Model for Optimal Design of Reinforced Concrete Beam

An infinite member of combinations of values of the effective depth, width, and area of reinforcement could yield the same nominal moment capacity of a reinforced concrete beam. In the conventional process, a designer often assumes a beam section not linked with cost, and the process is repeated if the assumed section is not adequate. This technical note presents a model for the optimal flexural design of singly reinforced concrete beam in which the process is reversed; i.e., applied bending moment and other parameters are inputs, and the beam section is the output of the model. Using this nonlinear programming model, the unique least-cost beam design could be achieved directly, exactly matching its ultimate moment of resistance with the ultimate applied bending moment, including that due to the self-weight. Application of this new design technique is illustrated with example problems showing considerable savings in cost and material consumption.