Application of DCOC to optimum prestressed concrete beam designs

This paper describes the application of discretized continuum-type optimality criteria (DCOC) to the minimum cost design of prestressed concrete beams. The costs to be minimized involve those of concrete, prestressing steel, non-prestressing steel and formwork. The design constraints include limits on the maximum deflection in a given span, on flexural and shear strength, in addition to supper and lower bounds on design variables. An explicit mathematical derivation of optimality criteria is given based on the Kuhn-Tucker necessary conditions, followed by an iterative procedure for designs when the design variables are the depth of beam, the eccentricity of prestressing steel at midspan and the non-prestressing steel ratio. The DCOC and computer code are developed for beam designs whose member cross-sections are uniform along the length. Self-weight of the structure is included in the equilibrium of the real system and the effect of prestressing force on deflection is included in the deflection constraint. Numerical examples of partially prestressed concrete beams with rectangular and T sections have been solved to show the accuracy and efficiency of the DCOC-based technique.