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Publication - Professor John Macdonald

    Lateral excitation of bridges by balancing pedestrians


    Macdonald, J, 2009, ‘Lateral excitation of bridges by balancing pedestrians’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol 465., pp. 1055 - 1073


    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.

    Full details in the University publications repository