Stresses in Beams, Plates, and Shells, Third Edition

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ISBN: 9781439802700 | 143980270X
Cover: Hardcover
Copyright: 8/26/2009

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Noted for its practical, student-friendly approach to graduate-level mechanics, this volume is considered one of the top references-for students or professioals-on the subject of elasticity and stress in construction. The author presents many examples and applications to review and support several foundational concepts. The more advanced concepts in elasticity and stress are analyzed and introduced gradually, accompanied by even more examples and engineering applications in addition to numerous illustrations.Chapter problems are carefully arranged from the basic to the more challenging. Newer computer methods, including FEA and computational/equation-solving software, are covered in the book, and in many cases, classical approaches and numerical/computer approaches are both presented.

Preface	p. xiii
Acknowledgments	p. xvii
List of Symbols	p. xix
*Fundamentals
Basic Concepts	p. 3
Introduction	p. 3
Methods of Analysis	p. 4
Conditions of Equilibrium	p. 5
Stress Defined	p. 7
Components of Stress	p. 8
Sign Convention	p. 9
Internal-Force Resultants	p. 9
Differential Equations of Equilibrium	p. 12
Transformation of Stress	p. 14
Mohr's Circle for Stress	p. 16
Strain Defined	p. 18
Components of Strain	p. 20
Conditions of Compatibility	p. 21
Large Strains	p. 22
Transformation of Strain	p. 23
Engineering Materials	p. 24
Stress-Strain Diagrams	p. 25
Hooke's Law, Poisson's Ratio	p. 26
Rational Design Procedure	p. 30
Factor of Safety	p. 31
Problem Formulation and Solutions	p. 32
Significant Digits	p. 33
Computational Tools	p. 33
References	p. 34
Problems	p. 34
Stresses in Simple Structural Members	p. 41
Introduction	p. 41
Types of Structures	p. 42
Axially Loaded Members	p. 45
Stress Concentration Factors	p. 48
Torsion of Circular Bars	p. 49
Shear Stress	p. 50
Angle of Twist	p. 51
Stresses in Beams	p. 52
Normal Stress	p. 53
Shear Stress	p. 54
Shear Flow	p. 55
Deflection of Beams by Integration	p. 56
Beam Deflections by Superposition	p. 61
Thin-Walled Pressure Vessels	p. 63
Yield and Fracture Criteria	p. 65
Maximum Principal Stress Theory	p. 65
Coulomb-Mohr Theory	p. 66
Maximum Shear Stress Theory	p. 67
Maximum Distortion Energy Theory	p. 68
A Typical Case of Combined Loadings	p. 68
Strain Energy	p. 71
CastigUano's Theorem	p. 73
Statically Indeterminate Structures	p. 76
References	p. 77
Problems	p. 77
Plates
Elements of Plate-Bending Theory	p. 87
Introduction	p. 87
Historical Development of Plate and Shell Theory	p. 88
General Behavior of Plates	p. 89
Strain-Curvature Relations	p. 91
Mohrs Circle of Curjvature	p. 93
Stresses and Stress Resultants	p. 94
Equations for Transformation of Moment	p. 97
Variation of Stress within a Plate	p. 98
The Governing Equation for Deflection of Plates	p. 101
Reduction of Plate-Bending Problem to That of Deflection of a Membrane	p. 102
Boundary Conditions	p. 103
Exact Theory of Plates	p. 106
Methods for Solution of Plate Deflections	p. 109
Strain Energy of Plates	p. 116
Energy Methods in Theory of Plates	p. 117
The Principle of Virtual Work	p. 117
The Principle of Minimum Potential Energy	p. 118
The Ritz Method	p. 119
*Natural Frequencies of Plates by the Energy Method	p. 119
References	p. 121
Problems	p. 122
Circular Plates	p. 127
Introduction	p. 127
Basic Relations in Polar Coordinates	p. 127
The Axisymmetrical Bending	p. 132
Equations of Equilibrium for AxisymmetricallyLoaded Circular Plates	p. 133
Uniformly Loaded Circular Plates	p. 135
*Effect of Shear on the Plate Deflection	p. 139
Local Stresses at the Point of Application of a Concentrated Load	p. 140
Circular Plates under a Concentrated Load at the Center	p. 141
A Short Catalog of Solutions	p. 144
Annular Plates with Simply Supported Outer Edges	p. 144
Deflection and Stress by Superposition	p. 152
Design Tables for Annular Plates	p. 152
The Ritz Method Applied to Bending of Circular Plates	p. 155
Asymmetrical Bending of Circular Plates	p. 161
*Deflection by the Reciprocity Theorem	p. 163
References	p. 164
Problems	p. 165
Rectangular Plates	p. 171
Introduction	p. 171
Navier's Solution for Simply Supported Rectangular Plates	p. 171
Simply Supported Rectangular Plates under Various Loadings	p. 174
Lévy's Solution for Rectangular Plates	p. 180
Simply Supported Rectangular Plate underUniform Loading	p. 183
Lévy's Method Applied to Rectangular Plates under Nonuniform Loading	p. 191
Rectangular Plates under ^Distributed Edge Moments	p. 195
Method of Superposition Applied to Bending ofRectangular Plates	p. 199
*The Strip Method	p. 202
*Simply Supported Continuous Rectangular Plates	p. 206
*Rectangular Plates Supported by Intermediate Columns	p. 209
Rectangular Plates on Elastric Foundation	p. 212
Simply Supported Plates	p. 213
Plates with Arbitrary Boundary Conditions	p. 213
The Ritz Method Applied to Bending of Rectangular Plates	p. 215
References	p. 222
Problems	p. 222
Plates of Various Geometrical Fprms	p. 229
Introduction	p. 229
*Method of Images	p. 229
Equilateral Triangular Plate with Simply Supported Edges	p. 232
Equilateral Triangtllar Plate under Uniform Moment M₀ along its Boundary	p. 233
Equilateral Triangular Plate under Uniform Load p₀	p. 234
Elliptical Plates	p. 235
Uniformly Loaded Elliptic Plate with Clamped Edge	p. 235
Uniformly Loaded Elliptic Plate with SimplySupporred Edge	p. 237
Sector-Shaped Plates	p. 237
*Stress Concentration around Holes in a Plate	p. 239
References	p. 243
Problems	p. 243
Numerical Methods	p. 247
Introduction	p. 247
Finite Differences	p. 248
Solution of the Finite Difference Equations	p. 252
Load Representation	p. 254
*Plates with Curved Boundaries	p. 264
*The Polar Mesh	p. 268
*The Triangular Mesh	p. 269
The Finite Element Method	p. 272
Properties of a Finite Element	p. 273
Displacement Matrix	p. 274
Strain, Stress, and Elasticity Matrices	p. 274
Formulation of the Finite Element Method	p. 276
Beam Element	p. 279
Methods of Assemblage of the [k]e's	p. 280
Triangular Finite Element	p. 282
Displacement Function	p. 283
The Stiffness Matrix	p. 285
External Nodal Forces	p. 285
Rectangular Finite Element	p. 287
Displacement Function	p. 287
The Stiffness Matrix	p. 288
External Nodal Forces	p. 291
References	p. 293
Problems	p. 294
Anisotropic Plates	p. 299
Introduction	p. 299
Basic Relationships	p. 300
Determination of Rigidities	p. 302
	p. 303
Application of Navier's Method	p. 305
Application of Lévy's Method	p. 307
Application of the Finite Difference Method	p. 308
Elliptic and Circular Orthotropic Plates	p. 310
Deflection by the Energy Method	p. 311
*Plates of Isotropic Multilayers	p. 315
The Finite Element Solution	p. 316
A Typical Layered Orthotropic Plate	p. 319
Laminated Composite Plates	p. 322
References	p. 327
Problems	p. 328
Plates under Combined Lateral and In-Plane Loads	p. 331
Introduction	p. 331
Governing Equation for the Deflection Surface	p. 331
Buckling of Plates	p. 335
Application of the Energy Method	p. 339
*The Finite Difference Solution	p. 345
Plates with Small Initial Curvature	p. 349
*Bending to a Cylindrical Surface	p. 351
References	p. 355
Problems	p. 355
Large Deflections of Plates	p. 359
Introduction	p. 359
Plate Behavior When Deflections Are Large	p. 360
Comparison of Small- and Large-Deflection Theories	p. 361
An Approximate Method for the Circular Plate	p. 361
Exact Solution for the Circular Plate Problem	p. 363
General Equations for Large Deflections of Plates	p. 364
Deflections by the Energy Method	p. 367
The Finite Element Solution	p. 371
Rectangular Finite Element373
References	p. 374
Problems	p. 375
Thermal Stresses in Plates	p. 377
Introduction	p. 377
Stress, Strain, and Displacement Relations	p. 378
Stress Resultants	p. 379
The Governing Differential Equations	p. 380
Simply Supported Rectangular Plate Subject to an Arbitrary Temperature Distribution	p. 382
Simply Supported Rectangular Plate with Temperature Distribution Varying over the Thickness	p. 383
Analogy between Thermal and Isothermal PlateProblems	p. 385
Plates with Clamped Edges	p. 385
Plates with Simply Supported or Free Edges	p. 386
Axisymmetrically Heated Circular Plates	p. 388
References	p. 391
Problems	p. 392
Shells
Membrane Stresses in Shells	p. 397
Introduction	p. 397
Theories and General Behavior of Shells	p. 397
Load Resistance Action of a Shell	p. 399
Geometry of Shells of Revolution	p. 401
Symmetrically Loaded Shells of Revolution	p. 402
Some Typical Cases of Shells: of Revolution	p. 405
Spherical Shell	p. 406
Conical Shell	p. 406
Circular Cylindrical Shell	p. 408
Axially Symmetric Deformation	p. 417
Asymmetrically Loaded Shells of Revolution	p. 419
*Shells of Revolution under Wind Loading	p. 421
Cylindrical Shells of General'shape	p. 424
*Folded Structures	p. 428
*Shells of General Form	p. 429
*Breakdown of Elastic Action in Shells	p. 433
References	p. 435
Problems	p. 435
Bending Stresses in Shells	p. 443
Introduction	p. 443
Shell Stress Resultants	p. 443
Force, Moment, and Displacement Relations	p. 445
Compound Stresses in a Shell	p. 448
Strain Energy in the Bending and Stretching of Shells	p. 448
Axisym metrically Loaded Circular Cylindrical Shells	p. 449
A Typical Case of the Axisym metricallyLoaded Cylindrical Shell	p. 453
Shells of Revolution under Axisym metrical Loads	p. 457
Conical Shells	p. 459
Spherical Shells	p. 459
Cylindrical Shells	p. 460
Governing Equations for Axisym metrical Displacements	p. 460
Spherical Shells under Axisym metrical Load	p. 462
Comparison of Bending and Membrane Stresses	p. 465
*Simplified Theory of Spherical Shells underAxisymmetrical Load	p. 466
The Finite Element Representations of Shells of General Shape	p. 470
The Finite Element Solution of Axisym metrically Loaded Shells	p. 471
References	p. 474
Problems	p. 475
Applications to Pipes, Tanks, and Pressure Vessels	p. 477
Introduction	p. 477
Pipes Subjected to Edge Forces and Moments	p. 478
Long Pipes	p. 478
Short Pipes	p. 480
Reinforced Cylinders	p. 482
Cylinders with Collars That Prohibit Deflection	p. 482
Cylinders with Collars That Resist Deflection	p. 483
Cylinders with Closed Ends	p. 484
Cylindrical Tanks	p. 484
Thermal Stresses in Cylinders	p. 488
Uniform Temperature Distribution	p. 488
Radial Temperature Gradient	p. 489
Thermal Stresses in Compound Cylinders	p. 491
Discontinuity Stresses in Pressure Vessels	p. 494
Cylindrical Vessel with Hemispherical Heads	p. 495
Cylindrical Vessel with Ellipsoidal Heads	p. 498
Cylindrical Vessel with Flat Heads	p. 499
*Design Formulas for Conventional Pressure Vessels	p. 500
References	p. 502
Problems	p. 503
Cylindrical Shells under General Loads	p. 507
Introduction	p. 507
Differential Equations of Equilibrium	p. 508
Kinematic Relationships	p. 509
The Governing Equations for Deflections	p. 512
*Approximate Relations	p. 513
A Typical Case of Asymmetrical Loading	p. 514
Curved Circular Panels	p. 518
*A Simple Theory of Bending of Curved Circular Panels	p. 520
*Curved Circular Panels with Ends Simply Supported and Straight Edges Free	p. 523
Inextensional Deformations	p. 527
A Typical Layered Orthotropic Cylindrical Shell	p. 531
Laminated Composite Cylindrical Shells	p. 535
*Symmetrical Buckling under Uniform Axial Pressure	p. 537
Nonsymmetrical Buckling under Uniform Axial Compression	p. 540
References	p. 544
Problems	p. 544
Appendices
Fourier Series Expansions	p. 547
Single Fourier Series	p. 547
Half-Range Expansions	p. 549
Double Fourier Series	p. 551
Reference	p. 552
Tables	p. 553
Conversion Factors: SI Units to U.S. Customary Units	p. 553
SI Unit Prefixes	p. 554
Typical Properties for Some Common Materials	p. 555
Properties of Common Areas	p. 577
Beam Deflection and Slopes	p. 558
Restrained Beam Reactions and Deflections	p. 560
Answers to Selected Problems	p. 563
Index	p. 56
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Stresses in Beams, Plates, and Shells, Third Edition

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