Keywords: cylindrical roof shells, horizontal earthquake, vertical earthquake, in-plane modes, out-of-plane modes, seismic analysis.

Despite the growing popularity of thin shells as efficient solutions for covering large column free spaces, there is a surprising scarcity of analyses looking at their response to dynamic loads. Especially in seismically active regions, this paucity of analyses could be of considerable significance. In this paper a verification study is provided for two independent methods of analysis - a finite element (FE) solution and a newly developed analytical method. For typical cylindrical shell roofs these methods have been used to determine the spectra of natural vibration modes. A second verification involved the prediction of the displacement and acceleration responses of the shell under the action of the vertical motions of a typical earthquake, again using both the analytical and FE method. The comparisons showed the FE and analytical results to be in excellent agreement for the natural frequencies and the displacement and acceleration responses of the shell under vertical components of earthquake.

Of practical importance are the numbers of modes required for accurate prediction of displacement, acceleration, stress response for a specific shell geometry. The results of a typical study in which the number of rank order modes is gradually increased showed that the convergence for a certain number of modes might have discouraged the inclusion of further modes, with potentially serious errors in predicted response. This study also showed that the participation of the modes in the stress response was quite different to that in the displacement response, with the dominant modes in the stress response usually having shorter wavelengths than the participating modes of the displacement response. It is shown how this could result in a need for considering substantial numbers of modes to achieve convergence of stresses.

Of the limited past investigations on how thin shell roofs respond to earthquakes, attention has been restricted to consideration of just the out-of-plane modes, with the contributions from the in-plane modes usually neglected. In this paper the importance of the inclusion of in-plane modes for a cylindrical shell subject to vertical components of typical earthquake loading is also investigated. The results show that these modes can have a major impact on the predicted levels of in-plane deformation and the associated membrane stresses. Although the in-plane modes generally correspond with frequencies an order of magnitude higher than those of the out-of-plane modes, it is demonstrated how in some circumstances they should be included for reliable estimates of earthquake response.

Finally, this paper assesses the relative importance of the horizontal and vertical components of earthquakes. For a typical earthquake, the differences in response to the vertical and horizontal components showed that vertical components result in higher accelerations and stresses compared with the horizontal components.

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