Optimum structure for a uniform load over multiple spans

This paper presents a new half-plane Michell structure that transmits a uniformly distributed load of infinite horizontal extent to a series of equally-spaced pinned supports. Full kinematic description of the structure is obtained for the case when the maximum allowable tensile stress is greater than or equal to the allowable compressive stress. Although formal proof of optimality of the solution presented is not yet available, the proposed analytical solution is supported by substantial numerical evidence, involving the solution of problems with in excess of 10 billion potential members. Furthermore, numerical solutions for various combinations of unequal allowable stresses suggest the existence of a family of related, simple, and practically relevant structures, which range in form from a Hemp-type arch with vertical hangers to a structure which strongly resembles a cable-stayed bridge

On the optimality of Hemp’s arch with vertical hangers

In 1974 W. S. Hemp constructed a prototype structure to carry a uniformly distributed load between two pinned supports. Although Hemp’s structure had a significantly lower volume than a parabolic arch with vertical hangers, it was shown to fail the Michell optimality criteria, and therefore to be non-optimal. In this paper we demonstrate that if limiting compressive and tensile stresses are unequal then Hemp’s structure is optimal for the half-plane provided the ratio of limiting tensile to compressive stresses falls below a certain threshold. An analytical proof is presented and the finding is confirmed by results from large scale numerical layout optimization simulations