Impact of unit prices on the optimal costs of reinforced concrete beams: A comparative study

Abstract

Numerous studies have been conducted on optimizing reinforced concrete (RC) structures. However, the existing literature focused on reducing the overall costs of the structural members based on materials' local prices, neglecting that these prices could vary from region to region. Thus, this article investigates the impact of materials' unit prices on the optimal costs of RC beams, considering the prices of three countries: Egypt, the UK, and Brazil. The evolutionary algorithm provided by MS Excel Solver was employed to obtain the optimum designs based on three target functions: total cost, steel weight, and concrete weight. Unlike earlier studies, we provided a sufficient number of discrete design variables that significantly influence the total cost and weights of concrete and steel; these variables include the concrete class, cross-sectional dimensions, and details of reinforcing bars at all the critical sections of the beams. Two benchmark examples were presented to illustrate the robustness of the proposed optimization model in dealing with different span lengths and continuity conditions. The results showed that the optimal designs could significantly vary based on the materials’ unit prices. In Egypt, minimizing the steel weight could save up to 50% of the total cost, compared to reducing the beam concrete dimensions. The optimal steel-to-concrete and span-to-depth ratios were as low as 0.7% and 9, respectively. On the other hand, in the UK and Brazil, cost-effective designs could be achieved by minimizing the concrete dimensions, with higher reinforcement ratio (up to 1.3%) and span-to-depth ratio (up to 11.5). The study outcomes could assist designers in the building sector estimate economical concrete quantities based on the materials’ unit prices during the conceptual stage, enabling more informed decisions.