Nonlinear Finite Element Analysis of Clamped Arches

A curved nonlinear finite element is developed to analyze the behavior of slender high-rise arches that undergo large deflections. The strain analysis is based on the assumptions that plane cross sections remain plane and strains are small. Rotations are unrestricted. In-plane bending and buckling modes for deep arches with fixed-end supports are analyzed. Concentrated loads and interacting concentrated and distributed loads are considered. The problem is formulated as a system of rate equations that govern the quasi-static deformation of an arch. These equations are integrated using a Runge-Kutta scheme to obtain load-deflection response.