Safety of structures subjected to seismic excitations should be evaluated in probabilistic manner. First excursion failure is one of the most important failure modes of structures. Many structures have nonlinear characteristics. Collision characteristic 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 collision characteristic is proposed. The first excursion probability is the function of many parameters. It is shown that when the tolerance level is normalized by the expected value of the maximum response of the structures, the first excursion probability can be shown to be in dependent of many parameters.

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