Consideration of uncertainties in seismic analysis of coupled building piping systems

Abstract

In this paper, we present an analytical study for incorporating the effect of uncertainties in modal properties of uncoupled primary and secondary systems in the seismic analysis of non-classically damped coupled systems such as building piping by response spectrum method. Monte Carlo simulation is used to illustrate that the secondary system design response when defined at a non-exceedence probability of 0.84 over the individual responses obtained from multiple response spectrum analyses by considering uncertainties in modal parameters is excessively higher than the design response specified at the same non-exceedence probability over the responses obtained from multiple time history analyses. This is so because the earthquake input in a response spectrum method is characterized by a design spectrum which by itself is specified at a non-exceedence probability of 0.84 over the multiple time histories with normalized peak ground acceleration. Accurate evaluation of design response at a non-exceedence probability of 0.84 in the response spectrum method requires that the individual modal responses be defined at appropriate probability levels that may be different than the conventionally used non-exceedence probability value of 0.84. The required probability values are evaluated by using first order reliability method. It is shown that the modal responses, when defined at a non-exceedence probability of 0.84, would give relatively accurate values of design response only if the individual modes are perfectly correlated or a single mode contributes to the particular response quantity of interest. For all other cases, the design response would be excessively high. The accurate probability values needed to specify each modal response evaluated using the first order reliability method cannot be incorporated directly in a response spectrum analysis due to computational inefficiency. Two simplified methods, based on total probability theorem, are developed in this paper to overcome this limitation. It is shown that these methods give design response values that are very close to the true values obtained from multiple time history analyses.