On the reliability of a simple model under nonstationary earthquake excitation

The aim of the paper is to determine the reliability of an earthquake - excited structure. In contrast to the time history and response spectrum analysis a stochastic approach is preferred, thus emphasizing the random feature of the nonstationary excitation process. Seismic response of the structure is analyzed in the sense of reliability. The structure is called reliable, if a characteristic value X(t) does not exceed a critical level within the lifetime of the structure. The probability of this event is calculated by determining the probability of the disjoint event of first passage. For exact determination of the first passage probability a partial differential equation with time-dependent coefficients exists. However, no solution is known because of the complex initial and boundary conditions. Therefore, an approximate solution of the problem must be performed. It can be done by determining upper and lower bounds for the first passage probability according to a formula by Shinozuka. The method is demonstrated with an elastic clamped-free bar model with small viscous damping and makes use of modal analysis. The suspension point of the bar is subjected to a nonstationary excitation process. The first step is to choose a suitable model for the excitation containing all significant features of a strong earthquake. In the following the Levy-Kozin-Moorman process will be used. The next step, therefore, is the computation of the joint-density function of a significant value X(t) (e.g. the maximal stress in the bar or a deflection) and its derivative X(t). The investigations are completed with generating 30 earthquake sample processes on a digital computer