Along‐Wind Motion of Building on Compliant Soil

Abstract

Theoretical investigation is presented for the along‐wind motion of a multistory building under random wind load excitation, taking into account the effect of soil compliancy under the footing. Assuming that the super‐structure is composed of identically constructed story‐units and the soil behavior is characterized by a known frequency dependent impedance matrix, closed form solutions are obtained for the frequency response functions and the spectral densities of structural response. Numerical examples show that soil compliancy decreases the structural response of a moderately tall 10‐story building by about 17%, but increases the response of a more flexible 40‐story building by 21–22%. Some of the frequency response functions are found to be dominated not by the first mode; thus, spectral peaks can theoretically occur near some higher mode frequencies if sufficient wind energy is available around these frequencies. The Davenport spectrum used in the numerical examples, however, has a dominant peak at a very low frequency and diminishes very quickly as frequency increases, resulting in only two peaks in the response spectra in both examples.