Dynamic Behaviour of a Long-Span Steel Footbridge. Characterisation and Modelling of the Dynamic Loading Induced by a Moving Crowd on the Solférino Footbridge in Paris

As footbridges increase in span, flexibility and lightness, they should be designed with greater care regarding vibration phenomena. Dynamic design rules and criteria related to pedestrian comfort become essentials. A description of both experimental and numerical investigations of the dynamic behaviour of such a structure induced by pedestrian walking (moving crowd) is presented here.

First, the vibration modes of the footbridge (frequencies, mode shapes and dampings) below 5 Hz were identified. A monitoring system was used to verify the efficiency of a tuned mass damper (TMD) set at mid span and to collect data to better understand pedestrian and crowd behaviour.

Then, the accelerations induced by the loading generated by a large number of pedestrians walking in various configurations (one way crossing, go and back and circular walking) were measured. The aim was to determine the critical number of pedestrians needed to produce significant vibrations and to explore the phenomena of synchronization between the walk of the pedestrians and the horizontal vibrations of the footbridge.

Later, considering the first lateral mode, a model was developed and tested in order to reproduce the measured events (resonance caused by the lateral force induced by the moving crowd). Parameters such as the crowd velocity, size, density and the level of synchronization of the pedestrians were tested. Various laws of correlation were defined and tested in order to match the tests as well as possible.