Abstract The following paper presents an original finite element formulation for the elasto-plastic analysis of planar homogeneous isotropic beams. The elastic-perfectly plastic material behaviour is considered. The approach is based on innovative shape functions able to capture the formation of elasto-plastic regions at the ends of the beam element. While the proposed shape functions can theoretically handle any cross section, in this paper the formulation is developed only for rectangular cross sections. Linear geometric behaviour is considered. The formulation is validated by comparisons with the upper bound method of plastic limit analysis in terms of ultimate loading and with simulations using shell finite element analyses in terms of load–displacement response and development of the plastic regions.
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