Design of Reinforced Concrete Deep Beams using Particle Swarm Optimization Technique

Abstract

Researches available in literature interrelating neural networks to civil engineering design problems, especially for beep beams, are very rare. Therefore, an optimization algorithm is developed and verified in this study and coded using MATLAB functions to determine the optimum cost design of reinforced concrete deep beams. ACI 318-14 code method is used benefiting from iterative particle swarm optimization technique due to its efficiency and reliability. Minimizing total cost is used as the objective function in terms of four decision variables. Self-adaptive penalty function technique is used to handle constraints for each of the 300 randomly selected particles, and in each of the 50 total iterations followed for each one of four suggested deep beam design case studies. Performing all iterations is used as a stopping criteria for the developed algorithm. Comparative studies are made to show the effect of concrete compressive strength, live load scheme, and length of deep beam, on the optimum total cost and the corresponding decision variables. Results presented in the form of graphs and tables show that the loading condition has a significant effect on the total cost of deep beams. The cost increase is accompanied by deep beam length increase, height increase, longitudinal reinforcement area increase and vertical shear reinforcement area decrease. The calculated optimum cost is noticed for beam DB1, which is 1255 US$, with 1.29 m beam height, 0.01445 m2 vertical shear reinforcement, 0.00914 m2 horizontal shear reinforcement and 0.00238 m2 main longitudinal reinforcement. The results show a relatively less difference in total cost between all the four beams at 4 m length compared to 8 m length. Also, a relatively mild increase in total cost is happened for beams DB3 and DB4 as the height increases, especially above 1.7 m height. As the main longitudinal reinforcement increases, cost of DB4 is affected more significantly than others, and as the vertical shear reinforcement increases, DB4 curve shows a relatively low degradation in cost.