Linear programming in prestressed trusses

This paper discusses the effect of prestress on the minimum weight design of singly loaded trusses of fixed geometry which are required to satisfy stress constraints. Both general trusses and trusses whose design requires a predetermined ratio for the cross-sectional areas (same for simplicity) are considered. Formally synthesized as nonlinear programming problems, they are later reduced to linear programming problems by removing the constitutive equations from the formulation by utilizing the results of theorems relating to realizability through prestressing. With equilibrium only left to be considered the general truss problem reduces identically to that of optimal design without prestress having the well-known properties of fully stressedness and statical determinacy. Prestressing, therefore, has no meaning as far as weight is concerned. However, for trusses in the special category, prestressing can reduce the weight as the structure is understressed because usually one member governs the design. Posterior considerations are given for attaining the prestress and an example that shows the weight advantages of prestressing is presented.