Optimum Design of Reinforced Concrete Rectangular Columns Subjected to Axial Compression and Biaxial Bending Moments

This study investigates the optimum design in terms of the minimum cost of reinforced concrete rectangular columns subjected to axial compression force and biaxial bending moments about x and y axes. For the optimisation process, the Generalised Reduced Gradient (GRG) technique, which is embedded within Excel Solver add-in tool, was implemented. The GRG method was adopted because of its robustness and efficiency in dealing with a wide range of engineering problems as demonstrated by several works available in the literature. GRG is regarded as one of the best deterministic local optimisation methods. Equally important, the GRG is a part and parcel of Microsoft Excel which means that there is no need to pay for an extra licence to run any optimisation problem. The formulated models for the design of reinforced concrete columns and the imposed constraints were based on the provisions of the Eurocode 2 (EC2). The design variables were the cross sectional dimensions (width and depth) and the reinforcing steel area. It is worthwhile to mention that the position and orientation of neutral axis were also considered as design variables in order to avoid solving the highly nonlinear simultaneous equations which are time consuming and do not necessarily lead to a convergent solution. Several design parameters, such as materials cost ratios and depth to width ratios were tested. Consequently, optimum design charts were developed for a wide range of practical combinations of axial compression forces and eccentricities in both x and y directions. Following a comprehensive investigation of the minimum cost problems carried out for different cases, one can conclude that a variation of the depth to width ratio may have a noticeable effect on the optimum width, depth and area of steel only when the eccentricity in y direction (ey) is much greater than the eccentricity in x direction (ex). Furthermore, the effect of steel to concrete unit cost ratio (Cs/Cc) is more obvious at larger loads and higher eccentricities.