Arch-profiles of bistable arches, in their two force-free equilibrium states, are related to each other. This bilateral relationship is derived for arches with fixed–fixed boundary conditions in two forms: a nonlinear single-variable equation for analysis and a closed-form analytical expression for design. Some symmetrical features of shape as well as necessary and sufficient conditions for bistability are presented as corollaries. Analysis and design of arch-profiles using the bilateral relationship are illustrated through examples.

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