PSI - Issue 78

Anna Brunetti et al. / Procedia Structural Integrity 78 (2026) 1729–1736

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3. Vibration serviceability analysis 3.1. Overview of the Adopted Code

Various guidelines address the issue of vibrations induced by pedestrian traffic on footbridges. In this work, the Sétra guidelines are adopted (Gong et al. 2022), and a brief overview of the document's recommendations for the numerical assessment of vibrations is provided below.

Fig. 2. Finite element model used for the simulation.

Fig. 3.Modal shapes from numerical model.

The load induced by pedestrians on a footbridge is a complex, dynamic phenomenon influenced by the random nature of human movement. The load of a single pedestrian can be represented as a sum of harmonics; conversely, collective behavior is inherently unpredictable. However, to simplify the analysis, the crowd load can be approximated by an equivalent harmonic load ( ) (1), using a fictitious number of synchronized pedestrians ( ) which induce dynamic effects equivalent to those generated by a randomly behaving crowd. However, the simplification that all pedestrians walk at the same frequency is also accepted. ( ) = · (2 ) · · (1) In (1) depends on pedestrian density, the overall deck area and the footbridge damping factor; expresses the magnitude of the force per unit area and depends on both the footbridge classification and the frequency risk interval; is the pacing frequency, which is equal to the resonance frequency of the footbridge under consideration. Finally, Ψ is a factor that considers the probability that the footfall frequency will approach the critical range of resonant frequencies under consideration. The main issue to be addressed is the risk of resonance, which occurs when the frequency of the applied load coincides with one of the structure’s resonant frequencies, leading to significant vibration amplitudes. The dynamic action associated with pedestrian walking is characterised by frequencies within a limited critical range. Consequently, if the natural frequencies of the footbridge are outside this