Modelling of lateral forces generated by pedestrians walking across footbridges

Abstract

The mechanism which results in the synchronization of people walking across footbridges with the bridges fundamental horizontal frequency is studied. The lateral vibration of a bridge subjected to walking pedestrians is modelled by considering the bridge to be a slender beam. The effect of bridge motion on the footfall forces of walking pedestrians is not considered. The contribution of pedestrians varies with their position on the bridge. It is assumed that the walking gait frequency of a pedestrian follows a Gaussian distribution and pedestrians can unconsciously adjust the phase of their walking cycle closer to that of the bridge, based on the theory of coupled oscillators. A time-dependent nonlinear dynamic equation is derived using the modal expansion approach. The model is then applied to the north span of the Millennium Bridge in London, to produce its excessive lateral vibrations. Agreement between the results and the existing observations supports the rationality and reliability of the method. Several parameters, in particular the walking gait frequency of pedestrians, crowd sensitivity to bridge motion, bridge frequency, bridge damping and different load conditions are investigated. The numerical simulation shows that these parameters have different degrees of impact on the critical number of pedestrians triggering excessive vibrations.