Institute for Transportation

An effective moment of inertia is developed for a rectangular, prismatic elastoplastic beam with elastic, linear-hardening material behavior. The particular solution for a beam with elastic, perfectly plastic material behavior is also presented in closed-form with applications for beam bending subjected to monotonic loading. Equations are presented for the direct application of the virtual work method for elastoplastic beams with concentrated and distributed loads. Comparisons are made between the virtual work method deflections and the deflections obtained by using the direct integration method and the approximate direct stiffness method using an average effective moment of inertia in the elastoplastic region. Elastoplastic moment-curvature expressions are also developed for reducing rigidity of a rectangular beam with elastic, perfectly plastic material behavior and for use in determining elastoplastic deflections of beams subjected to cyclic loading. These new moment-curvature expressions are developed using updated stress states after each cycle where unloading and reloading occurs with alternating yield. Yield envelopes are used to delineate the type and extent of the stress states from the various bending moment histories at a cross-section. Both linear and quadratic approximation methods are used for determining the areas and centroids of the curvature diagram when with the virtual work method is used to obtain the loaded and unloaded deflections of a determinate beam.