“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.” He cites the examples of the Millennium Bridge in London, which had to be adapted to prevent oscillations, and the wooden Squibb Park Bridge in New York, which has been closed since 2014 pending a fix, as its bouncing alarming the people who were crossing.
"The US 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, is designed to capture 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.
Belykh 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 analyses 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,” he said.