Numerical experimentation for the optimal design of reinforced rectangular concrete beams for singly reinforced sections

Abstract

This paper presents a model for the optimal design of reinforced rectangular concrete beams for singly reinforced sections. It develops an analytical approach to the problem, based on a criterion of minimum cost and minimum weight design with a reduced number of design variables. Representative examples are presented to illustrate the applicability of the formulation in accordance with building code requirements for structural concrete (ACI 318S-13), including the comments on the standards. A comparison is made between the optimal design solution and current design practice for reinforced rectangular concrete beams. The optimal solution for the design of reinforced rectangular concrete beams shows clearly that significant savings can be made in the costs of the construction materials used – i.e. reinforcement steel and concrete. In addition, the problem formulation can be applied using a nonlinear mathematical programming format.