Optimum design of frames under alternate loading condition

Abstract

A generalized formulation of a procedure for optimum design of linear elastic plane frames under alternate loading condition is presented. The condition of alternate loading is employed to ensure that the optimum design, under individual application of envisaged load events, does not violate the limit state requirements on strength. The behavioral constraints both on strength and on displacement, including those of the axial load – moment interaction prescribed in code specifications, and the side constraints on member sizes are incorporated in the formulation. The method permits grouping of members to effect repetition and uniformity of member sizes, to a desired extent, throughout the structure. A predictor–corrector scheme is employed to arrive at the optimum design. The predicted design vector is expressed in terms of true member forces by an implicit scheme. In the correction phase, dynamic scaling and a unique process of step-size reduction are employed on the predicted design vector in the fully stressed design iteration to avoid bypassing an optimum during the search procedure. An algorithm for implementation of the proposed optimal design procedure is presented. The limit state design procedure of the Canadian Standard S16.1-M89, for members subjected to combined axial and bending action, is embedded in the algorithm. The algorithm is illustrated with an example problem and verified with results available in the literature. Key words: frames, optimum design, alternate loading, fully stressed, optimization, limit state.