A new study from an international team of engineers and mathematicians, led by Georgia State University and the University of Bristol, has figured out the true cause of London’s Millennium Bridge’s infamous ‘wobble’.

The pedestrian crossing over the Thames River, between Tate Modern and St. Paul’s Cathedral, opened in June 2000, with thousands lining up to walk it. Unfortunately, it was forced to shut down two days later as users experienced a troubling sway in the structure as they crossed.

It remained closed for two years while engineers, Arup, investigated unexpected oscillation. It was eventually concluded that the phenomenon could not be stopped, and instead it was decided that the oscillation would be mitigated by retrofitting 37 viscous fluid dampers – 17 chevron dampers under the walkway to control lateral movement, 16 pier dampers to control lateral and torsional movement and four vertical dampers to control lateral and vertical movement.

Experts at the time claimed that the bridge movement was caused by a phenomenon called synchronous lateral excitation ­– when the people on the bridge subconsciously start to walk in sync.

However, the new study, published in the scientific journal Nature Communications, says that this is false.

In their report, experts from Bristol and Georgia explain that they have investigated many other bridges with similar oscillations and have found little to no evidence of synchronicity between walkers.

Instead, they assert that the swaying of the bridge is in fact caused by pedestrians trying not to fall over. The pedestrians walking randomly on the bridge provide ‘negative damping’ whereby the energy from a person’s wobbling is transferred to the bridge.

This conclusion was reached through observational and experimental evidence, new rigorous mathematical analysis and detailed computer simulation.

Large oscillations can occur on a range of bridges. Now, armed with this knowledge, future engineers can avoid unwanted oscillation by ensuring that their bridges’ frequencies are not aligned with typical pedestrian pace frequency.

University of Bristol’s Department of Civil Engineering professor John Macdonald said: “It wasn’t the form of the London Millennium Bridge that caused the problem. These large oscillations can occur on virtually any long bridge when carrying a sufficiently large crowd.

“It turns out that the forces from many random left and right footsteps do not cancel out, but positive feedback leads to the vibrations getting out of hand, a bit like when two or more laptops are too close to each other on a Zoom call, which is ironic because most of this work was conducted over Zoom with our collaborators in Cambridge, Atlanta and Wroklaw.”

Bristol’s Department of Engineering Mathematics professor Alan Champneys said: “This international, multi-university collaboration has been a long story, but shows the unique power of interdisciplinary collaboration between practical engineers, mathematicians and physicists.

“Sometimes the answer is hiding in plain sight, but the wisdom of the crowd has led for many years to an incorrect explanation of what is a very simple idea.”

Georgia State University professor Igor Belykh said: “I have long been fascinated by the mathematical theory of synchronisation, and attempted to apply the theory to bridge instability, but it was only after interaction with colleagues at the University of Bristol, that I realised there was a different story, which has been tremendous fun to finally understand together even if, because of the global pandemic, most of our work has been carried out over Zoom.”

Read the full Emergence of the London Millennium Bridge instability without synchronisation paper here.

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Tagged with: Arup millennium bridge

So if the retrofitted dampers were the right answer to the wrong problem, why did they work?

If the original conclusions were “false” and the dampers worked why should the idea that the problem was “caused by pedestrians trying not to fall over” be true. In a word why should people walking across the bridge be prone to falling over, presumably in large numbers? Seems an incredible conclusion!

Is it possible to produce a link from the paper to some form of visualisation of how this happens? What causes the bridge to move before pedestrians walk on it? What causes them to respond to that movement? Anyone who has been on a ferry or other vessel on the water will be familiar with the changes necessary for pedestrians to maintain balance on something that moves: the same applies to walking down a train, or getting up and walking down a bus before it stops.

Some of us will be aware that a single individual can stand on a small footbridge and jump with a regular timing, perhaps once every two seconds, and feel the bridge ‘spring’ in response, something I learned many years ago while I was an undergraduate. Similarly, and experienced much later in a multi-storey building under refurbishment, bare brick walls after plaster has been removed can be moved with little more than fingertip pressure.

So the main issue of pedestrians affecting structural movement is clear. A video virtual reality version of how this happens from initiation by, eg, wind, to serious oscillation would be helpful. This could be replicated on, eg, small suspension bridges, pedestrian bridges to demonstrate what could happen and ensure that the learning points are better understood.

This study appears to be far too academic and theoretical. There are two very old and well known causes which appear to be much more likely – Architectural Domination and Engineering Real World Subjugation. The aesthetic desires of architects with their rudimentary knowledge of structures backed up by inexpert clients and the position of leadership of design teams – even for engineering projects – which suppress the realities put forward by engineers as negative reaction to their visions. After all, if it has been done before then the architect hasn’t designed it, just copied it. There is a reason why a suspending member requires a reasonable dimension in the plane or planes of suspension in order to resist the component forces in those planes. The dimensions in this case appear to be driven by architectural aesthetics demanding flat catenaries rather than engineering realities. Engineers need to be more assertive or given more authority or someone is likely to get hurt.

This is not ‘new’ it was known about at the time. The original synchronisation of pedestrians wasn’t spontaneous, but a reaction to the movement of the structure once it reached a large enough movement to be detected by the body and reacted to. Professor Roberts (of Cardiff University at the time) talked to me about this in 2007 as part of my dissertation.

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