Analysis of Shifts in the Points of Maximum Deflection and Permanent Deflection for Elastic-Plastic Bending of Unsymmetrically Loaded Beams

An analysis of elastic-plastic bending of unsymmetrically loaded beams is carried out using the method of virtual work. The results show that the maximum deflection under load occurs at quite some distance from the point of loading but moves toward the point of loading as the load approaches ultimate. The residual or permanent deflections occur at points different than those developed under load and are shifted further toward the load point. However, even at a load equal to 99.5 of the ultimate the maximum permanent deflection still occurs at a considerable distance from the point of loading. The maximum strains under load and the permanent strains occur at the point where the load is applied.