A simplified multisupport response spectrum method

Abstract

A simplified multisupport response spectrum method is presented. The structural response is a sum of two components of a structure with a first natural period less than 2 s. The first component is the pseudostatic response caused by the inconsistent motions of the structural supports, and the second is the structural dynamic response to ground motion accelerations. This method is formally consistent with the classical response spectrum method, and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition. If the seismic inputs at each support are the same, the support displacements caused by the pseudostatic response become rigid body displacements. The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations. In other words, this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation. Moreover, most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise. The results indicate that this simplification can reduce the calculation time while maintaining accuracy. Furthermore, the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures. Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method, the values of internal forces near the supports are underestimated. These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.