Submerged Funicular Arches

Abstract

This paper evaluates momentless, or funicular, arches designed using Bernoulli-Euler beam theory and evaluates the errors associated with the Bernoulli-Euler and straight-beam approximations. When arches support hydrostatic pressure imposed by water of finite depth, the funicular arch shape depends on the ratio of the water depth to the arch height. Shallow momentless arches [in which the arch height is less than (1/10) the arch span] under deep water (where the water depth is greater than 10 times the arch height) are nearly parabolic in shape. On the other hand, tall momentless arches [in which the arch height is almost (1/2) the arch span] under deep water are nearly semicircular in shape. Momentless arches of intermediate aspect ratios are neither semicircular nor parabolic. The error arising from using straight beam theory (for the bending stresses only) is less than 5% for ratios of beam-depth to radius of curvature less than (1/2). Analyses including bending, shear, and axial deformations and hydrostatic pressure applied to the outer surface of the arch show that the internal moments can reach 10% of the moments of a straight beam of equal span, depending on the thickness and shape of the arch.