The secondary system such as pipings, tanks and other mechanical equipment are installed in the primary system such as building. The important secondary systems should be designed to maintain their function even if they are subjected to destructive earthquake excitations. First excursion failure is one of the most important failure modes. The secondary system has many nonlinear characteristics. In this paper, an estimation methods of the first excursion probability of the secondary system with gap and friction subjected to earthquake excitation is proposed. Restoring force with gap and friction force is equivalently linearized. When the tolerance level is normalized by the maximum response of the secondary system without gap and friction characteristics, variation of the first excursion probability is very small for various values of mass ratio of the secondary system to the primary system, the damping ratio and the natural period.
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