Minimum Weight Plastic Design of Continuous Beams

A plastic design method is presented on minimizing the structural weight of n-span continuous beams with variable cross sections. The loads applied to the beam are combined loads consisting of a concentrated live load and a uniformly distributed live and dead load. The method which obtains optimum cross sectional shapes is explored. The plastic design method of n-span continuous beams consisting of any span length is presented, and the obtained required plastic moment distributions under combined loading are shown. Optimum I-shape sections, which lead to minimizing the beam weight, are given. The modified stepped beams corresponding to the required plastic moment distributions are determined by the dynamic programming approach. Practical design charts are supplied.