Lateral stability of footbridges subjected to crowd loading

Footbridges can experience dynamic instability when subjected to crowd loading. This unstable behaviour is the effect of velocity-dependent forces exerted by walkers, that play the role of an apparent damping for the footbridge. For the case of lateral vibrations, such forces have been experimentally measured using an instrumented treadmill. The device allowed measurement of the in-phase and out-of-phase components of the self excited force as a function of the amplitude and frequency of lateral oscillation of the treadmill. The experimental data were then used to develop a dynamic model for the lateral loading of footbridges. In this paper some existing stability criteria for footbridges are summarized and discussed; it is found that these provide quite scattered results. Then an original criterion for lateral vibrations is proposed, and applied using the data derived from the experiments. The criterion evaluates the critical number of pedestrian required to generate a negative motion induced damping force that equals structural damping force. The results obtained though the proposed criterion are compared with those coming from literature criteria, and it is found that there is a quite good agreement with the criterion proposed by Arup based on the behaviour observed on the Millennium Bridge; the agreement with other criteria is worse.