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

Abstract

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 behavior of a non‐eccentric structure considering the effect of shear deformations in vertical members

“…Thus, the response increase due to the Q – Δ effect is likely overlooked. This study confirm that the equations of motion derived previously 3 can be applied to a structure in which the shear deformation is dominant in the vertical members. In other words, the proposed method can reveal the Q – Δ resonance risk for a large number of buildings without a 3D frame analysis.…”

“…In this chapter, we assume a single-story model with a square slab of side length 40.0 m and gyration radius r θ of 20.0 m, as used in a previous study. 3 Because the impact of the Q-Δ resonance on the story drift ratio is small, we focus on the increase in the acceleration response. When torsional vibration occurs, the absolute maximum acceleration response at the corner of the slab A Cmax becomes larger than the absolute maximum acceleration response at the center of the slab A Gmax .…”

“…In a previous study 3 the column was assumed to be an elastic Euler beam and the following equation was used to relate the cross‐sectional rotation angle to the deflection angle:…”

“…In Equations (20a-c), the coefficients of the nonlinear terms agree with those of a previous study. 3…”

“…The maximum acceleration amplification ratio (the K-NET Furukawa record)T y [s]Assuming the resonance condition of ω θ = ω x + ω y is satisfied3 Assuming the resonance condition of ω θ = ω x − ω y is satisfied…”