Experiment of torsional response induced by the Q–delta resonance

Abstract

Summary Because of geometric nonlinearities, vibrations in two horizontal directions can generate a torsional moment that induces a torsional response, even in a structure with no eccentricity; we term this phenomenon Q–Δ effect. In this study, the torsional response caused by the Q–Δ resonance was investigated by performing a shaking table test that involves a single‐layer symmetric specimen. The specimen was designed and fabricated by focusing on one of two resonance conditions. Its moment of inertia was adjustable by changing locations of weights, and the natural frequency in the torsional mode could be modified. We developed a numerical model of the specimen, in which the columns connected to the slab were integrated into an elastic Euler beam. It was confirmed that the torsional response increased near the predicted Q–Δ resonance point. In addition, the acceleration at the corner of the slab was significantly increased. The formulated equations of motion provided a better prediction of the actual phenomena. Because the specimen corresponds to a stiff and slender high‐rise building when converted into a full scale, the result suggests a need to be aware of the risk of torsional response increase due to the Q–Δ resonance.

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

“…However, when the results of a recent shaking‐table experiment were compared with simulation results, the resonance conditions were met, but the maximum amplitude of the steady torsional response was significantly different 25,26 . This is because the model did not fully capture the geometrical nonlinearity of the test body used in the experiment.…”

“…However, when the results of a recent shaking-table experiment were compared with simulation results, the resonance conditions were met, but the maximum amplitude of the steady torsional response was significantly different. 25,26 This is because the model did not fully capture the geometrical nonlinearity of the test body used in the experiment. Therefore, in this study, we intend to explain this phenomenon by using a model that assumes that the column is an elastic Euler beam, and we perform a more accurate modeling considering the bending-torsion interaction.…”

Study on a simplified model of a high‐rise shear‐type building for evaluation of Q–Δ resonance

“…The story stiffness values determined in each direction are listed in Table 9. The damping matrix of the simplified model was obtained from Equations ( 9) and (11) such that the damping factors were consistent with those of the reduced specimen, which are listed in Tables 5 and 6. Tables 10A,B show the natural frequencies of the simplified model derived using the aforementioned method, those of the reduced specimen, and the error rates.…”

“…This phenomenon is called the “Q–Δ effect.” When the natural frequencies of two orthogonal translational modes are different and the sum or difference of their natural frequencies coincides with that of the torsional mode, the Q–Δ effect induces resonance of the torsional mode. This phenomenon is called “Q–Δ resonance.” As the torsional moment generated by the Q–Δ effect is proportional to the product of the displacements in the two translational directions, special attention should be paid to this phenomenon in super‐high‐rise buildings, where large displacements occur during a long‐period earthquake motion input 11 . Mizutori and Kohiyama 11 demonstrated Q–Δ resonance via shaking table experiments using a one‐story specimen.…”

“…This phenomenon is called “Q–Δ resonance.” As the torsional moment generated by the Q–Δ effect is proportional to the product of the displacements in the two translational directions, special attention should be paid to this phenomenon in super‐high‐rise buildings, where large displacements occur during a long‐period earthquake motion input 11 . Mizutori and Kohiyama 11 demonstrated Q–Δ resonance via shaking table experiments using a one‐story specimen. Anamizu and Kohiyama 12 proposed an equation of motion that considered the Q–Δ effect for a two‐story non‐eccentric structure and theoretically derived 16 Q–Δ resonance conditions, which was considered up to the second mode in each direction.…”