Determining the peak spatial and resultant accelerations of tall buildings tested in the wind tunnel

This paper presents a frequency domain approach to determine the expected peak spatial (x, y, torsion) and resultant accelerations of tall buildings tested in the wind tunnel. Auto-spectra and cross-spectra are computed from the generalized force time series determined from measured wind tunnel data. Spectral analysis is used to determine the auto- and cross-spectra of the modal responses from which the covariance matrix of the modal responses is calculated. A Lagrangian multiplier technique is then used in conjunction with the mode shapes to determine the peak expected spatial responses in the x, y, and torsion directions, as well as the peak resultant acceleration. The method is applied to three buildings that were tested in the wind tunnel and range from straightforward mode shapes, to complicated mode shapes with a high degree of correlation among degrees of freedom. To evaluate the proposed model, time domain analysis is conducted using the time series of loading determined from the wind tunnel and using artificially-generated wind loading. In all cases considered, the peak spatial responses determined using the proposed method agree with the peak responses observed from the time domain analysis. The proposed method therefore provides a novel, simple, robust, and mathematically justifiable method to determine peak accelerations for buildings subjected to random wind-induced vibrations.