Introduction

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

1．Differential Equation for Cylindrical Bending of Plates

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

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

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

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

6．An Approximate Method of Calculating the Parameter u

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

8．Cylindrical Bending of a Plate on an Elastic Foundation

Chapter 2．Pure Bending of Plates

9．Slope and Curvature of Slightly Bent Plates

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

11．Particular Cases of Pure Bending

12．Strain Energy in Pure Bending of Plates

13．Limitations on the Application of the Derived Formulas

14．Thermal Stresses in Plates with Clamped Edges

Chapter 3．Symmetrical Bending of Circular Plates

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

16．Uniformly Loaded Circular Plates

17．Circular Plate with a Circular Hole at the Center

18．Circular Plate Concentrically Loaded

19．Circular Plate Loaded at the Center

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

Chapter 4．Small Deflections of Laterally Loaded Plates

21．The Differential Equation of the Deflection Surface

22．Boundary Conditions

23．Alternate Method of Derivation of the Boundary Conditions

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

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

26．Exact Theory of Plates

Chapter 5．Simply Supported Rectangular Plates

27．Simply Supported Rectangular Plates under Sinusoidal Load

28．Navier Solution for Simply Supported Rectangular Plates

29．Further Applications of the Navier Solution

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

31．Simply Supported Rectangular Plates under Hydrostatic Pressure

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

33．Partially Loaded Simply Supported Rectangular Plate

34．Concentrated Load on a Simply Supported Rectangular Plate

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

36．Rectangular Plates of Infinite Length with Simply Supported Edges

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

38．Thermal Stresses in Simply Supported Rectangular Plates

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

40．Rectangular Plates of Variable Thickness

Chapter 6．Rectangular Plates with Various Edge Conditions

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

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

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

44．Rectangular Plates with All Edges Built In

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

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

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

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

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

50．Semi-infinite Rectangular Plates under Uniform Pressure

51．Semi-infinite Rectangular Plates under Concentrated Loads

Chapter 7．Continuous Rectangular Plates

52．Simply Supported Continuous Plates

53．Approximate Design of Continuous Plates with Equal Spans

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

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

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

Chapter 8．Plates on Elastic Foundation

57．Bending Symmetrical with Respect to a Center

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

59．Rectangular and Continuous Plates on Elastic Foundation

60．Plate Carrying Rows of Equidistant Columns

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

Chapter 9．Plates of Various Shapes

62．Equations of Bending of Plates in Polar Coordinates

63．Circular Plates under a Linearly Varying Load

64．Circular Plates under a Concentrated Load

65．Circular Plates Supported at Several Points along the Boundary

66．Plates in the Form of a Sector

67．Circular Plates of Nonuniform Thickness

68．Annular Plates with Linearly Varying Thickness

69．Circular Plates with Linearly Varying Thickness

70．Nonlinear Problems in Bending of Circular Plates

71．Elliptical Plates

72．Triangular Plates

73．Skewed Plates

74．Stress Distribution around Holes

Chapter 10．Special and Approximate Methods in Theory of Plates

75．Singularities in Bending of Plates

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

77．Influence Functions and Characteristic Functions

78．The Use of Infinite Integrals and Transforms

79．Complex Variable Method

80．Application of the Strain Energy Method in Calculating Deflections

81．Alternative Procedure in Applying the Strain Energy Method

82．Various Approximate Methods

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

84．Experimental Methods

Chapter 11．Bending of Anisotropic Plates

85．Differential Equation of the Bent Plate

86．Determination of Rigidities in Various Specific Cases

87．Application of the Theory to the Calculation of Gridworks

88．Bending of Rectangular Plates

89．Bending of Circular and Elliptic Plates

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

90．Differential Equation of the Deflection Surface

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

92．Application of the Energy Method

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

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

95．Bending of Plates with a Small Initial Curvature

Chapter 13．Large Deflections of Plates

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

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

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

99．A Simply Supported Circular Plate under Uniform Load

100．Circular Plates Loaded at the Center

101．General Equations for Large Deflections of Plates

102．Large Deflections of Uniformly Loaded Rectangular Plates

103．Large Deflections of Rectangular Plates with Simply Supported Edges

Chapter 14．Deformation of Shells without Bending

104．Definitions and Notation

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

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

107．Shells of Constant Strength

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

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

110．Stresses Produced by Wind Pressure

111．Spherical Shell Supported at Isolated Points

112．Membrane Theory of Cylindrical Shells

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

Chapter 15．General Theory of Cylindrical Shells

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

115．Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells

116．Pressure Vessels

117．Cylindrical Tanks with Uniform Wall Thickness

118．Cylindrical Tanks with Nonuniform Wall Thickness

119．Thermal Stresses in Cylindrical Shells

120．Inextensional Deformation of a Circular Cylindrical Shell

121．General Case of Deformation of a Cylindrical Shell

122．Cylindrical Shells with Supported Edges

123．Deflection of a Portion of a Cylindrical Shell

124．An Approximate Investigation of the Bending of Cylindrical Shells

125．The Use of a Strain and Stress Function

126．Stress Analysis of Cylindrical Roof Shells

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

127．Equations of Equilibrium

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

129．Spherical Shell of Constant Thickness

130．Approximate Methods of Analyzing Stresses in Spherical Shells

131．Spherical Shells with an Edge Ring

132．Symmetrical Bending of Shallow Sphcrical Shells

133．Conical Shells

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

Name Index

Subject Index