Analytical Solutions for Torsional Response of Single-Story Frame Structure Subjected to Seismic Wave Passage Excitation

The torsional response of single-story symmetric frame structure subjected to seismic wave passage excitation is studied by analytical method. The dynamic equilibrium equation is established for the single-story frame structure subjected to wave passage excitation. The analytical solutions of translational and angular displacements of the roof centroid, torque and column shear forces of the structure with wave passage excitation are derived. Four sets of column shear forces of two single-story frame structures with two wave passage excitations are calculated and compared with the corresponding results of the uniform excitation. The calculating results show that the column shear forces in the exciting direction with wave passage excitation are related to the distance between the column and the roof centroid in the propagation direction. Compared with uniform excitation, the peak shear forces of columns near the centroid reduce respectively by 79.5%, 81.5%, 23.6% and 31.2%, while the peak shear forces of columns away from the centroid increase respectively by 17.2%, 73.1%, 83.6% and 5.6% with wave passage excitation. The peak shear forces of the distal columns in the direction of wave passage propagation are bigger than those of the proximal columns (facing the wave input). The peak shear forces of the distal columns are 22.9%, 4.4%, 50.8% and 11.3% higher than those of the proximal columns respectively.