Membrane Solution for a Catenary Dome

A membrane solution for a catenary dome is presented. The theory solves for the meridian and hoop stresses, assuming a symmetrical load. The theory is extended to solve for domes with an oculus, or rather a circular hole at the apex of the dome. The proposed theory does not include boundary effects, but a verification of the theory indicates that the boundary effects are minimal, compared to other dome shapes. The theory is verified by comparing the equations with a finite element analysis, which indicates an almost perfect match. Only a slight deviation occurs near the boundary, substantiating the legitimacy of the solution.