Multi-Support Seismic Analysis And Program Development Of Long-Span Structures

It is known that,under realistic conditions,there are differences among supports of long span structures due to variations of the ground motion,including the wave passage, incoherence and local effects.The differences in the support motions can significantly influence the internal forces generated in the structure.It is necessary to investigate seismic responses of long-span structures subjected to multi-support excitations.Presently,a seismic analysis can be performed either by the response spectrum method,the time history method or by the power spectrum method.This paper introduces these three methods in detail and discusses their advantages and disadvantages.Based on the power spectrum method of multi-support excitation(Pseudo Excitation Method),the multi-support response spectrum method and the multi-point ground motion time histories are investigated especially,and the finite element based program BPEM is developed.This paper is mainly includes three aspects as following:1) A numerical procedure is described for the response spectrum analysis of long-span structures subjected to multi-support excitations,attention is devoted to the programming strategy of this algorithm.Based on a finite element program BPEM,it has been implemented to make response spectrum analysis of long-span structures under multi-support excitations. Additionally,a simplified method is developed to obtain the cross correlation coefficients by line interpolating of the cross power spectral densities.The MSRS method is extended to deal with three different types of earthquake wave propagating along horizontal direction(i.e.,P wave,SH wave and SV wave),the corresponding formula are also developed.An example of an application is shown regarding the seismic responses of a FE model of a two-span beam for multi-supported excitations.The model is subjected to an extreme multiple-support seismic loading having a PGA equal to 0.5g.The seismic behavior in the three loading situations is illustrated and compared,showing some facets,especially in terms of multi-support excitations for long-span structures.2) The multi-points ground motion simulation method is introduced and a corresponding program is developed using the common trigonometric series method to synthesis seismic waves.The cross power spectral density function is used for consider the spatially varying ground motions.The cross power spectral density matrix is a Hermitian matrix,which can be decomposed into the product of a lower triangular matrix and a upper triangular matrix,so the amplitudes can be expressed by lower triangular matrix,and non-stationary time history is synthesized.Finally,an example is verified to fit a standard response spectrum by generating the acceleration time histories.3) Multi-support excitation seismic response analysis of a long-span bridge is fulfilled by all the three methods(the power spectrum method,response spectrum and time history analysis method) in the program BPEM.The results are compared as well as the program is verified.