Shapes of Submerged Funicular Arches

In this paper, the analytical forms of the shapes of submerged funicular arches are expressed in terms of elliptic integrals. The initial radius of curvature at the apex is related to the water depth at the apex and the axial compressive force. The shape of the submerged funicular arches depends on the ratio between this initial radius of curvature and the water depth at the apex. Using the analytical expressions, the maximum span and height of the submerged funicular arches can be determined explicitly. Besides, the analytical expressions are useful in determining the design parameters for the submerged funicular arches accurately.