Lateral excitation of bridges by balancing pedestrians

Abstract

On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian-structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to 'pedestrian synchronous lateral excitation' or 'pedestrian lock-in'. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field-the inverted pendulum model-for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.

Parallels between wind and crowd loading of bridges

“…The forces induced at the bridge frequency by walkers following Macdonald's [19] model parallel those of flutter, while the synchronization model of Strogatz et al [17] parallels vortex-induced lock-in. The recognition that flutter and vortex-induced vibration can interact led to the proposal that made minor adjustments to the Macdonald [19] model allowing walkers to lock-in.…”

“…The recognition that flutter and vortex-induced vibration can interact led to the proposal that made minor adjustments to the Macdonald [19] model allowing walkers to lock-in. The resulting synthesis appears capable of explaining the high c p values measured by the full-scale crowd load tests conducted by Arup over the full 0.5-1 Hz frequency range.…”

“…Building on an idea of Barker [18], Macdonald [19] models each walker as an inverted pendulum between successive foot placements, with foot placement strategies that provide stable long-term balance. The unobvious prediction of this model is that, even if the walker maintains a constant pacing frequency different from that of the bridge, there are force components created at the bridge frequency as a result of the modulation in foot placement offset relative to the deck.…”

Modelling human actions on lightweight structures: experimental and numerical developments

“…Macdonald [45] achieved the two improvements by utilising a model of human balance developed in the research field of biomechanics [46]. As in the case of Barker's model, he assumed instantaneous transfer of body from one foot to another (basically neglecting the double support phase in the walking cycle), but implemented a more realistic foot placement strategy based on the final displacement and velocity of the BCoM from the preceding step.…”

Balancing on tightropes and slacklines

“…Indeed, a stable upright stance can only be achieved by exploiting a feedback mechanism that creates a corrective torque based on multiple sensory inputs associated with body swaying [1]. In addition to its intrinsic neuromechanical importance, understanding the mechanisms involved with balance may help in the design of biped robots [2], in the diagnosis and amelioration of motor control problems in a range of neurological ailments [3,4], as well as in analysing games, such as stick-balancing [5] and even possibly in the active stabilization of large structures, such as buildings [6].…”