Equivalent spectral model for pedestrian-induced forces on Footbridges: A generalized formulation

This paper proposes a generalized equivalent spectral model of pedestrian-induced forces. The model can be applied for the serviceability analysis of footbridges subjected to unrestricted pe-destrian traffic, but also in crowded conditions, in absence of pedestrian-structure interaction. It is based on the introduction of a suitable physically-based expression for the coherence function and a pedestrian density – velocity law. The proposed coherence model is a function of both pedestrian density and distance among pedestrians: it reduces to perfect uncorrelation for low pedestrian density (i.e. spatially unrestricted traffic), and to perfect correlation for high pedes-trian density (i.e. crowded condition). Since the step frequency, the pedestrian speed and the pedestrian density are strictly correlated, the harmonic content of pedestrian-induced forces depends on pedestrian density. Based on the proposed equivalent spectral model of the loading, vibration serviceability analysis of footbridges subjected to any traffic conditions can be dealt with the classic methods of linear random dynamics. Similarly to classical procedures adopted in the wind engineering field, simple closed-form expressions for the evaluation of the maxi-mum dynamic response are provided.