Vibration of Asymmetrical Building‐Foundation Systems

Abstract

The vibrational effect caused by an earthquake on an asymmetrical building foundation system is determined by reducing the governing equations of motion to a set of coupled integro‐differential equations involving only the interaction displacements, with the degrees of freedom of the superstructure being eliminated by the modal analysis technique. The formulation facilitates to discard the insignificant modes of the superstructure and, as such, the effort involved in the solution of the eigenvalue problem required for the modal analysis is minimal, especially for a particular class of torsionally coupled buildings. The influence of the eccentricity, shear wave velocity, and the direction of earthquake on the dynamic response of the system is investigated; as the direction of the earthquake is not known a priori, an upperbound solution for the maximum response of the system is presented. It is found that this upperbound solution is satisfactory at low shear wave velocities. At high shear wave velocities, the prediction is slightly on the conservative side. Nonetheless, it is recommended that this upperbound value may be used for design purposes in lieu of obtaining the maximum response of the system by varying the angle of incidence of the earthquake.