Equations to evaluate elastic-plastic deformations of cantilever steel beams in simple bending

Abstract

This paper presents an analytical model to evaluate cross-section rotations and displacements in a cantilever beam subjected to a concentrated transversal load at its free end. The beam is made of an I-section, and its material is expected to follow an elastic-perfectly-plastic behaviour. The cross-section displacements and rotations may be evaluated by means of analytical expressions, which are presented both for the beam elastic and elastic-plastic domains. The latter is divided in two different phases: when only a portion of the flanges is yielded, the web remaining elastic, and when yielding progresses across the web of the most strained sections, after total yielding of their flanges. These analytical expressions also allow the evolution of the yielded areas to be controlled, along the beam cross-sections and length, as a function of the applied load.