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Introduction1

Chapter 1．Bending of Long Rectangular Plates to a Cylindrical Surface4

1．Differential Equation for Cylindrical Bending of Plates4

2．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Simply Supported Edges6

3．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Built-in Edges13

4．Cylindrical Bending of Uniformly Loaded Rectangular Plates with Elasti-cally Built-in Edges17

5．The Effect on Stresses and Deflections of Small Displacements of Longi-tudinal Edges in the Plane of the Plate20

6．An Approximate Method of Calculating the Parameter u24

7．Long Uniformly Loaded Rectangular Plates Having a Small Initial Cylin-drical Curvature27

8．Cylindrical Bending of a Plate on an Elastic Foundation30

Chapter 2．Pure Bending of Plates33

9．Slope and Curvature of Slightly Bent Plates33

10．Relations between Bending Moments and Curvature in Pure Bending of Plates37

11．Particular Cases of Pure Bending42

12．Strain Energy in Pure Bending of Plates46

13．Limitations on the Application of the Derived Formulas47

14．Thermal Stresses in Plates with Clamped Edges49

Chapter 3．Symmetrical Bending of Circular Plates51

15．Differential Equation for Symmetrical Bending of Laterally Loaded Cir-cular Plates51

16．Uniformly Loaded Circular Plates54

17．Circular Plate with a Circular Hole at the Center58

18．Circular Plate Concentrically Loaded63

19．Circular Plate Loaded at the Center67

20．Corrections to the Elementary Theory of Symmetrical Bending of Cir-cular Plates72

Chapter 4．Small Deflections of Laterally Loaded Plates79

21．The Differential Equation of the Deflection Surface79

22．Boundary Conditions83

23．Alternate Method of Derivation of the Boundary Conditions88

24．Reduction of the Problem of Bending of a Plate to That of Deflection of a Membrane92

25．Effect of Elastic Constants on the Magnitude of Bending Moments97

26．Exact Theory of Plates98

Chapter 5．Simply Supported Rectangular Plates105

27．Simply Supported Rectangular Plates under Sinusoidal Load105

28．Navier Solution for Simply Supported Rectangular Plates108

29．Further Applications of the Navier Solution111

30．Alternate Solution for Simply Supported and Uniformly Loaded Rectangu-lar Plates113

31．Simply Supported Rectangular Plates under Hydrostatic Pressure124

32．Simply Supported Rectangular Plate under a Load in the Form of a Tri-angular Prism130

33．Partially Loaded Simply Supported Rectangular Plate135

34．Concentrated Load on a Simply Supported Rectangular Plate141

35．Bending Moments in a Simply Supported Rectangular Plate with a Con-centrated Load143

36．Rectangular Plates of Infinite Length with Simply Supported Edges149

37．Bending Moments in Simply Supported Rectangular Plates under a Load Uniformly Distributed over the Area of a Rectangle158

38．Thermal Stresses in Simply Supported Rectangular Plates162

39．The Effect of Transverse Shear Deformation on the Bending of Thin Plates165

40．Rectangular Plates of Variable Thickness173

Chapter 6．Rectangular Plates with Various Edge Conditions180

41．Bending of Rectangular Plates by Moments Distributed along the Edges180

42．Rectangular Plates with Two Opposite Edges Simply Supported and the Other Two Edges Clamped185

43．Rectangular Plates with Three Edges Simply Supported and One Edge Built In192

44．Rectangular Plates with All Edges Built In197

45．Rectangular Plates with One Edge or Two Adjacent Edges Simply Sup-ported and the Other Edges Built In205

46．Rectangular Plates with Two Opposite Edges Simply Supported,the Third Edge Free,and the Fourth Edge Built In or Simply Supported208

47．Rectangular Plates with Three Edges Built In and the Fourth Edge Free211

48．Rectangular Plates with Two Opposite Edges Simply Supported and the Other Two Edges Free or Supported Elastically214

49．Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free218

50．Semi-infinite Rectangular Plates under Uniform Pressure221

51．Semi-infinite Rectangular Plates under Concentrated Loads225

Chapter 7．Continuous Rectangular Plates229

52．Simply Supported Continuous Plates229

53．Approximate Design of Continuous Plates with Equal Spans236

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

55．Flat Slab Having Nine Panels and Slab with Two Edges Free253

56．Effect of a Rigid Connection with Column on Moments of the Flat Slab257

Chapter 8．Plates on Elastic Foundation259

57．Bending Symmetrical with Respect to a Center259

58．Application of Bessel Functions to the Problem of the Circular Plate265

59．Rectangular and Continuous Plates on Elastic Foundation269

60．Plate Carrying Rows of Equidistant Columns276

61．Bending of Plates Resting on a Semi-infinite Elastic Solid278

Chapter 9．Plates of Various Shapes282

62．Equations of Bending of Plates in Polar Coordinates282

63．Circular Plates under a Linearly Varying Load285

64．Circular Plates under a Concentrated Load290

65．Circular Plates Supported at Several Points along the Boundary293

66．Plates in the Form of a Sector295

67．Circular Plates of Nonuniform Thickness298

68．Annular Plates with Linearly Varying Thickness303

69．Circular Plates with Linearly Varying Thickness305

70．Nonlinear Problems in Bending of Circular Plates308

71．Elliptical Plates310

72．Triangular Plates313

73．Skewed Plates318

74．Stress Distribution around Holes319

Chapter 10．Special and Approximate Methods in Theory of Plates325

75．Singularities in Bending of Plates325

76．The Use of Influence Surfaces in the Design of Plates328

77．Influence Functions and Characteristic Functions334

78．The Use of Infinite Integrals and Transforms336

79．Complex Variable Method340

80．Application of the Strain Energy Method in Calculating Deflections342

81．Alternative Procedure in Applying the Strain Energy Method347

82．Various Approximate Methods348

83．Application of Finite Differences Equations to the Bending of Simply Sup-ported Plates351

84．Experimental Methods362

Chapter 11．Bending of Anisotropic Plates364

85．Differential Equation of the Bent Plate364

86．Determination of Rigidities in Various Specific Cases366

87．Application of the Theory to the Calculation of Gridworks369

88．Bending of Rectangular Plates371

89．Bending of Circular and Elliptic Plates376

Chapter 12．Bending of Plates under the Combined Action of Lateral Loads and Forces in the Middle Plane of the Plate378

90．Differential Equation of the Deflection Surface378

91．Rectangular Plate with Simply Supported Edges under the Combined Action of Uniform Lateral Load and Uniform Tension380

92．Application of the Energy Method382

93．Simply Supported Rectangular Plates under the Combined Action of Lateral Loads and of Forces in the Middle Plane of the Plate387

94．Circular Plates under Combined Action of Lateral Load and Tension or Compression391

95．Bending of Plates with a Small Initial Curvature393

Chapter 13．Large Deflections of Plates396

96．Bending of Circular Plates by Moments Uniformly Distributed along the Edge396

97．Approximate Formulas for Uniformly Loaded Circular Plates with Large Deflections400

98．Exact Solution for a Uniformly Loaded Circular Plate with a Clamped Edge404

99．A Simply Supported Circular Plate under Uniform Load408

100．Circular Plates Loaded at the Center412

101．General Equations for Large Deflections of Plates415

102．Large Deflections of Uniformly Loaded Rectangular Plates421

103．Large Deflections of Rectangular Plates with Simply Supported Edges425

Chapter 14．Deformation of Shells without Bending429

104．Definitions and Notation429

105．Shells in the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis433

106．Particular Cases of Shells in the Form of Surfaces of Revolution436

107．Shells of Constant Strength442

108．Displacements in Symmetrically Loaded Shells Having the Form of a Surface of Revolution445

109．Shells in the Form of a Surface of Revolution under Unsymmetrical Loading447

110．Stresses Produced by Wind Pressure449

111．Spherical Shell Supported at Isolated Points453

112．Membrane Theory of Cylindrical Shells457

113．The Use of a Stress Function in Calculating Membrane Forces of Shells461

Chapter 15．General Theory of Cylindrical Shells466

114．A Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis466

115．Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells471

116．Pressure Vessels481

117．Cylindrical Tanks with Uniform Wall Thickness485

118．Cylindrical Tanks with Nonuniform Wall Thickness488

119．Thermal Stresses in Cylindrical Shells497

120．Inextensional Deformation of a Circular Cylindrical Shell501

121．General Case of Deformation of a Cylindrical Shell507

122．Cylindrical Shells with Supported Edges514

123．Deflection of a Portion of a Cylindrical Shell516

124．An Approximate Investigation of the Bending of Cylindrical Shells519

125．The Use of a Strain and Stress Function522

126．Stress Analysis of Cylindrical Roof Shells524

Chapter 16．Shells Having the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis533

127．Equations of Equilibrium533

128．Reduction of the Equations of Equilibrium to Two Differential Equations of the Second Order537

129．Spherical Shell of Constant Thickness540

130．Approximate Methods of Analyzing Stresses in Spherical Shells547

131．Spherical Shells with an Edge Ring555

132．Symmetrical Bending of Shallow Sphcrical Shells558

133．Conical Shells562

134．General Case of Shells Having the Form of a Surface of Revolution566

Name Index569

Subject Index575