Optimal Layout Theory: Allowance for selfweight

Abstract

Structural layout theory is based on two underlying concepts, i.e., the Prager‐Shield theory of plastic design and the notion of “structural universe.” In this paper, optimal layout theory is extended to allow for the effect of selfweight (dead load). The proposed extension is of practical importance because in the design of long‐span structures selfweight is a significant load component and the total weight is strongly dependent on the choice of layout. The application of the modified optimality criteria is illustrated with examples of minimum weight grillages (truss grids) as well as plane frames. The degree of economy achieved is then demonstrated through comparisons with nonoptimal solutions. It is also shown that in the preceding examples both primal and dual formulations give the same minimum weight. This comparison is a convenient check on the optimality of the proposed solutions.