Behaviour of cylindrical and doubly-curved shell roofs under earthquake

• Main Author: Ostovari Dailamani, Shadi
• Published: University College London (University of London) 2010
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727650

There are indications that thin shells are once again becoming a popular option for roofs covering large column free spaces. Relative to other structural forms there is relatively little analysis of their dynamic response. Especially in seismically active regions, this paucity of analyses could be of considerable significance. This research reports a verification study based upon two independent methods: a finite element 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, displacements, accelerations and stress resultants of the shell under the action of the vertical motions of a selected earthquake. The comparisons showed the FE and analytical results to be in practically excellent agreement. The study of the numbers of modes required for accurate prediction of displacement, acceleration, and stress response for a specific geometry of shell showed that unlike ordinary buildings, in roof shells there is a need to include substantial number of modes for a converged result. 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. The importance of the inclusion of in-plane modes for a cylindrical shell subject to the vertical component of a selected earthquake loading showed that these modes can potentially have a major impact on the predicted levels of in-plane deformation and the associated membrane stresses, and therefore depending on the type of earthquake should be included for reliable estimates of earthquake response. The assessment of the relative importance of the horizontal and vertical components of earthquakes showed that vertical components result in higher accelerations and stresses compared to the horizontal components. In the past investigations of how thin shell roofs respond to earthquakes, attention has been largely restricted to linear analysis, with contributions from pre-loading usually neglected. The independent approaches using finite element solution and a newly developed analytical method indicate that inclusion of self-weight and additional superimposed loading can significantly reduce the predicted natural frequencies. Consequently inclusion of pre-loading is shown to have a major influence on the levels of deformations and the associated membrane stresses. It is concluded that performing a modal analysis in which the effects of pre-loading are ignored could lead to serious underestimation of responses for large roof shells under earthquake loading. Furthermore a nonlinear snap buckling analysis showed that the snap buckling loads are much lower than the classical critical loads in cylindrical roof shell, which suggest a need for a complete nonlinear analysis for the cases of shell with pre-loading close to snap buckling loads. The final section of the present research compares the frequencies and linear responses of a doubly curved shell with a cylindrical shell. The results showed that the frequencies of a doubly curved shell are higher than a cylindrical shell. The increase in the natural frequencies resulted in much lower displacements and stress resultant responses in the doubly curved shell.