Keywords: structural optimization, harmony search algorithm, continuous beams, reinforced concrete, cost optimization, discrete variables.

Design optimization of reinforced concrete structures is more challenging than that of steel structures as a result of the complexity associated with reinforcement design. In this study, an 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 the span and supports, and the diameter of ties. The values of these variables are required to be selected from a design pool which contains discrete values for these variables. The design constraints are implemented from ACI 318-05 which covers the flexural and shear strength, the serviceability, the minimum and maximum steel percentage for flexural and shear reinforcement, the minimum and maximum spacing for stirrups and the upper and the lower bound requirements for the width and depth of the beam section. Furthermore the bar detailing requirements are also considered to obtain optimum designs acceptable to the practicing designers. The objective function is considered as the total cost of the 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 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 is utilized to obtain its solution. This technique simulates the music improvisation of a musician into a numerical optimization approach. As a musician tries to find a pleasing harmony determined by aesthetic standards, the optimization process tries to find the global optimum determined by an objective function. The harmony search algorithm has been applied to various engineering design optimization problems and found quite effective in finding the optimum solutions. It is quite simple and has few parameters to initialize. It has a high convergence rate. It needs relatively fewer numbers of function evaluations to reach the optimum solution. Due to these advantages the harmony search method is used to obtain the solution of the design problem. A numbers of design examples taken from the literature are included to demonstrate the efficiency and robustness of the optimum design algorithm presented.

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