Chapter 3 - Plastic Flow Rule and Elastoplastic Analysis

Abstract

This chapter deals with the elastoplastic analysis of structures. It begins with a description of general elastoplastic analysis of structures, with the help of equations and diagrams. An important aspect in elastoplastic analysis is determination of the load level at which the plastic hinge occurs. Apart from bending moments, structural members in most structures are also subjected to different types of actions such as axial forces, shear forces, and torsion. These forces may affect and usually reduce the plastic moment capacity of the section in some or all members and subsequently affect the plastic collapse loads or load factor of the structure. The influence of these forces on the plastic moment and the corresponding stiffness of the structural elements are described in this chapter. The derivation leads to use of the concept of yield surface whereby the relationship between the element stiffness matrix and force interactions can be established. There are four cases of yield condition for a beam element to be considered: both ends i and j are elastic, end i is plastic and end j is elastic, end i is elastic and end j is plastic, and both ends i and j are plastic. Furthermore, different yield surfaces used for the beam element with different yield conditions give different expressions for the elastoplastic stiffness matrices. These are discussed. Finally, the chapter deals with linearized yield surface.