When the system is subjected to excess seismic loading, spring element has hysteresis loop characteristic caused by plastic deformation. Energy is dissipated by hysteresis loop characteristic. Elastic-plastic damper which utilizes energy absorption is practically used. On the other hand, response is nonstationary random process because seismic loading is nonstationary random process. In such a case, reliability of the system should be evaluated in probabilistic manner. Some failure modes are observed. First excursion failure is one of the most important failure modes. First excursion probability, that is, probability of occurrence of first excursion failure, also represents the characteristic of random process. In this paper, the first excursion probability and absorbed energy by hysteresis loop characteristic are obtained from theoretical method. This method is based on equivalent linearization method. Bilinear hysteresis loop characteristic is used as force-deformation relation. It is concluded that the first excursion probability decreases with the increase of absorbed energy.

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