كتاب Stresses in Beams, Plates, And Shells - 3rd Edition - Ansel C. Ugural
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 كتاب Stresses in Beams, Plates, And Shells - 3rd Edition - Ansel C. Ugural

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عدد المساهمات : 14528
التقييم : 23592
تاريخ التسجيل : 01/07/2009
العمر : 29
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: كتاب Stresses in Beams, Plates, And Shells - 3rd Edition - Ansel C. Ugural   الإثنين 04 سبتمبر 2017, 10:18 am

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Stresses in Beams, Plates, And Shells - 3rd Edition
Ansel C. Ugural


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Contents
Preface xiii
Acknowledgments xvii
List of Symbols xix
PART I *FundAmenTAls
1 Basic Concepts 3
1 1 Introduction 3
1 2 Methods of Analysis 4
1 3 Conditions of Equilibrium 5
1 4 Stress Defned 7
1 4 1 Components of Stress 8
1 4 2 Sign Convention 9
1 5 Internal-Force Resultants 9
1 6 Di?erential Equations of Equilibrium 12
1 7 Transformation of Stress 14
1 7 1 Mohr’s Circle for Stress 16
1 8 Strain Defned 18
1 9 Components of Strain 20
1 9 1 Conditions of Compatibility 21
1 10 Large Strains 22
1 11 Transformation of Strain 23
1 12 Engineering Materials 24
1 12 1 Stress–Strain Diagrams 25
1 13 Hooke’s Law, Poisson’s Ratio 26
1 14 Rational Design Procedure 30
1 15 Factor of Safety 31
1 16 Problem Formulation and Solutions 32
1 16 1 Signifcant Digits 33vi ? Contents
1 16 2 Computational Tools 33
References 34
Problems 34
2 Stresses in Simple Structural Members 41
2 1 Introduction 41
2 2 Types of Structures 42
2 3 Axially Loaded Members 45
2 4 Stress Concentration Factors 48
2 5 Torsion of Circular Bars 49
2 5 1 Shear Stress 50
2 5 2 Angle of Twist 51
2 6 Stresses in Beams 52
2 6 1 Normal Stress 53
2 6 2 Shear Stress 54
2 6 3 Shear Flow 55
2 7 De?ection of Beams by Integration 56
2 8 Beam De?ections by Superposition 61
2 9 Tin-Walled Pressure Vessels 63
2 10 Yield and Fracture Criteria 65
2 10 1 Maximum Principal Stress Teory 65
2 10 2 Coulomb-Mohr Teory 66
2 10 3 Maximum Shear Stress Teory 67
2 10 4 Maximum Distortion Energy Teory 68
2 10 5 A Typical Case of Combined Loadings 68
2 11 Strain Energy 71
2 12 Castigliano’s Teorem 73
2 12 1 Statically Indeterminate Structures 76
References 77
Problems 77
PART II PlATes
3 Elements of Plate-Bending Teory 87
3 1 Introduction 87
3 2 Historical Development of Plate and Shell Teory 88
3 3 General Behavior of Plates 89
3 4 Strain-Curvature Relations 91
3 4 1 Mohr’s Circle of Curvature 93
3 5 Stresses and Stress Resultants 94
3 6 Equations for Transformation of Moment 97
3 7 Variation of Stress within a Plate 98
3 8 Te Governing Equation for De?ection of Plates 101Contents ? vii
3 8 1 Reduction of Plate-Bending Problem to
Tat of De?ection of a Membrane 102
3 9 Boundary Conditions 103
3 10 Exact Teory of Plates 106
3 11 Methods for Solution of Plate De?ections 109
3 12 Strain Energy of Plates 116
3 13 Energy Methods in Teory of Plates 117
3 13 1 Te Principle of Virtual Work 117
3 13 2 Te Principle of Minimum Potential Energy 118
3 13 3 Te Ritz Method 119
3 14 *Natural Frequencies of Plates by the Energy Method 119
References 121
Problems 122
4 Circular Plates 127
4 1 Introduction 127
4 2 Basic Relations in Polar Coordinates 127
4 3 Te Axisymmetrical Bending 132
4 4 Equations of Equilibrium for Axisymmetrically
Loaded Circular Plates 133
4 5 Uniformly Loaded Circular Plates 135
4 6 *E?ect of Shear on the Plate De?ection 139
4 7 Local Stresses at the Point of Application of
a Concentrated Load 140
4 8 Circular Plates under a Concentrated Load at the Center 141
4 8 1 A Short Catalog of Solutions 144
4 9 Annular Plates with Simply Supported Outer Edges 144
4 10 De?ection and Stress by Superposition 152
4 10 1 Design Tables for Annular Plates 152
4 11 Te Ritz Method Applied to Bending of Circular Plates 155
4 12 Asymmetrical Bending of Circular Plates 161
4 13 *De?ection by the Reciprocity Teorem 163
References 164
Problems 165
5 Rectangular Plates 171
5 1 Introduction 171
5 2 Navier’s Solution for Simply Supported Rectangular Plates 171
5 3 Simply Supported Rectangular Plates under Various Loadings 174
5 4 Lévy’s Solution for Rectangular Plates 180
5 4 1 Simply Supported Rectangular Plate under
Uniform Loading 183
5 5 Lévy’s Method Applied to Rectangular Plates under
Nonuniform Loading 191viii ? Contents
5 6 Rectangular Plates under Distributed Edge Moments 195
5 7 Method of Superposition Applied to Bending of
Rectangular Plates 199
5 8 *Te Strip Method 202
5 9 *Simply Supported Continuous Rectangular Plates 206
5 10 *Rectangular Plates Supported by Intermediate Columns 209
5 11 Rectangular Plates on Elastic Foundation 212
5 11 1 Simply Supported Plates 213
5 11 2 Plates with Arbitrary Boundary Conditions 213
5 12 Te Ritz Method Applied to Bending of Rectangular Plates 215
References 222
Problems 222
6 Plates of Various Geometrical Forms 229
6 1 Introduction 229
6 2 *Method of Images 229
6 3 Equilateral Triangular Plate with Simply Supported Edges 232
6 3 1 Equilateral Triangular Plate under Uniform Moment
M0
along Its Boundary 233
6 3 2 Equilateral Triangular Plate under Uniform Load p0 234
6 4 Elliptical Plates 235
6 4 1 Uniformly Loaded Elliptic Plate with Clamped Edge 235
6 4 2 Uniformly Loaded Elliptic Plate with Simply
Supported Edge 237
6 5 Sector-Shaped Plates 237
6 6 *Stress Concentration around Holes in a Plate 239
References 243
Problems 243
7 Numerical Methods 247
7 1 Introduction 247
7 2 Finite Di?erences 248
7 3 Solution of the Finite Di?erence Equations 252
7 3 1 Load Representation 254
7 4 *Plates with Curved Boundaries 264
7 5 *Te Polar Mesh 268
7 6 *Te Triangular Mesh 269
7 7 Te Finite Element Method 272
7 8 Properties of a Finite Element 273
7 8 1 Displacement Matrix 274
7 8 2 Strain, Stress, and Elasticity Matrices 274
7 9 Formulation of the Finite Element Method 276
7 10 Beam Element 279
7 10 1 Methods of Assemblage of the [k]e’s 280Contents ? ix
7 11 Triangular Finite Element 282
7 11 1 Displacement Function 283
7 11 2 Te Sti?ness Matrix 285
7 11 3 External Nodal Forces 285
7 12 Rectangular Finite Element 287
7 12 1 Displacement Function 287
7 12 2 Te Sti?ness Matrix 288
7 12 3 External Nodal Forces 291
References 293
Problems 294
8 Anisotropic Plates 299
8 1 Introduction 299
8 2 Basic Relationships 300
8 3 Determination of Rigidities 302
8 4 Rectangular Orthotropic Plates 303
8 4 1 Application of Navier’s Method 305
8 4 2 Application of Lévy’s Method 307
8 4 3 Application of the Finite Di?erence Method 308
8 5 Elliptic and Circular Orthotropic Plates 310
8 6 De?ection by the Energy Method 311
8 7 *Plates of Isotropic Multilayers 315
8 8 Te Finite Element Solution 316
8 9 A Typical Layered Orthotropic Plate 319
8 10 Laminated Composite Plates 322
References 327
Problems 328
9 Plates under Combined Lateral and In-Plane Loads 331
9 1 Introduction 331
9 2 Governing Equation for the De?ection Surface 331
9 3 Buckling of Plates 335
9 4 Application of the Energy Method 339
9 5 *Te Finite Di?erence Solution 345
9 6 Plates with Small Initial Curvature 349
9 7 *Bending to a Cylindrical Surface 351
References 355
Problems 355
10 Large De?ections of Plates 359
10 1 Introduction 359
10 2 Plate Behavior When De?ections Are Large 360
10 3 Comparison of Small- and Large-De?ection Teories 361
10 3 1 An Approximate Method for the Circular Plate 361
10 3 2 Exact Solution for the Circular Plate Problem 363x ? Contents
10 4 General Equations for Large De?ections of Plates 364
10 5 De?ections by the Energy Method 367
10 6 Te Finite Element Solution 371
10 6 1 Rectangular Finite Element 373
References 374
Problems 375
11 Termal Stresses in Plates 377
11 1 Introduction 377
11 2 Stress, Strain, and Displacement Relations 378
11 3 Stress Resultants 379
11 4 Te Governing Di?erential Equations 380
11 5 Simply Supported Rectangular Plate Subject to an Arbitrary
Temperature Distribution 382
11 6 Simply Supported Rectangular Plate with Temperature
Distribution Varying over the Tickness 383
11 7 Analogy between Termal and Isothermal Plate
Problems 385
11 7 1 Plates with Clamped Edges 385
11 7 2 Plates with Simply Supported or Free Edges 386
11 8 Axisymmetrically Heated Circular Plates 388
References 391
Problems 392
PART III shells
12 Membrane Stresses in Shells 397
12 1 Introduction 397
12 2 Teories and General Behavior of Shells 397
12 3 Load Resistance Action of a Shell 399
12 4 Geometry of Shells of Revolution 401
12 5 Symmetrically Loaded Shells of Revolution 402
12 6 Some Typical Cases of Shells of Revolution 405
12 6 1 Spherical Shell 406
12 6 2 Conical Shell 406
12 6 3 Circular Cylindrical Shell 408
12 7 Axially Symmetric Deformation 417
12 8 Asymmetrically Loaded Shells of Revolution 419
12 9 *Shells of Revolution under Wind Loading 421
12 10 Cylindrical Shells of General Shape 424
12 11 *Folded Structures 428
12 12 *Shells of General Form 429
12 13 *Breakdown of Elastic Action in Shells 433Contents ? xi
References 435
Problems 435
13 Bending Stresses in Shells 443
13 1 Introduction 443
13 2 Shell Stress Resultants 443
13 3 Force, Moment, and Displacement Relations 445
13 4 Compound Stresses in a Shell 448
13 5 Strain Energy in the Bending and Stretching of Shells 448
13 6 Axisymmetrically Loaded Circular Cylindrical Shells 449
13 7 A Typical Case of the Axisymmetrically
Loaded Cylindrical Shell 453
13 8 Shells of Revolution under Axisymmetrical Loads 457
13 8 1 Conical Shells 459
13 8 2 Spherical Shells 459
13 8 3 Cylindrical Shells 460
13 9 Governing Equations for Axisymmetrical Displacements 460
13 10 Spherical Shells under Axisymmetrical Load 462
13 11 Comparison of Bending and Membrane Stresses 465
13 12 *Simplifed Teory of Spherical Shells under
Axisymmetrical Load 466
13 13 Te Finite Element Representations of Shells of General Shape 470
13 14 Te Finite Element Solution of Axisymmetrically Loaded Shells 471
References 474
Problems 475
14 Applications to Pipes, Tanks, and Pressure Vessels 477
14 1 Introduction 477
14 2 Pipes Subjected to Edge Forces and Moments 478
14 2 1 Long Pipes 478
14 2 2 Short Pipes 480
14 3 Reinforced Cylinders 482
14 3 1 Cylinders with Collars Tat Prohibit De?ection 482
14 3 2 Cylinders with Collars Tat Resist De?ection 483
14 3 3 Cylinders with Closed Ends 484
14 4 Cylindrical Tanks 484
14 5 Termal Stresses in Cylinders 488
14 5 1 Uniform Temperature Distribution 488
14 5 2 Radial Temperature Gradient 489
14 6 Termal Stresses in Compound Cylinders 491
14 7 Discontinuity Stresses in Pressure Vessels 494
14 8 Cylindrical Vessel with Hemispherical Heads 495
14 9 Cylindrical Vessel with Ellipsoidal Heads 498xii ? Contents
14 10 Cylindrical Vessel with Flat Heads 499
14 11 *Design Formulas for Conventional Pressure Vessels 500
References 502
Problems 503
15 Cylindrical Shells under General Loads 507
15 1 Introduction 507
15 2 Di?erential Equations of Equilibrium 508
15 3 Kinematic Relationships 509
15 4 Te Governing Equations for De?ections 512
15 5 *Approximate Relations 513
15 6 A Typical Case of Asymmetrical Loading 514
15 7 Curved Circular Panels 518
15 8 *A Simple Teory of Bending of Curved Circular Panels 520
15 9 *Curved Circular Panels with Ends Simply Supported and
Straight Edges Free 523
15 10 Inextensional Deformations 527
15 11 A Typical Layered Orthotropic Cylindrical Shell 531
15 12 Laminated Composite Cylindrical Shells 535
15 13 *Symmetrical Buckling under Uniform Axial Pressure 537
15 14 Nonsymmetrical Buckling under Uniform Axial Compression 540
References 544
Problems 544
APPendICes
A Fourier Series Expansions 547
A 1 Single Fourier Series 547
A 2 Half-Range Expansions 549
A 3 Double Fourier Series 551
Reference 552
B Tables 553
B 1 Conversion Factors: SI Units to U S Customary Units 553
B 2 SI Unit Prefxes 554
B 3 Typical Properties for Some Common Materials 555
B 4 Properties of Common Areas 557
B 5 Beam De?ection and Slopes 558
B 6 Restrained Beam Reactions and De?ections 560
Answers to Selected Problems 563
Index 


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