Prediction of building response at any level from recorded roof response: The Kanai-Yoshizawa formula revisited

In the 1960s, Kanai and Yoshizawa proposed a simple formula for computing the response of a building at the base or at an intermediate level from recorded motion at the top (refered to here as KY formula). In that formula, derived based on the ray theory of shear wave propagation in a building, represented as a soft layer, the motion at the base is computed simply as the average of two time shifts of the motion at the roof. In this paper, we tested the goodness of the prediction of displacement response by the KY formula in 54 instrumented buildings in the Los Angeles area for which earthquake records are available both at base and top floor (or roof). The results show close agreement of the predicted and observed displacements for a variety of buildings and amplitudes and spectral content of the motions. It is concluded that the KY method can be a practical tool for extending the usefulness of earthquake recods in buildings in which only the roof record is available. It can also be used to predict displacements at any desired level which is useful for estimation of interstory drifts.