Harmonics in a Multi-Story Structure

Abstract

THE design of structures to withstand earthquakes is largely empirical. It is found, from experience, that, if the structure is designed to withstand a horizontal acceleration of one-tenth that of gravity, the building suffers no more than superficial damage even in a major earthquake. Spectra of earthquakes prepared by Housner¹ would appear to indicate that accelerations much greater than this design value are reached. If any tall building is postulated, the lack of a theoretical basis for the accepted design criterion causes considerable hesitation, particularly where one or more of the harmonic frequencies of the building may coincide with partial frequency components of the earthquake. This uncertainty is largely responsible for structure design in New Zealand, and in some American areas, being limited to a maximum height. (In New Zealand this maximum height is 100 ft.) Prof. L. Jacobsen and Robert S. Ayre² commented on a uniform building (mass and rigidity constant at each story): “Current design rules give reasonable results for the fundamental mode shears only and the higher mode shears require considerable increases in the proportionality or percentage factor, especially in the upper part of the building”.