A spectral model for pedestrian loading of footbridges

Modern footbridges can be very sensitive to walking-induced vibrations. The assessment of footbridges vibrations due to flows of unsynchronized pedestrians is a topical problem in the serviceability analysis of these structures. In this paper real pedestrian traffic conditions are modeled probabilistically, considering several sources of randomness among which pedestrian arrivals, walking frequencies and velocities, force amplitudes and pedestrian weights. Based on such a probabilistic model and on the analysis of peculiar non-dimensional parameters, a spectral model for the modal force induced by pedestrian groups, modeled as a stationary random process, is introduced under suitable simplifying assumptions. Numerical simulations with different values of the involved parameters are performed, in order to assess the limits of the proposed model. Starting from the proposed spectral model of the loading, vibration serviceability analysis can be tackled with the classical methods of linear random dynamics. Simple closed-form expressions for the evaluation of the maximum dynamic response are provided. The proposed loading model is based on the stationarity assumption for pedestrian-induced forces: the definition of a conventional duration of pedestrian flow that makes the loading process stationary is an open point for discussion that appears fundamental in order to validate the possibility of technically using a spectral approach, like the one here proposed.