Analytical formulation of the elastic–plastic behaviour of bi-symmetrical steel shapes

This paper presents the analytical relationships of a non-linear model for the in-plane elastic–plastic analysis of bi-symmetrical steel shapes bent about one of their main axes. The basic variables are the cross-section global deformations, from which it is possible to evaluate the internal loads and the cross-section stiffness matrix components by means of simple expressions. Furthermore, the values of stresses and strains at any point of the cross-section may be determined, knowing the values of the internal loads, in the elastic and elastic–plastic domains. The effects of progressive yielding spreading, as well as those of material strain-hardening, are taken into account in the evaluation of the cross-section resistance capacity in the elastic–plastic domain. This analytical model represents an efficient, simple and accurate alternative to the elastic–plastic models based on numerical methods.