A new study warns of potential risks to bridges around the world

Bridge designers should realize that there can always be serious cases of negative damping if the crowd is large enough.

Researchers at Georgia State university have revealed a surprising new explanation for why pedestrian bridges suddenly start shaking and swaying when so many people cross them at once.

This new interpretation contradicts the 20-year belief that bridges vibrate because the frequency of their vibration matches the frequency of the footsteps in what is scientifically called the Resonance phenomenon.

Large moving energy of individual steps

In the new study, published in the journal Nature Communications on December 10, a group of Georgia mathematicians led by Professor Igor Belych and colleagues at the University of Bristol and Cambridge University showed of Cambridge) and the University of Leicester in Britain how a well-designed bridge such as the Golden Gate Bridge or the Brooklyn Bridge can suddenly become unstable.

According to a report published on the "Science Alert" website, the scientists suggested that when there are enough people crossing on foot, and each walking at their own natural speed, they will transfer so much energy to the bridge that it can begin to swing with it. Once the bridge starts to vibrate, each person adjusts their steps to try not to fall, and this destabilizes the bridge.

The oscillation of the bridge can lead to a state of mass panic, as happened in 1987, on the 50th anniversary of the founding of the Golden Gate Bridge in San Francisco, when 300,000 people - who came to celebrate its opening - tried to cross the bridge, which took a sway, and caused So panicked and dizzy and people started throwing bikes and prams into the ocean to lighten the bridge's load.

The researchers studied data collected on 30 bridges and used complex mathematical equations that predict the exact transition point to the swing state of a given bridge based on determining the exact number of people who will cause it to move.

In a press release posted on the Georgia State University website, Belich said, "Our work shows that the very small vibrations generated by each person walking on the bridge can be greatly amplified."

Negative damping and vibration amplification

In 2003 New York City lost power, a crowd of pedestrians returned home across the Brooklyn Bridge in the dark, and the large crowd of pedestrians shook the bridge so hard that some pedestrians felt seasick and couldn't keep their balance when they stopped moving.

In 2000, the Millennium Bridge in London was called the wobbly bridge because of its oscillating movement that coincided with the crossing of crowds on opening day, causing the bridge to close immediately and not reopen for two years. Watching videos of pedestrians on the Millennium Bridge you will notice that their heads and torsos move in unison like a wave.

A study published by Belich and his colleagues in the journal Science Advances in 2017 showed that the Millennium Bridge in London remains stable when 165 people walk over it, and that adding another person completely reverses the scales. Thus, the researchers were interested in studying the effect of the number of transients on the turning point of the bridge from a state of stability to a state of continuous oscillation without fading or subsiding in what is scientifically called negative damping.

"Think of passengers walking on a boat swinging in rough seas, they will adapt their movement to the movement of the boat swinging left and right as well as forward direction in response to the boat's vibration; the passengers will slow their movement forward," Belich said. Scientifically called "negative damping or non-damping", and then the movement continues without fading.

"Bridge designers must realize that there can always be serious instances of negative damping if the crowd is large enough," Belich added. "Our developed formula provides useful estimates given the expected number of pedestrians who could be on a bridge."