Session: SE-01-01 Earthquake Resistance and Seismic Margin

Paper Number: 123215

123215 - Inelastic Response Analysis of 2dofs to Earthquake Motions Based on Superposition of Elastoplastic Response of Each Mode 

This study presents that a time history of the elastoplastic response of the 2-story DOF, consisting of two masses and two springs possessing a bilinear hysteresis and being subjected to a base excitation, can be obtained from the superposition of a time history of the elastoplastic response of each mode. The essence of the proposed analysis is that 1) the mode frequencies and the mode shapes during yielding of arbitrary springs are readily specified by the eigenvalue problem with the mass and the secondary stiffness of the yielding spring; 2) the restoring force vector explicitly includes an intercept of the restoring force axis where the line with slope of either the primary or the secondary stiffness of the spring intersects. First, the equation of motion governing the elastoplastic response of each mode according to the spring state are derived. Direct numerical integral of the equations of motion is carried out and an elastoplastic response history of each mode is calculated respectively. Here, at each time step, the displacement and velocity responses of each mode are superimposed to judge yielding of the springs and turn-around points of floors. Once yielding or tun-around is detected, the modal properties used for the equation of motion of each mode are replaced by the corresponding ones specified from the eigenvalue problem according to combinations of spring states. In addition, the last responses in the present spring state is converted into the initial responses in the next spring state; and then the time history analysis of each mode is continued until the end of the base excitation. Next, it is showed that the time history of the elastoplastic response of the 2DOF calculated by the proposed method is perfectly consistent with that computed by the commercial software TDAP III. Moreover, the time history of the elastoplastic displacement of each mode as well as the force-displacement diagram of each mode are also displayed. Finally, without in-depth discussion on correlation between modal responses, applicability of a modal combination rule for approximating the maximum plastic displacement of each floor is examined. 

Presenting Author: Tomoyo Taniguchi Tottori University

Presenting Author Biography: He finished the master’s course of the graduate school of the University of Tokyo in 1989. After experiencing design of steel structures in Kawasaki Heavy Industries, Ltd. for 13 years, he joined the faculty member of Tottori University in 2001. His research interests in the PVPD related area are analysis of the tank rocking motion, its design method and approximation of elasto-plastic displacement of piping. He served as the chair of the seismic engineering technical committee from 2013 to 2017 and the chair of the fluid-structure interaction technical committee from 2017 to 2021.

Authors:

Tomoyo Taniguchi Tottori University
Yasumasa Shoji YS Corporation
Yukinobu Kimura Kagoshima University