The biaxially symmetric column induces torsional moment owing to the bendingtorsion interaction when the top of the column is given horizontal displacement in the two directions of the principal axes of the cross section and the rotation of the column ends around the axes is constrained. Hence, horizontal ground motions in two directions can cause non-negligible torsional vibration in a highrise building owing to autoparametric resonance. To investigate this phenomenon, in this study, we focus on a single-story structure with an aggregated column, which is a model for columns or core structures in tall buildings and is assumed to be an elastic Euler beam; subsequently we derive the equations of motion under horizontal ground motions in two directions. The resonance condition in the torsional direction is also investigated. Time-series response analyses are performed for input ground motions of harmonic waves, white noise, acceleration records of prior earthquakes, and a long-period design wave, and the relationship between the ratio of two translational natural frequencies and the increase in maximum responses is explained. The results demonstrate that the absolute acceleration response to the long-period design wave could increase by more than 50% in the worst-case scenario.
Torsional moments can occur in a column owing to the geometric nonlinearity when the top of the column undergoes a large displacement in two horizontal directions. Periodically generated torsional moments can excite the torsional mode of a building owing to the internal resonance. For high‐rise buildings, there is a risk that long‐period seismic motions can cause a non‐negligible torsional response due to this phenomenon. To investigate this risk, this study focuses on non‐eccentric single‐story and two‐story shear‐type structural models with an aggregate column, which is assumed to be an elastic Timoshenko beam. We derived the equations of motion for the models under horizontal ground motions and confirmed that the equations were identical to those of the models with an aggregate column of an elastic Euler beam. We then performed time‐history response analyses of the models satisfying the internal resonance conditions under the input ground motions of harmonic waves, Gaussian white noise acceleration, acceleration records of previous earthquakes, and a long‐period design wave. The results showed that the maximum horizontal acceleration at the corner of the top floor slab could be increased by more than 60% of the acceleration at the center of the slab in the worst case.
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