A simplified method based on improved multiplication factors to assess crowd-induced vertical vibrations of footbridges

Due to the high mechanical performance of new structural materials, modern footbridges are usually slender and lightweight structures. It follows that their natural frequencies often fall within the typical range of pedestrian pacing frequencies, feature that renders them rather sensitive to human-induced vibrations. Special care is therefore needed to avoid excessive levels of swaying, both to safeguard pedestrians from being bothered by the sense of discomfort and to prevent the functionality of footbridges to be compromised. However, in contrast with the single person dynamic force, the characterisation of the crowd-induced loading is rather challenging, time-consuming, and thus scarcely compatible with the design stage needs. This paper proposes an analytical model based on the multiplication factor approach, which allows to predict the vertical crowd-induced response from that of a single pedestrian. The work is based on extensive numerical simulations, carried out in due respect of human-human interaction and pedestrian step forcing variability. Besides, the possibility of managing human-structure effects is also foreseen. The method is meant to handle the vibration serviceability check of a wide range of scenarios, including a broad spectrum of footbridge parameters and crowd densities. For validation purposes, model predictions are compared against regulations and experimental results.