A probabilistic approach for estimating the response of multi-degree-of-freedom structures

Abstract Due to the nonlinear nature of the transformation involved in various spectrum superposition techniques, use of a uniform risk design spectrum is not able to carry forward consistently all the effects of seismicity into the response of a multi-degree-of-freedom (MDOF) structure. Therefore, to have a realistic estimate of seismic risk for a MDOF structure, it is proposed to compute the probability distribution function directly for the response amplitudes as a function of the total seismicity expected to occur in the region of the structure. For this purpose, a detailed theoretical formulation has been presented to evaluate the probability of exceeding a given response amplitude due to specified earthquake magnitude and distance. The paper thus provides a basis to compute the response of MDOF structures with a desired risk level.