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 floor torsion angle is the same as both the inter-story and pure torsion angles caused by eccentric torsion and 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 a Steel Reinforced Concrete (SRC) frame structures. After comparative analysis, the lateral–torsional natural frequency ratio considering ground rotation, torsional effect, torsional stiffness, and seismic force of the special-shaped columns are similar to the test results.