An iterative form-finding method for antifunicular shapes in spatial arch bridges

This paper presents a new iterative method for finding antifunicular out-of-plane shapes for spatial arch bridges. For a given set of loads, this is the warped geometry that results in an equilibrium state free from bending stresses, i.e. simply under axial forces. These shapes appear when out-of-plane loads act upon the arch, for example, when the deck is curved in plan. A detailed formulation with two alternative algorithms is presented that solves the most generalised case, where unsymmetrical bridges with clamped ends and non-linear behaviour can be considered. An uncoupled formulation has also been developed, in order to minimise internal forces, in both vertical and leaning plane arches. The method can be used both for upper and lower deck arch bridges. It can also be easily adapted for tension elements or cables.