The Analysis of Stress and Deformation

1. Basic Principles of Stress and Strain
1.1 Introduction
1.2 Definition of Stress
1.3 Properties of Stress
1.4 Properties of Planar Stress Systems
1.5 Displacements and Strain in A Continuum
1.6 Relations Between Stress and Strains
1.7 Strain Energy

2. Equations of the Theory of Elasticity
2.1 Introduction
2.2 Equations of Elasticity :

Plane Stress and Plane Strain
2.3 A Unique Theorem
2.4 Equations of Equilibrium in Terms of Displacements
2.5 The Equations of Hydrodynamics and Elasticity
2.6 St. Venant’s Principle

3. Applications to Beams
3.1 Introduction
3.2 Extension of A Bar
3.3 Pure Bending of Prismatic Bars
3.4 Cantilever Beam Carrying A Concentrated Load
3.5 The Technical Theory of Bending
3.6 Composite Beams
3.7 Deflection of Transversly Loaded Beams
3.8 Statically Indeterminate Systems
3.9 Beam on An Elastic Foundation
3.10 Footing on An Elastic Foundation
3.11 Thin-Walled Tubes
3.12 Moving Load on A Beam on An Elastic Foundation

4. Elastic Instability
4.1 An Example of Elastic

Instability
4.2 Buckling of ASimply-Supported Column
4.3 Column with Initial Curvature
4.4 Column With Eccentric Loading
4.5 Considerations in The Design of Columns
4.6 Combined Axial and Lateral Loading of Slender Members
4.7 Rayleigh-Ritz Method
4.8 Other Types of BucklingProblems

5. Applications to AxiallySymmetrical Problems, Curved Beams and Stress Concentrations

5.1 Axially Symmetrical Problems
5.2 Thick-Walled Cylinders
5.3 Rotating Disc of Uniform Thickness
5.4 Bending of Curved Beams
5.5 The Technical Theory of Bending for Curved Bars
5.6 Stress Concentrations
5.7 Contact Stress

6. Applications to Torsion

Problems
6.1 Torsion of Prismatical Bars
6.2 Solution for A Circular Bar
6.3 Curved Circular Bars
6.4 Bars of Noncircular Cross Section
6.5 Membrane Analogy
6.6 Torsion of Tubular Sections
6.7 Restraint of Warping

7. Applications to Plates and Shells
7.1 The Bending of Plates
7.2 Bending Moments and Twisting Moments
7.3 Transverse Shear Forces
7.4 Equations of Equilibrium
7.5 Boundary Conditions for A Plate
7.6 Circular Plates
7.7 The Load Carrying Action of A Shell
7.8 Cylindrical Shell

8. Applications to Viscous and Plastic Behavior of Materials
8.1 Deviations from Linear Elastic Behavior
8.2 Simplified Stress-Strain Relations
8.3 The Yield Surface in Stress Space
8.4 Yield Hinge in A Beam
8.5 Plastic Collapse of Beams and Frames
8.6 Failures Due to Plastic Straining
8.7 Plastic Torsion
8.8 Inelastic Buckling of Columns
8.9 Plastic Extension, Drawing, and Rolling

9. Elastic Wave Propagation
9.1 The Wave Equation
9.2 General Equations of Motion
9.3 Displacement Potential Functions
9.4 Plane Waves in An Infinite Continuum
9.5 Waves in Nonhomogeneous Media
9.6 Sufrace Waves
9.7 Longitudinal waves in Rods
9.8 Vibration of Beams

10. NUmerical Methods
10.1 Solutions of Problems by Numerical Methosd
10.2 Numerical Solution of Column Buckling
10.3 Calculations with Finite Differences
10.4 Relaxation Method
10.5 Moment Distribution
10.6 Use of Digital Computers

App 1 Stresses and Strain in Tensor Notation

App 2 The Measurement of Strain

App 3 Photoelastic Strain Measurement

App 4 Variational Methods

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