Optimum Detailed Design of Reinforced Concrete Continuous Beams using the Harmony Search Algorithm

摘要

Design optimization of reinforced concrete structures is more challenging than that of steel structures due to the complexity associated with reinforcement design. In this study, optimum design algorithm is presented for reinforced concrete continuous beams. The design variables are selected as the width and the depth of beams in each span, the diameter and the number of longitudinal reinforcement bars along span and supports, and the diameter of ties. The design constraints are implemented from ACI 318-05 which covers the flexural and shear strength, serviceability, the minimum and maximum steel percentage for flexural and shear reinforcement, the spacing requirements for the stirrups and the upper and lower bound requirements for the width and the depth of the beam section. The objective function is considered as the total cost of continuous beam which includes the cost of concrete, formwork and reinforcing steel bars. The cost of any component is inclusive of material, fabrication and labour. The design algorithm automatically updates the value of the dead load which includes self-weight of the continuous beam depending on the cross-sectional dimensions during the design cycles. The optimum design problem formulated according to ACI 318-05 with the design variables mentioned above turns out to be a discrete programming problem. The harmony search algorithm (HS) is utilized to obtain its solution. Harmony search algorithm has been applied to various engineering design optimization problems and is found quite effective in finding the optimum solutions. It is quite simple and has few parameters to initialize. It needs relatively less number of function evaluations to reach the optimum solution. Due to these advantages, harmony search method is used to obtain the solution of the design problem. Numbers of design examples taken from the literature are included to demonstrate the efficiency and robustness of the optimum design algorithm presented.