An improved spectrum superposition method for structures with rigid modes Original Research Article

Based on a precise probabilistic formulation, a spectrum superposition method has been proposed to obtain very accurate estimate of the seismic response of structures with significant contribution from high-frequency rigid modes. The proposed approach computes the exact statistics of the ordered-peaks of response, which is defined in terms of the first few moments of the power spectral density function (PSDF) of the response. Like many other studies, the PSDFs for various response quantities have been defined in terms of the PSDF of input ground acceleration, the modal properties of a few lowest frequency modes and the pseudostatic response of the structure to an acceleration of unit magnitude. However, the other methods express the final results directly in terms of the response spectrum amplitudes under several simplifying assumptions, which results in unacceptable error in many cases. Due to its exactness, the proposed method has been found to give consistently good agreement with the exact solution for a wide variety of input excitations and structural systems. Furthermore, the present method also has the response spectrum as its basis by defining the PSDF of input excitation which is compatible with a given design spectrum.