Optimum Design of Reinforced Concrete Beams Using Polynomial Optimization Technique

Abstract

Structural optimization seeks the selection of design variables to achieve within the limit (constraints) placed on the structural behaviour, geometry or other factors; its goal of optimality defined by the objective function for specified loading conditions. The three basic features design variables, objective function and constraints contrive to form the design problem. There are several mathematical techniques to solve such problems. The polynomial optimization technique is a recently evolved procedure which is concerned with finding the minimum of a polynomial objective function subjected to constraints. A structural design problem has been formulated in this manner which enables minimum cost design to be derived rapidly and simply. A paper deals with the application of Polynomial optimization technique to R.C.C. beam-member design problem. In the present study this technique is used to determine the minimum cost of reinforced concrete members by considering several design variables such as breadth, depth, area of reinforcing steel etc. Since it is difficult for the designer in the office to become familiar with the mathematical computation required, further attempt is made to represent the resulting optimum design expressions in the form of “Nomograms” which will facilitate the work in the design office.