Maximum Spanning Capacity of a Catenary Arch Under Selfweight Against Buckling

This paper is concerned with a novel problem of determining the maximum spanning capacity of an elastic catenary arch under its own weight against in-plane buckling. The arch is assumed to have a uniform cross-section throughout its entire length and the arch length is assumed to be inextensible. The specific shape of the catenary arch is clearly dependent on the horizontal force which has to be determined for maximum buckling capacity of the arch. The Hencky bar-chain model is adopted for the elastic buckling analysis as it avoids the need to formulate the governing equation for buckling and it is also a simple model to understand and for coding. The maximum spanning capacity of the arch can be derived from the maximum in-plane buckling load of the optimal arch solution. This paper will illustrate the aforementioned Hencky bar-chain model for determining the maximum spanning capacity against in-plane buckling for arches under various support conditions and also for arches with a hinge at its crown.