Optimal Suspended-Bridge Design Deduced from Natural Wrinkling of Membranes

Optimal shapes for bridges are determined by drawing inspiration from the wrinkling patterns naturally originating in initially flat elastic membranes highly stretched in their plane. We examine classical schemes where the roadway is suspended by cables to either an overhanging arch or pylons and, starting from these, an idealised “web bridge” is conceived of, in which the deck is sustained by a membrane instead of cables. Clearly, since membranes cannot support compression stress, at equilibrium some regions may result taut, while others may become either slack (inactive) or wrinkled. In the latter regions, possible wrinkles are practically straight and, what is more, their final layout obeys to an optimal criterion, i.e., they develop in such a way as to offer maximum stiffness towards external actions. Thus, the idea is to place cables according to the tensile stress distribution resulting in the membrane when the deck is loaded. In particular, a net of orthogonal cables is placed in the taut regions (along the lines of principal stress), whereas straight cables follow the direction of the wrinkles in the corrugated zones. Thus, various “optimal” cable arrangements are determined for real bridges. Simply changing the membrane contours and the deck vs. pylon stiffness, the resulting shapes reproduce the classical cable-stayed bridges or mixed suspended and cable-stayed "hybrid" solutions. In the case of bow-string arch bridges, an optimal arrangement of hangers is envisaged. Finally, as a paradigmatic example, we discuss from this unusual point of view, the fancy design conceived by Calatrava for his Alamillo Bridge in Seville.