Torsional response of a bisymmetric structure induced by bending–torsion interaction in vertical members

The biaxially symmetric column induces torsional moment owing to the bending–torsion 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 high-rise 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.