  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 It\^o
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.
