Fundamental Study of Q-Δ Resonance Considering Higher-Order Modes by Shaking Table Experiments and Finite Element Analysis

Abstract

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.

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

“…Considering that there is currently a 300‐meter‐high building 15 in Japan and that further high‐rise development is expected in the future, the super‐high‐rise building model was assumed to be an 81‐story building with an eave height of 324 m. The plan dimensions were 100 m × 76.0 m, and the load per unit area for the mass calculation in the dynamic analysis model was 7350 N/m 2 . The height of each story was 4 m. Previous research 12 have shown that 16 Q–Δ resonance conditions exist when considering the second modes in the x , y , and θ directions. In addition, the occurrence of Q–Δ resonance was demonstrated for a specimen satisfying the Q–Δ resonance condition in which the sum of the first natural frequencies in the two translational directions, $$$ {}_1f_x $$$ and $$$ {}_1f_y $$$, coincided with the second natural frequency in the θ direction, $$$ {}_2f_{\theta } $$$.…”

“…In addition, the occurrence of Q–Δ resonance was demonstrated for a specimen satisfying the Q–Δ resonance condition in which the sum of the first natural frequencies in the two translational directions, $$$ {}_1f_x $$$ and $$$ {}_1f_y $$$, coincided with the second natural frequency in the θ direction, $$$ {}_2f_{\theta } $$$. The super‐high‐rise building model considered in this study was assumed to satisfy the same Q–Δ resonance condition that the sum of the first natural frequencies in the two translational directions coincided with the second natural frequency in the θ direction, 2 f θ = 1 f x + 1 f y , which was selected from the 16 Q–Δ resonance conditions 12 . The first natural frequencies in the x and y directions were set with respect to the natural frequencies of real buildings 16 .…”

“…The super-high-rise building model considered in this study was assumed to satisfy the same Q-Δ resonance condition that the sum of the first natural frequencies in the two translational directions coincided with the second natural frequency in the θ direction, 2 f θ = 1 f x + 1 f y , which was selected from the 16 Q-Δ resonance conditions. 12 The first natural frequencies in the x and y directions were set with respect to the natural frequencies of real buildings. 16 Table 1 lists the natural frequencies and periods of super-high-rise building models.…”

“…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. Shaking table experiments conducted using a two-story specimen confirmed that second torsional modes were excited when the Q-Δ resonance condition that the sum of the first natural frequencies in the two translational directions coincided with the second natural frequency in the torsional direction was satisfied.…”

Experiment and Simulation of Q–δ Resonance Using Four-Layer Bending-Shear Type Specimen

“…Mizutori and Kohiyama [3] confirmed the occurrence of Q-Δ resonance by shaking table experiments using a one-story specimen. Anamizu and Kohiyama [4] proposed an equation of motion that considers the Q-Δ effect for a two-story uneccentric structure, and theoretically derived the Q-Δ resonance condition that considers up to the second modes of each direction mode. Shaking table experiments using a two-story specimen confirmed that torsional vibration is excited even when the Q-Δ resonance condition for the second mode of torsion is satisfied.…”