363
Shear Formula 363
Rectangular Cross Section 366
8-7 Thin-Walled Cross Sections 371
8-8 Shear Center 377
Chapter Summary 385
Problems 390
9 Deflections of Beams 404
Differential Equation 406
9-1 Determination of the Deflection 406
Boundary Conditions 408
9-2 Statically Indeterminate Beams 414
Difierential Equation 419
9-3 Deflections Using the Fourth-Order Equation 419
Boundary Conditions 420
9-4 Method of Superposition 424
Chapter Summary 429
Problems 430
10 Buckling of Columns 438
10-1 Euler Buckling Load 440
10-2 Other End Conditions 447
Analysis of the Deflection 447
Effective Length 458
10-3 Eccentric Loads 461
Analysis of the Deflection 461
Secant Formula 464
Chapter Summary 467
Problems 469
11 Energy Methods 476
11-1 Work and Energy 478
Work 478
Strain Energy 480
Applications 482
11-2 Castigliano s Second Theorem 489
Derivation 489
Applications 491
Chapter Summary 496
Problems 498
12 Criteria for Failure and Fracture 502
12-1 Failure 504
Overloads 504
Repeated Loads 512
12-2 Stress Concentrations 520
Axially Loaded Bars 520
Torsion 521
Bending 524
12-3 Fracture 527
Overloads and Fast Crack Growth 528
Repeated Loads and Slow Crack Growth 535
Chapter Summary 539
Problems 542
Appendices 549
A Results from Mathematics 549
B Material Properties 555
C Centroids and Moments of Inertia 559
C-1 Centroids of Areas 559
C-2 Composite Areas 563
C-3 Moments of Inertia of Areas 566
C-4 Parallel Axis Theorems 570
C-5 Rotated and Principal Axes 577
Problems 583
D Properties of Areas 589
E Deflections and Slopes of Prismatic Beams 593
F Isotropic Stress-Strain Relations 599
G Answers to Even-Numbered Problems 605
Index 623