A mathematical optimisation model for the design and detailing of reinforced concrete beams

An evolutionary metaheuristic optimization model for sizing reinforced concrete beams is presented. The proposed optimization model transcends ones in the literature as it is able to consider characteristic concrete strength (f(ck)), cross-section area and reinforcement bars' diameters as discrete design variables, thus representing a more realistic model. The goal is to minimize construction costs via configuring cross-sectional dimensions, determining reinforcement layouts, and defining f(ck). The design constraints formulated in the mathematical model proposed are related to structural integrity, considering ultimate limit state, serviceability limit state, and good construction practices. A finite element method program was developed to obtain the stresses and strains of beams, geometries, and load forces. Additionally, a longitudinal reinforcement database generator was developed, ensuring that the reinforcement layouts generated are within codes of practice. A Genetic Algorithm was adopted to solve the resulting optimisation problem. Results of case studies demonstrate that the cost variance implications are directly related to the reinforcement detailing arrangements, with 3.63% to 17.07% improvements in costs that are achieved when compared with other studies in the literature.