Estimation of reliability of system subjected to earthquake excitations is important problem for aseismic design. Reliability of such system should be evaluated in probabilistic manner. First excursion failure is one of the most important failure modes of structures and one of a factor of reliability. Many structures have nonlinear characteristics. Hysteresis loop characteristic caused by plastic deformation is one of the most common nonlinear characteristics observed in pressure vessels and piping systems. In this paper, an estimation method for the first excursion probability of structure with hysteresis loop characteristic is proposed. The first excursion probability is the function of many parameters. First excursion probability is obtained by using artificial time histories. It is shown that when the tolerance level is normalized by the expected values of the maximum response of the structures, the first excursion probability can be shown independent of many parameters.

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