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.