The Q-Δ effect is a phenomenon that a column with different lateral stiffness generates a restoring torsional moment owing to geometric nonlinearity when its top displaces in two horizontal directions simultaneously. The Q-Δ resonance that is resonance of a torsional mode induced by the periodic torsional moment due to the Q-Δ effect could cause considerable torsional vibration even in non-eccentric buildings. However, the Q-Δ resonance in higher-order modes has not been investigated well. We first constructed a model of a two-story non-eccentricity structure and derived the conditions of the Q-Δ resonance considering higher-order modes.Then, we conducted shaking table experiments and finite element analysis to reproduce the experiments. As a result, it was confirmed that the second mode in the torsional direction was excited as predicted by the derived Q-Δ resonance condition. Moreover, the finite element analysis could reproduce the experimental result with high accuracy.

To evaluate Q-Δ resonance, which is a torsional resonance phenomenon caused by geometric non-linearity, we proposed a simplified model for an n-story non-eccentric building model with a shear-type structure. We designed and fabricated a four-story small-scale specimen assuming a noneccentric steel structure with a height of 324 m, and conducted shaking table tests. As a result, the occurrence of Q-Δ resonance was confirmed as predicted by the simplified model. In addition, the simplified model reproduced the resonance amplitude in a finite element model of the specimen with the out-of-plane rotation of slabs constrained and its validity was confirmed.