Stochastic prediction of maximum seismic response of light secondary systems

Abstract

A stochastic model is presented for predicting the elastic response of light multi-degree-of-freedom secondary systems to strong motion earthquakes. Secondary systems may include light mechanical or electrical equipment, piping, or other light systems attached at one or several points to walls or floors of the supporting or primary structures. The critical functions of these secondary systems in nuclear power plants make the accurate prediction of their maximum responses important. The response of such secondary structures may be obtained by a direct time-history analysis, or more approximately, by the response spectrum method. The time-history solution is, of course, expensive; moreover, there is no single representative earthquake and thus a number of possible earthquake ground motions have to be considered. On the other hand, the response spectrum method applied to secondary systems can lead to unreliable results. Within the framework of the normal mode method, a decoupled stationary random vibration model is developed based on the assumption of Gaussian response process and Poisson barrier crossings. The accuracy of the proposed model is verified by comparing the calculated responses, at the 10 and 50% probability of exceedance level, with the second highest and average of the time-history responses from eight normalized accelerograms. The influence of decoupling, i.e. ignoring the dynamic interaction between the primary and the secondary systems, on the response is examined. The influence of nonstationarity is also evaluated. It is observed that nonstationarity is unimportant for earthquakes of relatively long duration, and that for a given damping most of the error can be accounted for by a simple scaling. It is also shown that one aspect of the proposed method constitutes the basis for some of the approximations in the response spectrum method; however, the proposed method yields results that are consistently more reliable than the response spectrum method. Moreover, results obtained with the proposed method represent maximum response statistics from an ensemble of earthquakes rather than a single earthquake.