STOCHASTIC RESPONSE OF STRUCTURES SUBJECTED TO GROUND MOTIONS

Abstract

The 'first-passage' approach to safety assessment of a structure subjected to random excitations. alms at computing the probability that the response does not exceed a chosen barrier level throughout the duration of excitation. This probability is related to the statistical characteristics of the response. The work of Vaninarcke, and Corotis and Vanmarcke have shown that the first few moments of the power spectral density function of the response are related to the variance of the response and its derivative processes, and can be used to compute the mean failure rate (or hazard function). Two such hazard functons were derived, for both stationary and nonstationary processes-one based on independent barrier-crossings (Poisson hazard function) and another using a two-state description (Markov hazard function). The probability of non-exceedance was expressed in terms of the hazard function. This study was concieved with the aim of gaining an understanding of the first-passage analysis, implications of assuming the response to be stationary or nonstationary and of adopting the Poisson or Markov hazard functions. Using the results of nonstationary analysis, it was intended to construct response spectra which would be useful in design of structures. The scope of the study was restricted to linear single degree-of-freedoni (SDOF) systems subjected to ground motions. An equal, two-sided barrier was chosen as the safe region. A computer program was written to implement the formulation and a series of SDOF systems with damping ratios of 5% and 10%, and tine-periods in the range 0.5s to 4.0s were analysed for two values of the non-dimensional reduced barrier level 2.0 and 3.0. Two ensembles of input excitations, sine wave and earthquake, were used. The results of nonstationary analysis using Markov hazard function were compared with those of other analyses. Poisson stationary analysis predicted the lowest probability of non-exceedance. Its error was in the range of 18% to 50% while Poisson nonstationary analysis showed an error upto 13%. Increase in the damping ratio from 5% to 10% produced a negligible reduction in the probability of non-exceedance. Increase in probability of non-exceedance was upto 20% when 'r' increased from 2.0 to 3.0. Nonstationary response spectra of the sine wave