Analytical simulation of 3D wind-induced vibrations of rectangular tall buildings in time domain

The Monte Carlo simulation method for along-wind loads on tall buildings performed in the time and space domain may be the only analytical viable option for specific problems such as nonlinearity behavior, nonclassically damping, and detailed structural models in commercial software. However, both across-wind and torsional-wind loads due to vortex shedding are not usually simulated in time domain because the vertical decay constants are unknown or the empirical coherence functions cannot be applied in Monte Carlo simulation methods. In this paper, the spectral representation (SR) method is used to simulate in time domain the along-wind, across-wind, and torsional-wind loads on rectangular tall buildings considering the vertical correlation between the signals. The Krenk root-coherence function is used for the normalized cross-spectrum on the along-wind direction, whereas the Davenport root-coherence function is used for the other two types of wind loads. For both across-wind and torsional-wind loads, the Davenport root-coherence function was assessed at the vortex shedding frequency by changing the vertical decay constants until converge between the Davenport model and the Liang empirical coherence model was achieved. Based on a three-dimensional model with two translational and one torsional degree of freedom for each floor, the proposed vertical decay constants were validated by comparing the elastic response between frequency domain and time domain approaches. Generally speaking, the results show that peak displacements are significantly underestimated for both across-wind and torsional directions when vertical correlation is neglected. In addition, the advantages of time domain simulation were shown by performing a nonlinear time history analysis considering a bilinear isotropic material hardening model in both translational directions.