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When we cross a bridge, we expect it to remain level, but a big enough group of pedestrians can cause a bridge to sway. This happened in 2000 when London’s Millennium Bridge first opened. The sleek suspension footbridge wobbled dangerously underfoot as thousands of pedestrians crossed the river Thames, forcing a shutdown and millions of pounds in alterations.
Igor Belykh at Georgia State University in Atlanta says the Millennium Bridge’s swaying steel was a result of the footfalls of pedestrians lining up with the bridge’s natural frequency, the rate at which it must be subjected to force to start moving. Every bridge has a natural frequency based on its length, width, and the material it is made of, and Belykh has created a model that shows just how many people would need to cross any bridge to send it wobbling.
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Imagine you’re swaying on a swing, trying to get it to rise by moving your body back and forth. If you rock too quickly or too slowly nothing happens. But moving your legs at the right interval gets you swinging. The same is true for people stepping left and right on a bridge at a certain pace. If a crowd’s footfalls match the bridge’s frequency, it’ll start to sway, too.
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A noticeable jump
It used to be believed that the bigger the crowd, the bigger the wobble. But Belykh’s model shows that it isn’t just synchronised steps that start the swaying. Instead, it’s a numbers game. Once the crowd reaches a critical size, the bridge beneath them will wobble.
“We’re trying to accurately describe the magic number of people who can be on a bridge at a time,” he says. Before you hit that crucial threshold, any wobbles on the bridge – say, from wind – would be too small to feel. But when the right number of people are walking across a bridge at the same time, there’s a noticeable jump in swaying.
And once this jump happens, the fact that we all move similarly to stabilize ourselves can make a bridge sway even more. Belykh says people will adjust their natural gait to counteract the motion and stay upright.
Bruno Eckhardt at the Philipps-Universität Marburg in Germany says there’s still a key element missing from Belykh’s study: experimental studies of actual people walking on bridges, in lieu of computer simulations and mathematical models.
“Before any of these models end up in a civil engineering code, you have to collect evidence from each of these bridge swaying incidents – detailed studies of when they happen, the bridges’ properties and the number of people – and see if these models help make a good prediction,” he says.
Journal reference: Science Advances, DOI: 10.1126/sciadv.1701512
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