Keywords: pedestrian loading, crowd synchronisation, human-structure interaction, footbridge, vibration serviceability.

Improvements in the performance of structural materials and the growing influence of more daring architectural designs have led to lighter and more slender footbridges in recent times. An associated feature of these lighter structures is that they tend to be more susceptible to dynamic excitation from various sources, including pedestrian induced forces.

Some high profile examples exist where bridges exhibited lateral sway under crowd loading which resulted in feelings of discomfort to the bridge users. Consequently, much of the latest research into vibration serviceability performance of footbridges has concentrated on the lateral excitation, with less focus on the vertical response.

This paper presents some of the load models currently proposed for predicting the vertical structural response of footbridges due to pedestrian loading, which require not only pedestrian load factors, but which also feature interaction characteristics both between the individual pedestrians and the vibrating structure and also interaction between a number of pedestrians in a crowd situation.

Several techniques for simulating the vertical forces caused by crowds of pedestrians walking across a flexible footbridge were examined. Approaches adopted in international codes of practice for dealing with vibrations due to crossing pedestrians were described, along with a number of models used to represent individual pedestrians.

The phenomenon of crowd-structure interaction is essentially composed of two elements: the interaction between the crowd members and a moving surface and also the interaction between pedestrians within a crowd. This paper addresses both of these issues.

Approaches reported in the literature for dealing with this are presented and evaluated for a test 50m long test structure with a vertical natural frequency in the range susceptible to excitation from walking pedestrians.

A new approach, whereby a spring-mass-damper model, which has been shown to accurately represent the response from an individual pedestrian, is employed to model each of the individual pedestrians present on the test bridge. This model is examined for the effects of different crowd densities and a range of levels of synchronisation within the crowd.

The results do show that the predicted response is not necessarily linearly proportional to the level of crowd synchronisation, as suggested by previous attempts to model this phenomenon. Nonetheless, the level of acceleration predicted for a crowd density of 1.5 persons/m² and a synchronization level of 20%, which appear to be realistic values for normal crowd behaviour, are within the range predicted by the earlier approaches. This new model considers both interaction between the individual pedestrian and the moving surface and also pedestrian behaviour within a crowd, which has not been done before. It therefore lends itself well to use as a basis of a stochastic approach to the issue of crowd structure interaction in terms of vertical vibration serviceability of footbridges.

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