Methodology for determining optimal design of funicular arches under point loads and selfweight against in-plane buckling

Abstract

This paper presents a simple methodology for determining the optimal design of an elastic funicular arch under point loads and selfweight for maximum in-plane buckling capacity. This class of optimization problem has hitherto not been investigated. The cross-section of the arch is assumed to be geometrically similar and constant through its entire length. The arch is assumed to be inextensible. The supporting points of the arch may be either pinned or fixed. The methodology for determining the optimal arch shape involves first finding the funicular shape of the arch under point loads and selfweight. Next, the arch is modelled by the Hencky bar chain model (HBM) for the buckling analysis. The HBM is adopted because it eliminates the requirement for formulating the governing equation for buckling and it is a straightforward model to comprehend and implement in a computer code. Each funicular arch shape is specified by a horizontal force value, and it has to be optimally selected to maximise the buckling capacity of the arch. As it is a single parameter optimization problem, the Golden Section search was used to determine the optimal horizontal force, and hence the optimal funicular arch shape. The methodology is illustrated by solving two example problems: (1) an arch under a point load and selfweight and (2) a symmetric arch under two equal point loads and selfweight. By solving the self-buckling problem of a catenary arch, the maximum spanning capacity of the catenary arch can be obtained as shown herein.