written by LaTina Emerson
When crossing a bridge by car or on foot, most people take for granted the bridge will remain steady and support them, but history shows that’s not always the case.
“The list of faulty bridges is long,” said Dr. Igor Belykh, associate professor of applied mathematics and mathematical biology at Georgia State. “Many bridges have experienced dramatic vibrations or have even fallen down.”
The London Millennium Bridge, a steel pedestrian bridge crossing the River Thames, is infamous for its opening-day oscillations in 2000. As thousands of pedestrians walked over it, the bridge began to sway slightly, and the wobbling intensified as people fell into step, planting their feet wider as they tried to steady themselves as they walked. The $32 million bridge was closed almost immediately.
Watch a video of the London Millennium Bridge’s opening day.
The Squibb Park Bridge in Brooklyn, N.Y. was closed in 2014 after unusual movement. While the wooden bridge was designed to have a subtle bounce, the bridge started to bounce more and move from side to side, alarming the people who were crossing. The $4.1 million bridge has remained closed, and the Brooklyn Bridge Park Corporation is suing the engineering firm that designed it.
Belykh is working to make bridges safer, particularly pedestrian bridges.
“The U.S. code for designing pedestrian bridges does not have explicit guidelines which account for pedestrian or crowd dynamics,” Belykh said. “That’s the gap we’re trying to fill. We want to contribute to revamping the industry-standard computer programs for designing bridges and attempt to avoid faulty designs.”
With funding from the National Science Foundation, Belykh is developing a biomechanically inspired model of pedestrian response to bridge motion. The model, derived from complex mathematical equations, captures the key properties of pedestrian lateral balance and pedestrian foot forces on the bridge.
“Our work could be used as a safety guideline for designing pedestrian bridges or limiting the maximum occupancy of an existing bridge,” he said.
Some attribute the wobbling of pedestrian bridges to a phenomenon called synchronous lateral excitation or crowd synchrony. When pedestrians walk across a bridge, they interact with it, causing the bridge to oscillate.
Belykh explores pedestrian-bridge interactions in his latest research. He recently published a paper in the journal Chaos: An Interdisciplinary Journal of Nonlinear Science that studies the interaction of a single pedestrian with a bridge. Using a biomechanically inspired model of human balance, he analyzes the model’s interaction with a lively bridge.
He found that pedestrian-bridge interactions can make the pedestrian walk with two distinct lateral gaits. Both gaits can correspond to pedestrians walking out of phase with the bridge, but one gait produces significantly larger bridge oscillations than the other. A pedestrian can initiate wilder vibrations of the bridge by switching between the gaits.
“If you walk across a light bridge and something happens and you misstep, that misstep can switch your gait and you start walking differently,” Belykh said. “Then, this would cause the bridge to sway. Our results support a claim that the overall foot force of pedestrians walking out of phase can cause significant bridge vibrations.”
In a paper that will soon be published in a journal for the Society for Industrial and Applied Mathematics, Belykh used biomechanically inspired models of lateral crowd movement to investigate the degree to which pedestrian synchrony must be present for a bridge to wobble significantly. He also tried to determine a critical crowd size. The pedestrian models can be used as “crash test dummies” when numerically testing a specific bridge design.
Belykh hopes to one day make these pedestrian models available to bridge engineers through software programs.
“What we want to do is better help engineers understand the role of pedestrians in the initial formation of a bridge formula and avoid the range of dangerous frequencies, which cannot be identified through conventional linear calculations, to eventually design robust bridges,” Belykh said.
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Belykh has also partnered with researchers at the Georgia Institute of Technology and the University of Bristol in the United Kingdom to study the transition from bobbing to jumping on grandstands. This transition to unwanted crowd jumping as the response to vertical vibrations of grandstands in sports stadiums and concert stages is a major safety concern because it may cause a fatal structural collapse.
In the following video, watch supporters making the concrete arena bouncing.
“When designing sports stadiums, possible bidirectional interactions between the supporters and the vibrating ground structure are typically ignored. This calls for reliable models of human bobbing and jumping in large crowds,” Belykh said.
Beauty Vs. Function
Belykh also studies the effect of similar identical units on wind-induced oscillations of suspension bridges.
While humans enjoy symmetrical, aesthetically pleasing bridges, these designs could possibly take away from the safety of bridges. Many suspension bridges are constructed of identical units, such as supports and load-bearing elements, and Belykh and his group will investigate whether bridges with similar units have a tendency to exhibit wind-induced collective pedestrian behavior that could cause bridge vibration.
“One immediate hypothesis or potential guideline is that engineers should probably start building ugly bridges or asymmetrical bridges where the elements are not necessarily the same to avoid dangerous vibrations caused by unwanted, collective dynamics of a bridge’s load bearing elements,” Belykh said.
Another project led by Belykh and funded by the U.S. Army Research Office was recently featured in a Georgia State article: