Cost-optimum design for shear reinforced concrete beams

An optimization procedural method for the shear design of rectangular beams is presented. The optimization procedure is formulated as finding the minimum cost of design with constraints imposed based on ACI code provisions. The cost of concrete, shear reinforcement, and formwork is included in the formulation of the objective function. The behavioral constraints, i.e., ACI requirements for shear strength, and practical constraints, ie., cross-sectional dimensions of beams, are included in the formulation. A closed-form solution of the optimization problem expresses the optimal values of the shear reinforcement, spacing, and section dimensions in terms of material costs, strength and ductility parameters. A complete flow chart and a computer program of the algorithm is presented and several numerical examples are given to show the validity of the proposed optimization method.