Design of Optimally Reinforced RC Beam, Column, and Wall Sections

Abstract

A conjugate gradient search method is coupled with a general model for the ultimate strength of a rectangular reinforced concrete (RC) cross section. Reinforcement required to provide reliable resistance identically equal to required strengths (due to factored load effects) is determined. The total reinforcement is determined optimally, either to obtain a global minimum or to obtain a minimum subject to various constraints, such as the use of equal reinforcement on opposite faces or the use of equal reinforcement on all faces. The model is useful for the design of beam, column, and wall sections that are subjected to uniaxial or biaxial bending. Solutions are obtained directly, and make use of computing power contained within spreadsheet programs that are widely available. Avoiding the somewhat tedious hand calculations and approximations required in conventional iterative design approaches avoids errors and potentially unsafe designs, while the use of optimum reinforcement quantities advances the aim of improving the sustainability of RC construction.