Analysis of Inelastic Deformations

Abstract

When analyzing the deformations of inelastic beams and shafts, current structural analysis procedures that account for the reduced rigidity in the elasto-plastic regions have been limited to simple, idealized conditions. This paper presents a straight-forward approach for teaching this subject to undergraduate students whereby the actual conditions of stress and reduced rigidity in the elasto-plastic regions remain apparent throughout and are applicable over a broad-range of structural conditions. The structural analysis methods that are commonly taught at the undergraduate level to calculate the deflection of beams and the angle of twist of circular shafts are extended for the inelastic condition using closed-form expressions for the reduced rigidity. To assist with teaching the material, a step-by-step procedure is presented for both the elastic and inelastic beam conditions. Several examples illustrate the ease with which the procedure is used, and discussion is provided that highlights the learning opportunities offered by each example.