1  Force Systems

  1.1  Introduction

  1.2  Types of Force Distributions

  1.3  Closure

2  Stress

  2.1  Introduction

  2.2  Stress Notation

  2.3  Transformation Formulations for Stress

  2.4  The Stress Tensor Is Symmetric

  2.5  Evaluation of Principal Stress Tensor Invariants

  2.6  Plane Stress

  2.7  Mohr's Circle

  2.8  Threedimensional Mohr's Circle

  2.9  Summary

3  Strain

  3.1  Introduction

  3.2  Small Domain Viewpoint

  3.3  Small Deformation Restriction

  3.4  Rigidbody Rotation and Pure Deformation of an Element

  3.5  Physical Interpretation of Strain Terms

  3.6  Transformation Equations for Strain

  3.7  Equations of Compatibility

  3.8  A Note on Simply and Multiply Connected Bodies

  3.9  Closure

4  Stressstrain Relations

  4.1  Introduction

  4.2  The Tensile Test

  4.3  Strainhardening

  4.4  Other Properties Pertaining to the Tensile Test

  4.5  Idealized Onedimensional Stressstrain Laws

  4.6  Generalized Hooke's Law

5  Basic Equations of Elasticity

  5.1  Introduction

  5.2  Equations of the Theory of Elasticity

  5.3  Boundaryvalue Problems

  5.4  Method of Analysis

  5.5  St. Venant's Principle

  5.6  Uniqueness Condition

  5.7  Prismatic Bar Hanging by Its Own Weight

  5.8  Closure

6  Problems in Plane Strain and Plane Stress from the Theory of Elasticity

  6.1  Introduction

  6.2  Airy's Function

  6.3  Problems in Cylindrical Coordinates

  6.4  Axiallysymmetric Stress Distributions

  6.5  Discussion of Basic Equations

  6.6  Planestress Solutions:Plate with a Hole

  6.7  The Case of the Curved Beam

  6.8  Closure

7  Plasticity

  7.1  Introduction

  7.2  Comparison of Elasticity and Plasticity

  7.3  Models for Plastic Deformation

  7.4  The Yield Locus and Surface

  7.5  Yield Criteria

  7.6  Tresca Criterion

  7.7  Von Mises Criterion

  7.8  Distortion Energy

  7.9  Octahedral Shear Stress

  7.10  Flow Rules or Plastic Stressstrain Relationships

  7.11  Normality and Yield Surfaces

  7.12  Plastic Work

  7.13  Comparison of Mohr's Circles for Stress and Plastic Strain Increments

  7.14  A Geometrical Considerations

  7. 15  Isotropic Hardening

8  The Examples of Elastoplastic Analysis

  8.1  Introduction

  8.2  Plane Strain Compression of a Block

  8.3  Plane Straln Bending of a Beam

  8.4  Cylindrical Bars under Pure Torsion

  8.5  Pure Bending of Prismatic Beams

  8.6  Pure Bending of Rectangular and Circular Cross Section Beam

Appendix  Reference Answers

Reference