Submerged funicular arches

This paper evaluates momentless, or funicular, arches designed using Bernou lli-Euler beam theory and evaluates the errors associated with the Bemoulli -Euler and straight-beam approximations. When arches support hydrostatic pr essure imposed by water of finite depth, the funicular arch shape depends o n the ratio of the water depth to the arch height. Shallow momentless arche s [in which the arch height is less than (1/10) the arch span] under deep w ater (where the water depth is greater than 10 times the arch height) are n early parabolic in shape. On the other hand, tall momentless arches [in whi ch the arch height is almost (1/2) the arch span] under deep water are near ly semicircular in shape. Momentless arches of intermediate aspect ratios a re neither semicircular nor parabolic. The error arising from using straigh t 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 bend ing, shear, and axial deformations and hydrostatic pressure applied to the outer surface of the arch show that the internal moments can reach 10% of t he moments of a straight beam of equal span, depending on the thickness and shape of the arch.