Minimum cost design of RC frames using the DCOC method Part I: Columns under uniaxial bending actions

The paper solves the minimum-cost design problem of RC plane frames. The cost to be minimized includes those of concrete, reinforcing steel and formwork, whereas the design constraints include limits on maximum deflection at a specified node, on bending and shear strengths of beams and on combined axial and bending strength of columns, in accordance with the limit state design (LSD) requirements. The algorithms developed in this work can handle columns under uniaxial bending actions. In the companion paper the numerical procedure is generalized to include columns subjected to biaxial bending. On the basis of discretized continuum-type optimality criteria (DCOC), the design problem is systematically formulated, followed by explicit mathematical derivation of optimality criteria upon which iterative procedures are developed for the solution of design problems when the design variables are the cross-sectional parameters and steel ratios. For practical reasons, the cross-sectional parameters are chosen to be either uniform per member or uniform for several members at a given floor level. The procedure is illustrated on several test examples. It is shown that the DCOC-based methods are particularly efficient for the design of large RC frames.