| Abstract: | An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent. |
