Seismic Forces in Spherical Domes: Membrane Solution

With the increase in dome construction that has accompanied the advent of economical balloon-forming techniques, many engineers are now involved in thin-shell dome design. For simple spherical domes of nominal size that are not used as critical or essential structures, a design based on membrane analysis is often adequate. The literature generally available provides equations based on the membrane theory for the analysis a shell subjected to many load cases, including equations for wind loading, however no equations appear to be readily available for determining membrane forces due to seismic loading. Engineers currently use an adaptation of wind-load membrane equations when doing a membrane analysis of shells subjected to seismic loads. This paper presents the development of equations that determine the membrane forces due to seismic forces in a spherical dome in the same manner that membrane forces due to wind load are determined by the wind-load membrane equations. The paper also illustrates the inadequacy of the modified wind membrane equations for approximating seismic membrane forces.