Deflection approximations of a catenary dome for uniform gravity loads

Membrane stress equations for the catenary dome have been recently developed, but the deflection theory remains to be solved. This article, therefore, presents theory for the analysis of the x- and y-deflections of a catenary dome, for the load case of uniform gravity loads. The deflection in the x-direction is based on previously developed shell theory but adapted for the catenary dome. Historically, the y-direction deflections have not been fully developed for domes; thus, no precedence has been established to base the solution. However, it is found that deflections in domes must be divided into two separate theories, based on the geometry of the dome. Shallow domes respond differently to steep domes and therefore necessitates separate theories. A shallow dome is defi ned where the ratio of the height and span of the dome is less than 0.75, and a steep dome where the ratio is greater than 0.75. Shallow and steep dome theories are presented. The developed equations provide a good approximation, which is demonstrated by a comparison with a finite element analysis.