Optimum detailed design of reinforced concrete continuous beams using Genetic Algorithms V. Govindaraj a, * , J.V. Ramasamy b a Department of Civil Engineering, Kumaraguru College of Technology, Coimbatore 641 006, TamilNadu, India b Department of Civil Engineering, P.S.G. College of Technology, Coimbatore 641 004, TamilNadu, India Received 27 January 2005; accepted 9 September 2005 Available online 2 November 2005 Abstract This paper presents the application of Genetic Algorithms for the optimum detailed design of reinforced concrete continuous beams based on Indian Standard specifications. The produced optimum design satisfies the strength, serviceability, ductility, durability and other constraints related to good design and detailing practice. While most of the approaches reported in the literature consider the steel reinforcement as a variable, the cross-sectional dimensions of the beam alone are considered as the variables in the present optimum design model. The areas of longitudinal steel obtained from the design are converted into a least weight detailing of steel reinforcements. This is achieved by generating a database of reinforcement templates containing different available reinforcement bar diameters in a pre- specified pattern, satisfying the user specified bar rules and other bar spacing requirements. The optimum design results are compared with those in the available literature. An example problem is illustrated and the results are presented. It is concluded that the proposed optimum design model yields rational, reliable, economical and practical designs. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Beams; Costs; Optimization; Reinforced concrete; Reinforcement detailing; Genetic Algorithm 1. Introduction The traditional practice in the design of continuous Reinforced Concrete (RC) beams involves performing preliminary elastic analysis based on an assumed cross- section and checking the member for its adequacy against strength, serviceability and other requirements as imposed by the design codes. If the requirements are not satisfied, then the sectional dimensions are modified repeatedly until it satisfies the codal requirements. This iterative pro- cess is carried out without considering the relative costs of concrete, steel and formwork. In order to arrive at mini- mum cost design within reasonable amount of time, a method based on certain optimality criteria becomes necessary. Many researchers have investigated the optimum design of RC beams. Friel [1] derived an equation for finding an optimum ratio of steel to concrete area for a singly rein- forced beam based on a moment constraint alone. Chou [2] uses the Lagrange multiplier method for minimum cost design of a singly reinforced T-beam using the ACI code. Kirsch [3] presents a simplified three level iterative proce- dure for cost optimization of multi-span continuous RC beams with rectangular cross-sections. He optimized the amount of reinforcement at first level, the concrete dimen- sions at the second level and the design moments at the third level. Lakshmanan and Parameswaran [4] derived a formula for the direct determination of span to effective depth ratios which can avoid the trial and error approach necessary for the flexural design of RC sections as per 0045-7949/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2005.09.001 * Corresponding author. Tel.: +91 0422 2669401; fax: +91 0422 2669406. E-mail address: vgr_ga@rediffmail.com (V. Govindaraj). www.elsevier.com/locate/compstruc Computers and Structures 84 (2005) 34–48