Incremental Resistance and Deformations of Elastoplastic Beams

A key step in a numerical analysis of an elasto-plastic frame using the plastic hinge concept is the calculation of the incremental resistance and plastic deformations of a beam element for a given incremental member displacement vector. An algorithm is presented, based on the assumption that during the load or time increment the change of the displacement is linear. That is, in the member displacement space, the vector is straight so that at any stage within the total increment, the current displacement increment is a scalar times the total displacement increment vector. Following an iterative process, the new member force point is made to stay on the yield surface and the corresponding plastic deformation increment is computed in a manner more strictly conformable to the theory of plasticity. The incremental displacement can be large enough so that the element may undergo the process of changing from a state of total elasticity to having one yielded end and then on to having both ends yielding. A numeri...