Post‐Yield Analysis of Rigid‐Plastic Beams with Variable Restraints

Abstract

A theoretical study is undertaken in this paper to investigate the influence of finite deflections on transversely loaded rigid‐perfectly plastic beams. The support conditions are specified through both variable rotational and axial restraint factors. Quasi‐static loading conditions and a small strain assumption are adopted throughout. The analysis, based on continuing the initial deformation mode, leads to a determination of the load‐deflection relationship, thereby highlighting the significant influence of both geometry changes and support conditions. In particular, it is found that the load‐carrying capacity of the structure can be increased considerably, even for moderate support restraints. For the case of distributed loading, the method is only approximate in view of its assumption of a single deformation mode that leads to a violation of the yield conditions. However, reasonable results, as evidenced by comparisons with existing exact solutions, are obtained. It is also shown that further simplification in the analysis can be achieved without great loss of accuracy through piecewise linearization of the nonlinear yield curve.