Crowd
modelling and development of pedestrians load model
The unexpected horizontal vibrations induced by crowds in many footbridges (for instance the Solferino and the Millennium Bridges) highlight the still partial reliability of the design and analysis instruments that are at present available. The incidence of such phenomena on the serviceability state behaviour of footbridges is destined to increase as increasingly light and flexible structures are being conceived. In order to accurately model the crowd force and predict the structural response, the pedestrians action can no longer be simply viewed as an imposed load, because interaction phenomena (e.g. synchronisation) takes place with the structure. Hence, the crowd has been modelled as a dynamic system on the basis of a macroscopic description according to the hydrodynamic analogy, i.e. the crowd is compared to a compressible continuous fluid, whose dynamics is described by means of the mass conservation equation (I order model). The equation system is closed by a phenomenological relation, the so-called fundamental equation, that expresses the crowd velocity as a function of the crowd density, of the travel purpose, of the mean biometric characteristic of the pedestrians and of the bridge deck acceleration. The effect of the latter on the pedestrian density express the action of the structure motion on the crowd, while the action of the crowd on the structure takes place by means of the pedestrians added mass and their lateral force. The latter is modelled by means of a new approach, based on the assumption that the force exerted by a number of pedestrians walking along a portion of the bridge span is given by the sum of three components due to the synchronization between the pedestrians and the structure, to the synchronization among pedestrians and to uncorrelated pedestrians.
