On the Formulation of an Elastic-Plastic Beam Model: the Pre-Integration Idea

Abstract

Abstract This paper provides a formulation of an elastic-plastic beam model. The constitutive behaviour of material after elasticity limit is considered perfect plastic. Although this is not a general plastic behaviour, it allows to minimize mathematical difficulties to fulfil the idea: pre-integration trough the thickness extended to material non-linearity. Three types of deformation mechanisms are found: fully elastic, plasticization over only one side or both of sides. The complete kinematic set of equations are obtained, together with the analytical stress trends. Yield stress-continuity equations are used to separate the elastic and plastic domains. These domains define a quasi-state diagram; Allowing to associate the normal force and bending moment acting on the section to the elastic-plastic state within the section. Note that in the case of a rectangular section, the solution is given in a fully analytical form, otherwise the domains are solved numerical solutions. But these last, may be obtained once for all, for any one-symmetrical section.