Model for Optimal Design of Reinforced Concrete Beam

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Abstract
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.

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