CRITICAL EARTHQUAKE RESPONSE OF WOODEN HOUSES MODELED BY SINGLE-DEGREE-OF-FREEDOM BILINEAR+SLIP SYSTEM SUBJECTED TO PULSE-LIKE GROUND MOTIONS

Abstract

 After Parkfield earthquake in 1966 and San Fernando earthquake in 1971, pulse-like ground motions with a long period and short duration have been observed near earthquake source faults, and structural damages due to these pulse-like ground motions have been reported after the large earthquake events, e.g. Northridge earthquake in 1994, Hyogoken-Nanbu earthquake in 1995, Taiwan Chi-Chi earthquake in 1999, Niigata-Chuetsu earthquake in 2004 and Kumamoto earthquake in 2016. The pulse-like ground motions with a predominant period of more than 1 second can damage two-story wooden houses, and many wooden houses were collapsed during Hyogoken-Nanbu earthquake in 1995.

 Various types of models that can represent the load-deformation relation or restoring force-deformation characteristics of shear walls or mainframes in wooden houses have been proposed. A bilinear + slip model, which consists of the normal bilinear hysteresis and slip-type hysteresis with tri-linear skeleton curve, is one of the restoring force-deformation characteristics for the time-history response analysis of the wooden structures or the shear walls.

 In this paper, a double impulse input is introduced as a substitute for the main part of the pulse-like ground motions which can be modeled by a one-cycle sinusoidal wave or wavelets. Then, in order to estimate the maximum responses of the two-story wooden houses under the critical pulse-like ground motion, the closed-form solutions are derived for maximum deformation angles of a single-degree-of-freedom (SDOF) bilinear + slip model subjected to the critical double impulse input. The critical double impulse input can be defined as the double impulse input with the time interval which maximizes the maximum deformation after the second impulse, and the critical timing of the second impulse can be characterized as the zero restoring force timing. Similarly, the critical pulse-like ground motion can also be defined as the pulse-like ground motion which maximizes the earthquake response. Furthermore, two types of reduction methods of the two-degree-of-freedom (2DOF) bilinear + slip model into the SDOF bilinear + slip model are introduced, and the closed-form solutions for the critical responses and the reduction method can provide the simple evaluation method of the maximum deformation of the 2DOF wooden structures subjected to the critical pulse-like ground motion.

 The validity of the double impulse as substituted for the pulse-like ground motions is investigated through the comparison with the elastic-plastic response of SDOF bilinear + slip model under the one-cycle sinusoidal wave in the critical case and actual recorded ground motions. The accuracy of the proposed estimation method of the critical earthquake response of the two-story wooden houses by using the closed-form solution and the reduction method into the SDOF system is checked through the comparison with the maximum displacement response of the 2DOF bilinear + slip model under the critical double impulse input and the critical one-cycle sinusoidal wave.