Probabilistic earthquake response analysis of single degree of freedom structures

Abstract

For evaluation of seismic safety of structures, estimation of peak response values has an important role, since the main principle is comparing the capacity of the structure and the demand from exposed strong ground motion. However, the demand shall not be characterized with only the highest peak of the response. Especially, considering overall damage, performance of the structure is related with the amplitude of remaining peaks in the whole duration of the ground motion. In this study, a probabilistic theory, based on order statistics, has been utilized to determine theoretical distribution functions for amplitudes of the local maximum values in the response of different SDOF systems, having five per cent damping ratio, assumed as a characteristic value for a wide range of structures. In this determination procedure, a set of 317 pairs of horizontal earthquake acceleration records from PEER/NGA database has been used, of which the Mw vary between 4.5 and 8 with lowest usable frequency of 0.2 Hz. At first, the amplitudes of all the absolute peaks were calculated from the displacement response time histories of different SDOF systems for each ground motion. Secondly, the highest 50 of normalized peaks were chosen from both horizontal components of the records in order to analyze Probability Density Function (PDF) of the peaks at different oscillator periods. Also alignment of the results of the previous studies on the issue of probabilistic analysis of random functions or of the response of structures under the earthquake excitations which were created by using different methods with the results of this study was investigated. At the end of this study, key parameters, which define the distribution of the peaks for each oscillator period, have been presented for use in the probabilistic estimations of displacement response values of SDOF systems, having a natural period of vibration vary between 0.1 sec and 5 sec. It can be said that the results of this study will contribute to the earthquake resistant design of structures.