Shear and Overturning Moment for Earthquake-resistant Building Design

Abstract

The provisions of the present Canadian and U.S. seismic codes are examined with respect to their requirements on the distribution of seismic forces and overturning moments throughout the heights of building structures. Assuming the code design base shears to be correct, it is shown that the prescribed distribution of lateral forces may underestimate the shear forces in the upper stories of the building. It is further shown that the contribution of the higher modes is not directly related to the height-to-width ratio of the building, but rather to its fundamental period of vibration. By idealizing the building as an average uniform cantilever deflecting partly in a shear mode and partly in a bending mode and by taking a root-sum-square combination of the modal responses to a standard seismic acceleration spectrum, the envelope of the resultant maximum shears throughout the building height is obtained; the maximum overturning moments throughout the building height are obtained in a similar manner. By comparing these with the cantilever overturning moments computed from the shear envelope referred to above, the moment reduction factors applicable to the various levels of a building are calculated. New empirical relationships are then developed to approximate the shape of the maximum shear and overturning moment envelopes.