THEORY OF PLATES AND SHELLSPDF电子书下载

Introduction 1

Chapter 1．Bending of Long Rectangular Plates to a Cylindrical Surface 4

1．Differential Equation for Cylindrical Bending of Plates 4

2．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Simply Supported Edges 6

3．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Built-in Edges 13

4．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Elasti-cally Built-in Edges 17

5．The Effect on Stresses and Deflections of Small Displacements of Longi-tudinal Edges in the Plane of the Plate 20

6．An Approximate Method of Calculating the Parameter u 24

7．Long Uniformly Loaded Rectangular Plates Having a Small Initial Cylin-drical Curvature 27

8．Cylindrical Bending of a Plate on an Elastic Foundation 30

Chapter 2．Pure Bending of Plates 33

9．Slope and Curvature of Slightly Bent Plates 33

10．Relations between Bending Moments and Curvature in Pure Bending of Plates 37

11．Particular Cases of Pure Bending 42

12．Strain Energy in Pure Bending of Plates 46

13．Limitations on the Application of the Derived Formulas 47

14．Thermal Stresses in Plates with Clamped Edges 49

Chapter 3．Symmetrical Bending of Circular Plates 51

15．Differential Equation for Symmetrical Bending of Laterally Loaded Cir-cular Plates 51

16．Uniformly Loaded Circular Plates 54

17．Circular Plate with a Circular Hole at the Center 58

18．Circular Plate Concentrically Loaded 63

19．Circular Plate Loaded at the Center 67

20．Corrections to the Elementary Theory of Symmetrical Bending of Cir-cular Plates 72

Chapter 4．Small Deflections of Laterally Loaded Plates 79

21．The Differential Equation of the Deflection Surface 79

22．Boundary Conditions 83

23．Alternate Method of Derivation of the Boundary Conditions 88

24．Reduction of the Problem of Bending of a Plate to That of Deflection of a Membrane 92

25．Effect of Elastic Constants on the Magnitude of Bending Moments 97

26．Exact Theory of Plates 98

Chapter 5．Simply Supported Rectangular Plates 105

27．Simply Supported Rectangular Plates under Sinusoidal Load 105

28．Navier Solution for Simply Supported Rectangular Plates 108

29．Further Applications of the Navier Solution 111

30．Alternate Solution for Simply Supported and Uniformly Loaded Rectangu-lar Plates 113

31．Simply Supported Rectangular Plates under Hydrostatic Pressure 124

32．Simply Supported Rectangular Plate under a Load in the Form of a Tri-angular Prism 130

33．Partially Loaded Simply Supported Rectangular Plate 135

34．Concentrated Load on a Simply Supported Rectangular Plate 141

35．Bending Moments in a Simply Supported Rectangular Plate with a Con-centrated Load 143

36．Rectangular Plates of Infinite Length with Simply Supported Edges 149

37．Bending Moments in Simply Supported Rectangular Plates under a Load Uniformly Distributed over the Area of a Rectangle 158

38．Thermal Stresses in Simply Supported Rectangular Plates 162

39．The Effect of Transverse Shear Deformation on the Bending of Thin Plates 165

40．Rectangular Plates of Variable Thickness 173

Chapter 6．Rectangular Plates with Various Edge Conditions 180

41．Bending of Rectangular Plates by Moments Distributed along the Edges 180

42．Rectangular Plates with Two Opposite Edges Simply Supported and the Other Two Edges Clamped 185

43．Rectangular Plates with Three Edges Simply Supported and One Edge Built In 192

44．Rectangular Plates with All Edges Built In 197

45．Rectangular Plates with One Edge or Two Adjacent Edges Simply Sup-ported and the Other Edges Built In 205

46．Rectangular Plates with Two Opposite Edges Simply Supported,the Third Edge Free,and the Fourth Edge Built In or Simply Supported 208

47．Rectangular Plates with Three Edges Built In and the Fourth Edge Free 211

48．Rectangular Plates with Two Opposite Edges Simply Supported and the Other Two Edges Free or Supported Elastically 214

49．Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free 218

50．Semi-infinite Rectangular Plates under Uniform Pressure 221

51．Semi-infinite Rectangular Plates under Concentrated Loads 225

Chapter 7．Continuous Rectangular Plates 229

52．Simply Supported Continuous Plates 229

53．Approximate Design of Continuous Plates with Equal Spans 236

54．Bending of Plates Supported by Rows of Equidistant Columns(Flat Slabs) 245

55．Flat Slab Having Nine Panels and Slab with Two Edges Free 253

56．Effect of a Rigid Connection with Column on Moments of the Flat Slab 257

Chapter 8．Plates on Elastic Foundation 259

57．Bending Symmetrical with Respect to a Center 259

58．Application of Bessel Functions to the Problem of the Circular Plate 265

59．Rectangular and Continuous Plates on Elastic Foundation 269

60．Plate Carrying Rows of Equidistant Columns 276

61．Bending of Plates Resting on a Semi-infinite Elastic Solid 278

Chapter 9．Plates of Various Shapes 282

62．Equations of Bending of Plates in Polar Coordinates 282

63．Circular Plates under a Linearly Varying Load 285

64．Circular Plates under a Concentrated Load 290

65．Circular Plates Supported at Several Points along the Boundary 293

66．Plates in the Form of a Sector 295

67．Circular Plates of Nonuniform Thickness 298

68．Annular Plates with Linearly Varying Thickness 303

69．Circular Plates with Linearly Varying Thickness 305

70．Nonlinear Problems in Bending of Circular Plates 308

71．Elliptical Plates 310

72．Triangular Plates 313

73．Skewed Plates 318

74．Stress Distribution around Holes 319

Chapter 10．Special and Approximate Methods in Theory of Plates 325

75．Singularities in Bending of Plates 325

76．The Use of Influence Surfaces in the Design of Plates 328

77．Influence Functions and Characteristic Functions 334

78．The Use of Infinite Integrals and Transforms 336

79．Complex Variable Method 340

80．Application of the Strain Energy Method in Calculating Deflections 342

81．Alternative Procedure in Applying the Strain Energy Method 347

82．Various Approximate Methods 348

83．Application of Finite Differences Equations to the Bending of Simply Sup-ported Plates 351

84．Experimental Methods 362

Chapter 11．Bending of Anisotropic Plates 364

85．Differential Equation of the Bent Plate 364

86．Determination of Rigidities in Various Specific Cases 366

87．Application of the Theory to the Calculation of Gridworks 369

88．Bending of Rectangular Plates 371

89．Bending of Circular and Elliptic Plates 376

Chapter 12．Bending of Plates under the Combined Action of Lateral Loads and Forces in the Middle Plane of the Plate 378

90．Differential Equation of the Deflection Surface 378

91．Rectangular Plate with Simply Supported Edges under the Combined Action of Uniform Lateral Load and Uniform Tension 380

92．Application of the Energy Method 382

93．Simply Supported Rectangular Plates under the Combined Action of Lateral Loads and of Forces in the Middle Plane of the Plate 387

94．Circular Plates under Combined Action of Lateral Load and Tension or Compression 391

95．Bending of Plates with a Small Initial Curvature 393

Chapter 13．Large Deflections of Plates 396

96．Bending of Circular Plates by Moments Uniformly Distributed along the Edge 396

97．Approximate Formulas for Uniformly Loaded Circular Plates with Large Deflections 400

98．Exact Solution for a Uniformly Loaded Circular Plate with a Clamped Edge 404

99．A Simply Supported Circular Plate under Uniform Load 408

100．Circular Plates Loaded at the Center 412

101．General Equations for Large Deflections of Plates 415

102．Large Deflections of Uniformly Loaded Rectangular Plates 421

103．Large Deflections of Rectangular Plates with Simply Supported Edges 425

Chapter 14．Deformation of Shells without Bending 429

104．Definitions and Notation 429

105．Shells in the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis 433

106．Particular Cases of Shells in the Form of Surfaces of Revolution 436

107．Shells of Constant Strength 442

108．Displacements in Symmetrically Loaded Shells Having the Form of a Surface of Revolution 445

109．Shells in the Form of a Surface of Revolution under Unsymmetrical Loading 447

110．Stresses Produced by Wind Pressure 449

111．Spherical Shell Supported at Isolated Points 453

112．Membrane Theory of Cylindrical Shells 457

113．The Use of a Stress Function in Calculating Membrane Forces of Shells 461

Chapter 15．General Theory of Cylindrical Shells 466

114．A Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis 466

115．Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells 471

116．Pressure Vessels 481

117．Cylindrical Tanks with Uniform Wall Thickness 485

118．Cylindrical Tanks with Nonuniform Wall Thickness 488

119．Thermal Stresses in Cylindrical Shells 497

120．Inextensional Deformation of a Circular Cylindrical Shell 501

121．General Case of Deformation of a Cylindrical Shell 507

122．Cylindrical Shells with Supported Edges 514

123．Deflection of a Portion of a Cylindrical Shell 516

124．An Approximate Investigation of the Bending of Cylindrical Shells 519

125．The Use of a Strain and Stress Function 522

126．Stress Analysis of Cylindrical Roof Shells 524

Chapter 16．Shells Having the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis 533

127．Equations of Equilibrium 533

128．Reduction of the Equations of Equilibrium to Two Differential Equations of the Second Order 537

129．Spherical Shell of Constant Thickness 540

130．Approximate Methods of Analyzing Stresses in Spherical Shells 547

131．Spherical Shells with an Edge Ring 555

132．Symmetrical Bending of Shallow Sphcrical Shells 558

133．Conical Shells 562

134．General Case of Shells Having the Form of a Surface of Revolution 566

Name Index 569

Subject Index 575