The Millennium Bridge, a suspension bridge that links St Paul’s Cathedral in the City of London with the Tate Modern gallery in Southwark in south London, is a pedestrian-only bridge that is 320m long and allows people to cross the River Thames. London’s first new river crossing in over a century, the Millennium Bridge was inaugurated by the Queen in May 2000 and was thrown open to the public on June 10, 2000.
The end is the beginning
But wait. When we are generally talking about new bridges in this column, don’t we usually talk about how it came to be, before going on to finish the article with its inauguration? Why then did I mention the inauguration in the very first paragraph this time? Only because what would have generally been the grand finale of a giant project turned out to be the start of something quite unexpected.
Designed in collaboration between the architects, Foster and Partners, the British sculptor, Sir Anthony Caro and the consulting engineers, Arup, the Millennium Bridge was constructed at a cost of £18.2 million. The promoters called it a “blade of light” and the hype and hoopla surrounding it through the construction meant that people were thronging the area to make the crossing in the opening weekend.
Things get shaky
And that’s when things started to get shaky. A large number of people on the bridge meant that a fault was exposed. People felt a swaying sensation, akin to sea-sickness, as the bridge developed an unexpected and potentially dangerous lateral wobble. An estimated 1,60,000 people crossed the bridge that weekend, before it was closed down to conduct repairs.
By February 2001, the Millennium Bridge Trust announced that they had raised over £5 million to carry out the recommended modifications. Work to install 91 dampers, similar to car shock absorbers, was then carried out to reduce the movement of the structure. Following a walking test on the bridge with 2,000 volunteers, it was deemed to be safe and was reopened to public in February 2002.
A chance to learn
While the bridge has been working fine ever since, it hasn’t stopped scientists from looking at this particular example and learn more from it. Though engineers expect all bridges to move a little with the weight of cars, people or even wind conditions, it is dangerous conditions like these that provide insights into how to further improve the industry standards.
One of the earliest studies on this incident, from Cornell University in 2005, suggested that people unwittingly walking synchronously had caused the bridge to wobble. This does account for the wobble increasing once the bridge had started to sway and explains how the problem is as much about crowd dynamics as it is about engineering.
Phase-locking
This phenomenon, also referred to as phase-locking or the collective behaviour in mechanical systems, has been known for centuries. The military have been aware that troops marching in step can create enough vertical force to destroy a bridge. It is for this reason that there is a standard practice for troops to break step while crossing bridges.
As the movement was more lateral in the case of the Millennium Bridge, the search for better explanations continued. In 2008, a study by civil engineers at the University of Bristol looked at how humans stay balanced while walking and how it influenced this particular situation. The initiation of the wobble, they said, could well be because the pedestrians were balancing themselves while walking.
Balance and energy
Based on the final displacement and speed of the centre of mass from the previous step, an individual achieves balance by placing the foot appropriately in each step. When the same strategy of walking on a stationary surface is applied to walking on a bridge, the individual can act as a damper, feeding energy into the bridge oscillations.
The most recent study in this subject came out in November 2017 from applied mathematicians at Georgia State University. Using complex mathematical models they were able to determine that wobble in bridges happen suddenly after the crowd goes past a critical threshold – 165 in the case of the Millennium Bridge. The cause for the initial wobbling, they guessed, could have something to do with switching one’s gait in order to find balance.
So the next time you are on a bridge, remember that when you are walking on it, you are pushing it as well. You might not always feel it, but it sways, you respond and it sways again. On and on. Understanding this helps us to tackle the vibration problems, and hence construct better bridges. Now, and for the future...
