Residual stress profiles of elasto-plastic bendings of beams with hollow cross-sections

In cyclic bending processes where plastic deformation occurs, residual stresses develop along a beam cross-section. A residual stress profile governs the load-carrying capacity and the shape of the beam. In the present study, residual stress profiles for solid and hollow beam cross-sections of square and circular shapes are studied. The scope of the present study is limited to the Euler-Bernoulli beam with small strain, elastic perfectly plastic material model without the Bauschinger effect under quasi-static loading. A layered approach is utilized to obtain the moment-curvature (M-kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}) response diagram. The induced residual stress profiles of solid and hollow cross-sections possessing equal net-bending resisting areas are compared. It is found that hollow sections are better in carrying moment as compared to their solid section counterparts. However, hollow sections are more prone to plasticity-induced damage and local buckling compared to solid sections. These two phenomena are adequately addressed in the article. The relevant variables of the governing equation are properly normalized to aid in developing deeper dimensionless insight into the elasto-plastic bending problems. The appropriate normalization and consideration of the limitations of the hollow section in elasto-plastic bending are expected to help a design engineer choose the right section for her/his applications.