Elasto-plastic optimal profile of the flanges of a double-T steel beam

For a given amount of steel we look for the optimal profile of the width of the symmetrical flanges of a double-T steel beam, in order to optimize a weighted compromise between elastic performance, measured by the compliance, and collapse factor. We approximately determine curves of optimal profiles when varying the relative weight given to each performance measure and use these profiles to obtain a plot showing the variation of the ductility and the collapse factor as functions of the relative weights. The steel is assumed elastic-perfectly plastic.