Synopsis
1 General Properties of Stress Systems in Shells.- 1.1 Definitions.- 1.1.1 Definition of a Shell.- 1.1.2 Stress Resultants.- 1.1.3 Membrane Forces.- 1.2 Membrane Forces in Arbitrary Directions.- 1.2.1 Rectangular Coordinates.- 1.2.2 Mohr's Circle.- 1.2.3 Oblique Coordinates and Skew Forces.- 1.3 Transformation of Moments.- 2 Direct Stresses in Shells of Revolution.- 2.1 General Differential Equations.- 2.1.1 Geometrical Relations.- 2.1.2 Equilibrium of the Shell Element.- 2.2 Loads Having Axial Symmetry.- 2.2.1 Differential Equations.- 2.2.2 Solution for some Typical Cases.- 2.2.2.1 Spherical Dome.- 2.2.2.2 Boiler End.- 2.2.2.3 Pointed Shells.- 2.2.2.4 Toroidal Shell.- 2.2.2.5 Tanks.- 2.2.2.6 Conical Shell.- 2.3 Shells of Constant Strength.- 2.3.1 Drop-shaped Tank.- 2.3.2 Dome of Constant Strength.- 2.4 Loads without Axial Symmetry.- 2.4.1 General Equations.- 2.4.2 Spherical Shell.- 2.4.2.1 General Solution.- 2.4.2.2 Distributed Load.- 2.4.2.3 Edge Load.- 2.4.2.4 Concentrated Forces and Couples.- 2.4.3 Conical Shell.- 2.4.3.1 General Solution.- 2.4.3.2 Homogeneous Solution.- 2.4.4 Solution for Shells of Arbitrary Shape.- 2.4.4.1 Solution by an Auxiliary Variable.- 2.4.4.2 Solution by Numerical Integration.- 2.4.5 Shell Formed as a One-sheet Hyperboloid.- 2.5 Deformations.- 2.5.1 Strains and Displacements.- 2.5.2 Inextensional Deformation.- 2.5.2.1 Differential Equation.- 2.5.2.2 Finite Solution for the Spherical Shell.- 2.5.2.3 Solution for Arbitrary Shape of the Meridian.- 2.5.3 Inhomogeneous Solution.- 2.5.3.1 General Solution.- 2.5.3.2 Axially Symmetric Deformation.- 2.5.4 Toroidal Shell.- 2.5.5 Strain Energy.- 2.5.6 Statically Indeterminate Structures.- 3 Direct Stresses in Cylindrical Shells.- 3.1 Statically Determinate Problems.- 3.1.1 General Theory.- 3.1.1.1 Differential Equations.- 3.1.1.2 General Solution.- 3.1.1.3 Homogeneous Solution.- 3.1.2 Tubes and Pipes.- 3.1.2.1 Circular Cylinder.- 3.1.2.2 Elliptic Cylinder.- 3.1.2.3 Inclined Cylinder.- 3.1.2.4 Fourier Solutions for the Circular Cylinder.- 3.1.3 Barrel-Vaults.- 3.1.3.1 Circular Cylinder.- 3.1.3.2 Elliptic Cylinder.- 3.1.3.3 Cycloidal Cylinder and Related Shapes.- 3.1.3.4 Special Cylinders°.- 3.1.3.5 Critical Remarks.- 3.2 Deformations.- 3.2.1 General Theory.- 3.2.1.1 Differential Equations.- 3.2.1.2 Solution in General Terms.- 3.2.2 Application to Pipes and Barrel Vaults.- 3.2.2.1 Circular Shell.- 3.2.2.2 Barrel Vaults of Other than Circular Profile.- 3.2.2.3 Fourier Series Solutions for the Circular Cylinder.- 3.3 Statically Indeterminate Structures.- 3.4 Polygonal Domes.- 3.4.1 Regular Dome under Regular Load.- 3.4.2 Regular Dome under Arbitrary Load.- 3.4.3 Non-regular Domes.- 3.5 Folded Structures.- 3.5.1 Uniform Load.- 3.5.2 Fourier Series Form of Solution.- 3.5.3 Examples.- 3.5.4 Limitations of the Theory.- 4 Direct Stresses in Shells of Arbitrary Shape.- 4.1 Conditions of Equilibrium.- 4.2 Elliptic Problems.- 4.2.1 Paraboloid of Revolution, Triangular Shell.- 4 2 2 Elliptic Paraboloid.- 4.2.3 Solution by Relaxation Method.- 4.3 Hyperbolic Problems.- 4.3.1 Hyperbolic Paraboloid, Edges Parallel to Generators.- 4.3.2 Hyperbolic Paraboloid, Edges Bisecting the Directions of the Generators.- 4.4 Membrane Forces in Affine Shells.- 4.4.1. General Theory.- 4.4.2 Applications.- 4.4.2.1 Vertical Stretching of a Shell of Revolution.- 4.4.2.2 Horizontal Stretching of a Shell of Revolution.- 4.4.2.3 The General Ellipsoid.- 4.4.2.4 Polygonal Domes.- 4.4.2.5 Cylindrical Shells.- 5 Bending of Circular Cylindrical Shells.- 5.1 Differential Equations.- 5.1.1 Equilibrium.- 5.1.2 Deformation.- 5.1 2 1 Exact Relations.- 5.1.2.2 Approximate Relations.- 5.1.2.3 Secondary Stresses in Membrane Theory.- 5.1.3 Differential Equations for the Displacements.- 5.2 Solution of the Inhomogeneous Problem.- 5.3 Loads Applied to the Edges x = const.- 5.3.1 General Solution.- 5.3.2 Semi-infinite Cylinder.- 5.3.3 Cooling Tower.- 5.3.4 Simplified Theory.- 5.4 Loads Applied to the Edges ? =
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