Modal coupling and earthquake response of tall buildings

The major dynamic features of tall buildings are within the scope of a shear beam model. Herein the usual one-dimensional model is extended to three dimensions to include modes with translational and rotational components. The analysis is restricted to the continuous model with linear response. A class of models for tall buildings is presented which possesses three sets of mutually orthogonal coupled modes. The amount of modal coupling is related to the eccentricities divided by the translational-torsional frequency differences. Strong modal coupling can occur if the eccentricities and frequency differences are small, as in a rectangular building with a smooth distribution of columns. A perturbation scheme is developed for buildings almost in this class. The perturbation method is applicable to buildings with nearly vertical mass and rigidity centers and with ith-modes of nearly the same shape. Rotational components of earthquake response in buildings primarily results from modal coupling, and it is shown that modal coupling can increase response on the building's perimeter. Furthermore, rectangular buildings with modal coupling can show a beating-type frequency response, for which the more usual r.m.s. combination should be replaced by an absolute sum. These effects can significantly increase certain response parameters. The corners of a rectangular building can have a 95% increase in shear, as compared with 30% implied by a 5% eccentricity in the codes. Base shears and overturning moments can be increased by 40%.