Optimum cost of prestressed and reinforced concrete beams using genetic algorithms

Abstract

This study aims at obtaining the cost of Prestressed Concrete (PC) beams and Reinforced Concrete (RC) beams. These beams are designed according to the requirements of the ACI 318-05 code. The objective function comprised the cost of concrete and the cost of reinforcement. Two computer models were developed for the cost optimization of PC and RC simple beams using MATLAB software. The design variables of RC simple beams were beam width, effective beam depth, number of flexural bars and reinforcement bar diameter. Beam width, effective beam depth, number of flexural bars, reinforcement bar diameter, number of tendons, tendon diameter and eccentricity of the centre of gravity of the tendons represented the design variables of PC simple beams. Practical design situations were considered using integer values for beam dimensions, number and diameter of bars/tendons. A catalogue of the common values of the beam dimensions and bar/tendon numbers and diameter dimensions were prepared for this purpose. A cost reduction of 27.9 and 16.7% for the 4 and 8 m span RC beams, respectively and 29.8 and 17.8% of the 10 and 20 m span PC beams was obtained by the GA model over the generalized reduced gradient method. The effect of concrete compressive strengths and wider design parameters bounds on the outputs of the optimization process were examined. The comparison showed that the GA models were smart in keep moving towards the optimum cost of the beams.