Prestressed Concrete Design Using Linear Programming Techniques

Linear programming techniques provide a direct design approach for optimizing the cross-section of a simply supported prestressed concrete member. A cross-section is determined by solving the linear transformation of the elastic working stress relationships that are required for the design. A graphical procedure is used to determine the optimal solution which satisfies the working stress constraints. It was found that this solution does not always satisfy the ultimate strength requirements. A computer program was developed to incorporate the working stress relationships along with the ultimate moment strength equation and the limiting reinforcement criterion. The design constraints are transformed to a linear form so that a graphical procedure can be used to locate the optimal solution to the design problem. The shear capacity and the deflection criterion are then compared with the allowable values. The use of linear optimization techniques is shown to be a suitable method for designing prestressed concrete members