Partially Prestressed Concrete Beam Optimization

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Abstract
A comprehensive method for minimum cost design of simply supported, uniformly loaded, partially prestressed concrete beams is presented. Nine design variables are used—six geometrical dimensions, area of prestressing steel and area of tensile and compressive mild reinforcement. The optimum design is in accordance with ACI 318/77. The imposed constraints are on the four flexural stresses, initial camber, dead and live load deflections, ultimate shear and ultimate moment capacity with respect to both the cracking moment and the applied load. The nonlinear optimization is performed using the Penalty‐Functions method coupled with Quasi‐Newton unconstrained optimization techniques. The method, successfully applied to several design problems, both cracked uncracked, clearly indicates that numerical optimization can be used to solve design problems of interest to practicing engineers.

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