Coupled arches: A new class of free-form funicular structures

Abstract

We investigate form finding of funicular structures composed of two slender, planar arches connected by a dense sequence of cables. Two problem formulations based on nonlinear algebraic equations, and on differential equations are developed. Both of them accept prescribed arch geometry and loads as input, and generate an appropriate geometry of connectors enabling static equilibrium of all components without shear or bending. Investigation of the solution sets reveals rich geometric structures, bifurcations, and singularities. Our results have a wide range of applications including the conceptual design and form finding of planar arch, suspension, cable-stayed, and harp bridges, cable trusses, and beams with external post-tensioning.