On the layout of a least weight single span structure with uniform load

This paper focuses on identifying an analytical description for the layout of a minimum volume pin-jointed structure (truss) that is uniformly loaded. The methodology utilized takes advantage of the properties of reciprocal diagrams (as described by the authors in a previous paper). Therefore, the optimization is conducted on the dual truss associated with the force diagram of the original structure rather than on the original structure itself. An analytical expression for the volume of the dual truss, which coincides with that of the original truss, is also derived in the form of a functional. Numerical integration is then conducted on the functional to obtain the optimal layout, and the numerical sensitivity of the solution with respect to the selection of the approximation function is investigated. The final results show that simple formulas describe the geometric properties of the dual (reciprocal) structure and thus the original truss. Finally, this paper shows that the results presented agree with previous numerical studies in the literature.