Civil Engineering Technical Report Series - Strong Motion Group Contributions CE 96-01

The earthquake ground motion and the resulting structural response can both be viewed as nonstationary stochastic processes. A stationary process is characterized by a time-independent power spectral density function (PSDF), whereas the PSDF of a nonstationary process evolves with time. The probability distributions of stationary processes are used to study the statistics of nonstationary processes, under the assumption that a nonstationary process behaves like a stationary process at each instant of time. In the present study, detailed simulation tests have been carried out to find which of the available probability distributions best describe the statistics of peaks in the stationary processes. When the peaks of a stationary stochastic process are arranged in decreasing order of amplitude, the probability distribution of the n-th ordered peak is defined in terms of the root-mean-square amplitude, α sub RMS, a parameter, ε, related to the band-width of the PSDF, and the total number of peaks, N, in the process, all of which are defined in terms of,the zeroth, second and fourth order moments of the PSDF.; The nonstationarity of ground acceleration is most commonly modelled by an idealized deterministic envelope function multiplying a stationary stochastic process, which is invariably defined by a Kanai-Tajimi PSDF. The nonstationary seismic response of structures to such an excitation is strongly dependent on the subjectively chosen envelope function and the parameters of the Kanai-Tajimi PSDF, and thus cannot be considered as accurate, unique and realistic. Further, this involves very lengthy calculations and does not provide any additional information of practical use, other than the maximum response amplitude and the approximate duration over which such large amplitudes are sustained. Thus the conventional nonstationary response analysis is not worthwhile. On the other hand, it is shown that by using the statistics of ordered peaks, the amplitudes of all the significant peaks of the response can be evaluated accurately by a simple stationary analysis only. For this purpose, an equivalent stationary PSDF has been defined to represent the strong-motion stationary part of the ground acceleration such that it is compatible to the response spectrum of the accelerogram. Because the response spectrum inherently includes the effects of the nonstationarity in the maximum response of SDOF systems, the spectrum compatible PSDF automatically accounts for the nonstationarity of the input excitation in computing the highest few peaks of the response of MDOF structures.; A comparison of a large number of theoretical results obtained by using the equivalent stationary PSDF with the exact time-history results for the strong-motion peaks of the response has shown very good agreement for the responses of MDOF structures with classical as well as nonclassical damping. In the present study, the effect of modal correlations has been computed very accurately, and the fact that structures with long natural periods may not attain their final steady state response has been taken into account. The use of equivalent stationary PSDF can be easily extended to evaluate the response to multi-component and rotational excitations including the effect of soil-structure interaction. This provides a more convenient, simple and accurate approach compared to all the available studies.