Effective stress method to be used in beam finite elements to take local instabilities into account

In the fire situation, Bernoulli beam finite elements are the workhorse used in numerical calculation model for simulating the behaviour of the structure. Such finite elements treat all sections as class 1 (stocky) sections whatever the slenderness of the plates that make the section, allowing the development of a full plastic stress distribution in the section which leads to complete plastic redistribution along the members in the structure. This type of element is thus not adapted for modeling structures that contain slender sections of class 2, 3 or 4. This document presents a new approach to take into account local instabilities in slender sections using beam finite elements. The new approach is based on an effective constitutive law of steel. The effective law is not symmetrical with respect to tension and compression because, in tension, the stress-strain relationship is not modified whereas, in compression, the stress-strain relationship is modified.