Introduction to engineering mechanics : a continuum approach

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Title:

Personal Author:

Rossmann, Jenn Stroud

Publication Information:

Boca Raton, FL : CRC, 2009

Physical Description:

xvii, 472 p. : ill ; 25 cm.

ISBN:

9781420062717

Subject Term:

Mechanics, Applied

Added Author:

Dym, Clive L.

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010193095	TA350 R73 2009	Open Access Book	Book	Searching... Unknown
Searching... SPACE KL Main Library	30000003506007	TA350 R73 2009	Open Access Book	Book	Searching... Unknown

The essence of continuum mechanics -- the internal response of materials to external loading -- is often obscured by the complex mathematics of its formulation. By building gradually from one-dimensional to two- and three-dimensional formulations, this book provides an accessible introduction to the fundamentals of solid and fluid mechanics, covering stress and strain among other key topics. This undergraduate text presents several real-world case studies, such as the St. Francis Dam, to illustrate the mathematical connections between solid and fluid mechanics, with an emphasis on practical applications of these concepts to mechanical, civil, and electrical engineering structures and design.

Author Notes

Jenn Stroud Rossmann, Lafayette College, Easton, Pennsylvania, USA
Clive L. Dym, Harvey Mudd College, Claremont, California, USA

Reviews 1

Choice Review

This book is a welcome addition to the family of resources for undergraduates majoring in mechanical, aerospace, civil, and other allied engineering fields. It offers a unified treatment of solid and fluid mechanics using a continuum mechanics approach. This approach helps students understand both disciplines and prepares them to face problems in interdisciplinary areas such as biomechanical engineering. Rossmann (Lafayette College) and Dym (Harvey Mudd College; Structural Modeling and Analysis, CH, Mar'98, 35-3890; Engineering Design, CH, Feb'95, 32-3326) have taught courses based on this work with good success. The topics on stress, strain, material behavior, basic elasticity equations, bars, torsion, beams, and column buckling relate to solid mechanics. The fluid dynamics coverage includes chapters on motion and deformations, fluid statics, fluid dynamics, and applications. A special chapter devoted to solid dynamics completes the book. All chapters include numerous solved problems and clearly emphasize the common thread of continuum mechanics. An attractive feature is the introduction of case studies that illustrate concepts with practical applications, giving an excellent appreciation of the tools developed in the book. Overall, this lucidly presented work provides a valuable introduction to engineering mechanics using a continuum approach. Summing Up: Highly recommended. Upper-division undergraduates, faculty, and practitioners. R. Kolar Naval Postgraduate School

Preface	p. xv
About the Authors	p. xvii
1 Introduction	p. 1
1.1 A Motivating Example: Remodeling an Underwater Structure	p. 2
1.2 Newton's Laws: The First Principles of Mechanics	p. 4
1.3 Equilibrium	p. 5
1.4 Definition of a Continuum	p. 6
1.5 Mathematical Basics: Scalars and Vectors	p. 9
1.6 Problem Solving	p. 12
1.7 Examples	p. 13
Example 1.1	p. 13
Solution	p. 13
Example 1.2	p. 15
Solution	p. 16
1.8 Problems	p. 17
Notes	p. 18
2 Strain and Stress in One Dimension	p. 19
2.1 Kinematics: Strain	p. 20
2.1.1 Normal Strain	p. 20
2.1.2 Shear Strain	p. 23
2.1.3 Measurement of Strain	p. 24
2.2 The Method of Sections and Stress	p. 25
2.2.1 Normal Stresses	p. 27
2.2.2 Shear Stresses	p. 28
2.3 Stress-Strain Relationships	p. 32
2.4 Equilibrium	p. 36
2.5 Stress in Axially Loaded Bars	p. 37
2.6 Deformation of Axially Loaded Bars	p. 40
2.7 Equilibrium of an Axially Loaded Bar	p. 42
2.8 Indeterminate Bars	p. 43
2.8.1 Force (Flexibility) Method	p. 44
2.8.2 Displacement (Stiffness) Method	p. 46
2.9 Thermal Effects	p. 48
2.10 Saint-Venant's Principle and Stress Concentrations	p. 49
2.11 Strain Energy in One Dimension	p. 51
2.12 A Road Map for Strength of Materials	p. 53
2.13 Examples	p. 55
Example 2.1	p. 55
Solution	p. 55
Example 2.2	p. 56
Solution	p. 57
Example 2.3	p. 57
Solution	p. 58
Example 2.4	p. 59
Solution	p. 59
Example 2.5	p. 60
Solution	p. 61
Example 2.6	p. 62
Solution	p. 62
Example 2.7	p. 64
Solution	p. 65
Example 2.8	p. 66
Solution	p. 66
Example 2.9	p. 67
Solution	p. 68
2.14 Problems	p. 69
Case Study 1 Collapse of the Kansas City Hyatt Regency Walkways	p. 76
Problems	p. 82
Notes	p. 82
3 Strain and Stress in Higher Dimensions	p. 85
3.1 Poisson's Ratio	p. 85
3.2 The Strain Tensor	p. 87
3.3 Strain as Relative Displacement	p. 90
3.4 The Stress Tensor	p. 92
3.5 Generalized Hooke's Law	p. 96
3.6 Limiting Behavior	p. 97
3.7 Properties of Engineering Materials	p. 101
Ferrous Metals	p. 103
Nonferrous Metals	p. 103
Nonmetals	p. 104
3.8 Equilibrium	p. 104
3.8.1 Equilibrium Equations	p. 105
3.8.2 The Two-Dimensional State of Plane Stress	p. 107
3.8.3 The Two-Dimensional State of Plane Strain	p. 108
3.9 Formulating Two-Dimensional Elasticity Problems	p. 109
3.9.1 Equilibrium Expressed in Terms of Displacements	p. 110
3.9.2 Compatibility Expressed in Terms of Stress Functions	p. 111
3.9.3 Some Remaining Pieces of the Puzzle of General Formulations	p. 112
3.10 Examples	p. 114
Example 3.1	p. 114
Solution	p. 115
Example 3.2	p. 116
Solution	p. 116
3.11 Problems	p. 116
Notes	p. 121
4 Applying Strain and Stress in Multiple Dimensions	p. 123
4.1 Torsion	p. 123
4.1.1 Method of Sections	p. 123
4.1.2 Torsional Shear Stress: Angle of Twist and the Torsion Formula	p. 125
4.1.3 Stress Concentrations	p. 130
4.1.4 Transmission of Power by a Shaft	p. 131
4.1.5 Statically Indeterminate Problems	p. 132
4.1.6 Torsion of Inelastic Circular Members	p. 133
4.1.7 Torsion of Solid Noncircular Members	p. 135
4.1.8 Torsion of Thin-Walled Tubes	p. 138
4.2 Pressure Vessels	p. 141
4.3 Transformation of Stress and Strain	p. 145
4.3.1 Transformation of Plane Stress	p. 146
4.3.2 Principal and Maximum Stresses	p. 149
4.3.3 Mohr's Circle for Plane Stress	p. 151
4.3.4 Transformation of Plane Strain	p. 154
4.3.5 Three-Dimensional State of Stress	p. 156
4.4 Failure Prediction Criteria	p. 157
4.4.1 Failure Criteria for Brittle Materials	p. 158
4.4.1.1 Maximum Normal Stress Criterion	p. 158
4.4.1.2 Mohr's Criterion	p. 159
4.4.2 Yield Criteria for Ductile Materials	p. 161
4.4.2.1 Maximum Shearing Stress (Tresca) Criterion	p. 161
4.4.2.2 Von Mises Criterion	p. 162
4.5 Examples	p. 162
Example 4.1	p. 162
Solution	p. 163
Example 4.2	p. 163
Solution	p. 163
Example 4.3	p. 165
Solution	p. 165
Example 4.4	p. 165
Solution	p. 165
Example 4.5	p. 166
Solution	p. 166
Example 4.6	p. 168
Solution	p. 168
Example 4.7	p. 170
Solution	p. 170
Example 4.8	p. 171
Solution	p. 171
Example 4.9	p. 172
Solution	p. 172
Example 4.10	p. 177
Solution	p. 177
Example 4.11	p. 180
Solution	p. 180
4.6 Problems	p. 183
Case Study 2 Pressure Vessel Safety	p. 188
Why Are Pressure Vessels Spheres and Cylinders?	p. 189
Why Do Pressure Vessels Fail?	p. 194
Problems	p. 197
Notes	p. 200
5 Beams	p. 201
5.1 Calculation of Reactions	p. 201
5.2 Method of Sections: Axial Force, Shear, Bending Moment	p. 202
Axial Force in Beams	p. 203
Shear in Beams	p. 203
Bending Moment in Beams	p. 205
5.3 Shear and Bending Moment Diagrams	p. 206
Rules and Regulations for Shear and Bending Moment Diagrams	p. 206
Shear Diagrams	p. 206
Moment Diagrams	p. 207
5.4 Integration Methods for Shear and Bending Moment	p. 207
5.5 Normal Stresses in Beams	p. 210
5.6 Shear Stresses in Beams	p. 214
5.7 Examples	p. 221
Example 5.1	p. 221
Solution	p. 221
Example 5.2	p. 223
Solution	p. 224
Example 5.3	p. 229
Solution	p. 230
Example 5.4	p. 231
Solution	p. 232
Example 5.5	p. 234
Solution	p. 235
Example 5.6	p. 236
Solution	p. 237
5.8 Problems	p. 239
Case Study 3 Physiological Levers and Repairs	p. 241
The Forearm Is Connected to the Elbow Joint	p. 241
Fixing an Intertrochanteric Fracture	p. 245
Problems	p. 247
Notes	p. 248
6 Beam Deflections	p. 251
6.1 Governing Equation	p. 251
6.2 Boundary Conditions	p. 255
6.3 Solution of Deflection Equation by Integration	p. 256
6.4 Singularity Functions	p. 259
6.5 Moment Area Method	p. 260
6.6 Beams with Elastic Supports	p. 264
6.7 Strain Energy for Bent Beams	p. 266
6.8 Flexibility Revisited and Maxwell-Betti Reciprocal Theorem	p. 269
6.9 Examples	p. 273
Example 6.1	p. 273
Solution	p. 273
Example 6.2	p. 275
Solution	p. 275
Example 6.3	p. 278
Solution	p. 278
Example 6.4	p. 281
Solution	p. 282
6.10 Problems	p. 285
Notes	p. 288
7 Instability: Column Buckling	p. 289
7.1 Euler's Formula	p. 289
7.2 Effect of Eccentricity	p. 294
7.3 Examples	p. 298
Example 7.1	p. 298
Solution	p. 298
Example 7.2	p. 300
Solution	p. 301
7.4 Problems	p. 303
Case Study 4 Hartford Civic Arena	p. 304
Notes	p. 307
8 Connecting Solid and Fluid Mechanics	p. 309
8.1 Pressure	p. 310
8.2 Viscosity	p. 311
8.3 Surface Tension	p. 315
8.4 Governing Laws	p. 315
8.5 Motion and Deformation of Fluids	p. 316
8.5.1 Linear Motion and Deformation	p. 316
8.5.2 Angular Motion and Deformation	p. 317
8.5.3 Vorticity	p. 319
8.5.4 Constitutive Equation (Generalized Hooke's Law) for Newtonian Fluids	p. 321
8.6 Examples	p. 322
Example 8.1	p. 322
Solution	p. 323
Example 8.2	p. 324
Solution	p. 324
Example 8.3	p. 325
Solution	p. 326
Example 8.4	p. 327
Solution	p. 327
8.7 Problems	p. 328
Case Study 5 Mechanics of Biomaterials	p. 330
Nonlinearity	p. 332
Composite Materials	p. 333
Viscoelasticity	p. 336
Problems	p. 338
Notes	p. 339
9 Fluid Statics	p. 341
9.1 Local Pressure	p. 341
9.2 Force Due to Pressure	p. 342
9.3 Fluids at Rest	p. 345
9.4 Forces on Submerged Surfaces	p. 348
9.5 Buoyancy	p. 355
9.6 Examples	p. 357
Example 9.1	p. 357
Solution	p. 357
Example 9.2	p. 358
Solution	p. 359
Example 9.3	p. 360
Solution	p. 361
Example 9.4	p. 363
Solution	p. 364
Example 9.5	p. 365
Solution	p. 36
9.7 Problems	p. 368
Case Study 6 St. Francis Dam	p. 373
Problems	p. 375
Notes	p. 376
10 Fluid Dynamics: Governing Equations	p. 377
10.1 Description of Fluid Motion	p. 377
10.2 Equations of Fluid Motion	p. 379
10.3 Integral Equations of Motion	p. 379
10.3.1 Mass Conservation	p. 380
10.3.2 F = ma, or Momentum Conservation	p. 382
10.3.3 Reynolds Transport Theorem	p. 385
10.4 Differential Equations of Motion	p. 386
10.4.1 Continuity, or Mass Conservation	p. 386
10.4.2 F = ma,, or Momentum Conservation	p. 388
10.5 Bernoulli Equation	p. 391
10.6 Examples	p. 392
Example 10.1	p. 392
Solution	p. 393
Example 10.2	p. 394
Solution	p. 395
Example 10.3	p. 396
Solution	p. 397
Example 10.4	p. 398
Solution	p. 399
Example 10.5	p. 402
Solution	p. 402
Example 10.6	p. 404
Solution	p. 405
10.7 Problems	p. 406
Notes	p. 408
11 Fluid Dynamics: Applications	p. 411
11.1 How Do We Classify Fluid Flows?	p. 411
11.2 What's Going on Inside Pipes?	p. 413
11.3 Why Can an Airplane Fly?	p. 417
11.4 Why Does a Curveball Curve?	p. 419
11.5 Problems	p. 423
Notes	p. 426
12 Solid Dynamics: Governing Equations	p. 427
12.1 Continuity, or Mass Conservation	p. 427
12.2 F = ma, or Momentum Conservation	p. 429
12.3 Constitutive Laws: Elasticity	p. 431
Note	p. 433
References	p. 435
Appendix A Second Moments of Area	p. 439
Appendix B A Quick Look at the Del Operator	p. 443
Divergence	p. 444
Physical Interpretation of the Divergence	p. 444
Example	p. 445
Curl	p. 445
Physical Interpretation of the Curl	p. 445
Examples	p. 446
Example 1	p. 446
Example 2	p. 446
Laplacian	p. 447
Appendix C Property Tables	p. 449
Appendix D All the Equations	p. 455
Index	p. 457

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