Structural analysis of parabolic arches defined in Global Coodinates

Abstract

This paper deals with curved beams, particularly, parabolic arches defined in global coordinates. The problem is approached differentially and expressed in a unique system of twelve linear ordinary differential equations given by Gimena et al. [2]. The lowertriangular form of the system of equations permits the determination of the exact analytical solution through successive integrations row by row. The system can also be solved using a numerical method with boundary conditions. Axial and shearing deformations, varying cross section area, non-symmetric section, generalized loads and different support conditions can be taken into account. In special cases, this system is particularized, and different subsystems arise, to model the mechanical behavior of special structural elements.This study presents the way to proceed with parabolic arches, which have an optimal response transmitting vertical load (Gimena et al. [3]). Analytic expressions and results of forces, moment, rotation and displacements for parabolic arches (spans, heights, load cases and supports) are given and plotted.