This paper presents a semi-analytical estimate of the response of a grandstand occupied by an active crowd and by a passive crowd. Filtered Gaussian white noise processes are used to approximate the loading terms representing an active crowd. Lumped biodynamic models with a single degree of freedom are included to reflect passive spectators occupying the structure. The response is described in terms of the first two moments, employing the Itô formula and the state augmentation method for the stationary time domain solution. The quality of the approximation is compared on the basis of three examples of varying complexity using Monte Carlo simulation based on a synthetic generator available in the literature. For comparative purposes, there is also a brief review of frequency domain estimates. 
The response of grandstands driven by filtered Gaussian white noise processes