Inelastic Bending of Beams Under Time-Varying Moments—A State Variable Approach

Abstract

The inelastic response of a beam to several time-varying moments is presented in this paper. The constitutive equations used to describe the beam material are due to Hart. This is one of several state variable theories of inelastic deformation that have been proposed recently. Hart’s equations have been previously shown to accurately predict the response of uniaxial specimens to time-varying loads. It is seen from this paper that Hart’s theory is able to qualitatively simulate various phenomena in creep and plasticity such as the effect of previous deformation history, stress redistribution, yielding, strain recovery, material hardening and strain rate sensitivity in this case of bending of a beam. The computational scheme used to integrate the equations is very efficient.