A mathematical optimisation model for the design and detailing of reinforced concrete beams. (15th October 2021) - Pierott, Rodrigo; Hammad, Ahmed W.A.; Haddad, Assed; Garcia, Sergio; Falcón, Gines
Graphical abstract: Highlights: A mathematical optimization model for sizing reinforced concrete beams is presented. Decision variables include characteristic concrete strength, cross-section area and reinforcement. Goal is to minimize construction costs. Ultimate limit state, serviceability limit state, and good construction practices are conisdered. Genetic algorithm is adopted. Abstract: 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.