Approximate solution for the shape of submerged funicular arches with self-weight

Abstract

In this study, the effect of self-weight on the funicular shape of submerged arches is found to be significant in cases of long span arches submerged in shallow water. Since no analytical solution hitherto exists for fully stressed arches with self-weight and hydrostatic pressure, an approximate solution is presented for easy determination of the funicular arch shape. The Cartesian coordinates of the funicular arch are expressed as analytical functions of the tangent angle, which is convenient for defining the shape without the need to solve a set of nonlinear differential equations. Numerical examples show that the approximate solution is sufficiently accurate for practical design.