Pedestrian-induced oscillation phenomenon in footbridges
When a pedestrian walks in sync with a ground oscillation, the lateral foot forces exacerbate already existing oscillations, leading to a positive feedback loop known as synchronous lateral excitation. Adapted from Figure 5-15 of Butz, C., et al. "Advanced load models for synchronous pedestrian excitation and optimized design guidelines for steel footbridges (SYNPEX)." RFCS-Research Project RFS-CR-03019 (2007).[1]
Synchronous lateral excitation is a dynamic phenomenon where pedestrians walking on a footbridge subconsciously synchronize their lateral footsteps with the bridge’s natural swaying motion, amplifying lateral vibrations.[2][3] First widely recognized during the 2000 opening of the London Millennium Bridge, synchronous lateral excitation has since become a critical consideration in the design of lightweight pedestrian structures.[4][5][6]
Mechanism
As the number of pedestrians on a footbridge increases (black line in steps), the lateral oscillations increase (gray area). After a critical number of pedestrians is reached (166 in this example), the bridge enters a stage of synchronous lateral excitation. Simplified graph based on page 37 of Parker, Matt. Humble Pi: A Comedy of Maths Errors. Penguin UK, 2019.[3]
Synchronous lateral excitation arises from two interrelated synchronization processes. The first is the pedestrian-structure synchronization, where slight lateral bridge movements (e.g., from wind or random pedestrian steps) prompt walkers to adjust their gait to match the bridge’s oscillation frequency, increasing lateral forces.[7]
The second is pedestrian-pedestrian synchronization, where individuals unconsciously align their stepping patterns, further reinforcing the resonant force.[8][9]
Key cases
The London Millennium Bridge experienced lateral vibrations up to 70 mm due to synchronous lateral excitation, requiring a £5M retrofit with dampers.[2][4]
The Birmingham NEC Link bridge experienced a lateral frequency of 0.7 Hz.
The Toda Park Bridge in Japan is an early documented case (1990s) studied by Fujino et al., informing later synchronous lateral excitation models.[7]
Mitigation strategies
Some ways to avoid synchronous lateral excitation are the implementation of tuned mass dampers, which were used in the Millennium Bridge to increase damping from 0.5% to 20% critical.[4] Other strategies involve designing bridges with lateral frequencies outside the 0.5–1.1 Hz range as well as managing crows by limiting pedestrian density during events.[5]
