Probability Distribution of Torsional Response by Qﾖ? Resonance of Multi-Story Building under Long-Period Seismic Motion

Abstract

When the sum or difference of the natural frequencies in the two horizontal translational modes coincides with the natural frequency in the torsional mode, an internal resonance phenomenon occurs because the torsional moment owing to geometric nonlinearity synchronizes with the torsional response. The authorﾒs research group calls this phenomenon Qﾖ? resonance. Since Qﾖ? resonance is not considered at all in current seismic design, it may be a potential danger in high-rise buildings. Therefore, the probability distribution of torsional response was evaluated by Monte Carlo simulations using a multi-story building model. The input wave was simulated using nonstationary colored-noise ground motion, which was based on the response spectrum for long-period long-duration seismic design motion. The results of the Monte Carlo simulations for a 60-story building showed that, when it has close proximity to the resonance condition where the sum of the natural frequencies in the translational directions corresponds to the second natural frequency in the torsional mode, the percentile values of the angular acceleration of the top slab tend to increase with the proximity to the resonance condition. It was also confirmed that even on the low frequency side, the response tended to increase accidentally due to different resonance condition of other higher modes.