Generalized Equivalent Spectral Model for Serviceability Analysis of Footbridges

This paper proposes a generalized equivalent spectral model of pedestrian-induced forces on footbridges that can be applied in serviceability analysis, from unrestricted traffic to crowded conditions. The model is based on experimental relationships among pedestrian density, step velocity, and step frequency taken from the literature. A suitable physically based expression for the coherence function is introduced that is dependent on pedestrian density and distance among pedestrians; it reduces to perfect uncorrelation for spatially unrestricted traffic and to perfect correlation for crowded conditions. Furthermore, the harmonic content of pedestrian-induced forces is defined as a function of the pedestrian density. Based on the proposed spectral model of the loading, the classic methods of linear random dynamics can be adopted for vibration serviceability analysis of footbridges. Similar to in the wind engineering field, simple closed-form expressions are provided for the evaluation of the maximum dynamic response.