Theorem of optimal reinforcement for reinforced concrete cross sections

A theorem of optimal (minimum) sectional reinforcement for ultimate strength design is presented for design assumptions common to many reinforced concrete building codes. The theorem states that the minimum total reinforcement area required for adequate resistance to axial load and moment can be identified as the minimum admissible solution among five discrete analysis cases. Therefore, only five cases need be considered among the infinite set of potential solutions. A proof of the theorem is made by means of a comprehensive numerical demonstration. The numerical demonstration considers a large range of parameter values, which encompass those most often used in structural engineering practice. The design of a reinforced concrete cross section is presented to illustrate the practical application of the theorem.