Simplified Estimation Method for First Excursion Probability of Secondary System withHysteresis Characteristics

摘要

When the secondary system such as pipings, tanks and other mechanical equipment installed on the primary system such as buildingsis subjected to excess seismic load, the response of the system exceeds yield deformation. In this paper, an simplified estimation method ofthe first excursion probability of the secondary system with hysteresis loop characteristics caused by plastic deformation is proposed. As ananalytical model, the primary system and the secondary system are simulated as single-degree-of-freedom system respectively for simplicity.As restoring force-deformation relation, bilinear hysteresis loop characteristics is used. First, an analytical method for the secondary systemwith hysteresis loop characteristics caused by plastic deformation is presented. This method is based on equivalent linearization method. Asinput excitations, two kinds of artificial time histories are used. One is nonstationary filtered white noise and the other is artificial time historycompatible to the design response spectrum. Next, by using the proposed method, some numerical examples are shown. From the numericalexamples, it is found that when the tolerance level is normalized by the maximum response or the maximum standard deviation of responseof the linear secondary system without plastic deformation, the first excursion probability is independent of mass ratio of the secondarysystem to the primary system, the damping ratio and the natural period of the sexondary system. For aseismic design of structures, responsespectrum which corresponds to the maximum response of the single-degree-of-freedom system is used. The maximum response of thesecondary system can be estimated by amplification factor or modal analysis. The maximum standard deviation corresponds to the maximumresponse. The proposed method is expected to be practical and simplified estimation method of the first excursion probability of thesecondary system.