Minimum cost design of RC beams using DCOC Part I: Beams with freely-varying cross-sections

Abstract

A procedure for the economic design of reinforced concrete beams under several design constraints is outlined on the basis of discretized continuum-type optimality criteria (DCOC). The costs to be minimized involve those of concrete, reinforcing steel and formwork. The design constraints include limits on the maximum deflection in a given span, on bending and shear strengths, in addition to upper and lower bounds on design variables. An explicit mathematical derivation of optimality criteria is given based on the well known Kuhn-Tucker necessary conditions, followed by an iterative procedure for designs when the design variables are the depth and the steel ratio, or the depth alone. The computer code developed in Part I can handle freely-varying design variables along the members of any multispan beam. In Part II the DCOC and computer code are developed for designs when the member cross-section is assumed to be uniform along its entire length. Several test examples have been solved to prove the accuracy and efficiency of the DCOC-based techniques.