Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects

The establishment of a linear seismic response analysis model that considers ground rotation effects and eccentric torsion informed the investigation of the linear response characteristics of coupled lateral–torsional vibration, considering eccentricity and ground rotation, after which the lateral–torsional coupling linear response pattern of special-shaped column structures is examined. The results show that the torsion angle of a floor is equal to the sum of the interlayer torsion angle caused by eccentric torsion and the pure torsion angle caused by ground rotation, respectively. The natural vibration frequency of the structure considering ground rotation effects is a function of relative eccentricity; the period ratio of translation to torsion caused by ground rotation; and the period ratio of translation to torsion when considering only eccentric torsion. When the translation to torsion period ratio, considering eccentric torsion, is greater than 1.0, the torsional amplitude increases remarkably, but the first-order participation mode is considerably higher under the same conditions. The natural vibration characteristics, translational response, torsional response, and seismic force distribution are obtained for special-shaped columns by conducting the shaking table test on steel-reinforced concrete (SRC) frame structures. After comparative analysis, the maximum ratio of the maximum torsional displacement of the bottom layer of the structure to the horizontal displacement in the X direction is 0.0007. The maximum ratio of the base shear force to the theoretical base shear force of the structure without considering coupling is 0.93. The maximum ratio of the measured shear force of the special-shaped column to the theoretical shear force without considering coupling is 0.65. This indicates that ground rotation has a significant amplification effect on structural response. The research results provide a reference for the seismic design of special-shaped column structures.