Study on the Accuracy of Response Spectrum Method for Long-span Reticulated Shells

Abstract

Due to large number of degrees of freedom, long-span reticulated shells have densely distributed natural frequencies and complex vibration modes. The accuracy of response spectrum method (RSM) is then often doubted for this kind of structures. In this paper, the seismic design of Laoshan Cycling Gymnasium for Beijing 2008 Olympic Games was taken as a case study. The result of RSM was verified by comparing with that of time history analysis. Modal effective mass was defined for reticulated structures to illustrate the direction of mode vibration and identify effective modes along specific directions. The required number of modes to ensure the accuracy of RSM for long-span reticulated shells was then determined based on effective mass ratio along the excitation direction. It was concluded that if the effective mass ratio exceeds 90%, the result of RSM with CQC as the modal combination rule will be accurate enough for practical seismic design of long-span reticulated shells.