Analytical model for the elastic-plastic analysis of simply supported I-Shaped beams in simple bending

Abstract

An analytical model allowing the mechanical behaviour of simply supported beams under concentrated transversal loads to be evaluated, is presented in this paper. The beams are made of I-sections. The constitutive material is supposed to present an elastic-perfectly-plastic behaviour. The cross-sections displacements and rotations are evaluated through analytical expressions presented for the beam elastic and elastic-plastic domains; this last being divided into two different phases, when the flanges are partially yielded as the web remains elastic, or when yielding progresses across the webs of the most strained sections, after complete yielding of the flanges. These analytical relationships allow also the evolution of the yielded areas, along the beam cross-sections and length, as a function of the applied load, to be controlled.