Optimum structure to carry a uniform load between pinned supports: exact analytical solution

What is it about?

What is the lightest structure to carry an evenly spread load between two supports? That question has been asked by physicists and engineers since the time of Gallileo. In this paper, we provide a rigorous mathematical proof that the structure long assumed to be optimal when the weight of the structure itself is negligible compared to the applied load (a parabolic arch or cable) can be bettered by structure comprising a parabolic arch and more intricate net-like regions.

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Why is it important?

An old definition of an engineer is "one who can do well for one dollar that which any bufoon can do after a fashion for two." Certainly a key aspect of structural engineering is finding efficient forms to carry loads safely to supports. This structure presented in this paper is only marginally lighter than a parabola. But the question remains: if we couldn't find the optimal solution for such a simple problem, can we use optimisation methods find much better solutions for more complex cases?