Elastic In-Plane Buckling of Funicular Arches

Abstract

Buckling loads of arches could be significantly affected by the assumptions made on the load behavior during buckling. For a funicular arch whose centerline coincides with the compression line, we may consider two types of load behaviors based on how the line of load action shifts during buckling. This paper presents the governing differential equations for the elastic in-plane buckling problem of funicular circular arches under uniform radial pressure based on the two different load behavior assumptions, as well as analytical and numerical methods for analysis. For the analytical method, buckling criteria of rotationally-restrained ended circular arches with an internal rotational spring are formulated by using the general solution of the governing differential equation. For the numerical method, the Hencky bar-chain model (HBM) and its simple matrix formulations for general funicular arches are established. The buckling loads and mode shapes of funicular circular arches are solved by using HBM and verified against exact solutions obtained from the analytical method. For funicular catenary arches and parabolic arches, the buckling load solutions by HBM with various number of segments are also obtained and compared with the solutions presented by the previous researchers.