ENGINEERS who designed London’s wobbly Millennium Bridge admitted last week
that the computer simulations they used to model its behaviour couldn’t cope
with the effect of people walking across it. The blunder, say observers,
resulted from an out-of-date standard for testing bridges and poor dissemination
of information in the industry about previous incidents.
The 320-metre footbridge over the Thames, which cost £18 million, was
closed on its opening weekend last month, when it was found to wobble more than
expected. Since then Arup, the engineering firm responsible for the bridge, has
been analysing its response to vibrations.
The engineers used shaking machines to send vibrations through the bridge.
They found that horizontal vibrations at 1 hertz (one complete cycle per second)
sent the bridge into the kind of S-shaped lateral wobble that was seen when it
opened.
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This was a clue to the source of the problem, says Pat Dallard of Arup,
structural adviser on the bridge project. “Normal walking pace is about two
strides a second, so you produce a vertical force at around 2 hertz,” he says.
But the horizontal frequency is half that. “As we walk, one foot pushes left,
then the other pushes right, so you have a 1-hertz horizontal force,” he
says.
To make the bridge wobble, a lot of people would have to be walking in step,
says Tony Fitzpatrick, Arup’s head of engineering. And when engineers checked TV
news footage, this is exactly what they found. “What we saw was unintentional
synchrony of walking,” says Fitzpatrick. People on the bridge were adjusting
their balance as the bridge moved slightly—probably because of high winds
on the day, Fitzpatrick says.”When what you’re walking on moves, you start to
steady yourself. And here, everybody is doing the same thing.” Synchronised
walking made the bridge wobble even more.
“Everyone knows that troops have to break step before they cross bridges so
that they don’t set up huge vibrations,” says Dallard. But when Arup’s engineers
ran computer simulations of crowds crossing the bridge, they didn’t account for
synchronous walking. “We did not think we were in that category,” he says. “The
way we were modelling the pedestrian loading wasn’t accurate. We were missing
the effect of this swaying in synchrony.”
According to Alex Pavic, a structural engineer at the University of
Sheffield, the official standard on which engineers in Britain base their
simulations is out of date. “It only looks at what happens in the vertical
direction when people go over it,” he says. Dallard agrees that updating the
standard would help: “Conventional wisdom is so strong that walking input is
vertical and 2 hertz that it blinds you to the fact that there’s also a 1-hertz
horizontal force.”
Don Holman of the British Standards Institution says: “If those concerned
feel there are problems with the standard, they should let us know and give us
the background information so we can look at it.”
So why didn’t Arup engineers know small movements of the bridge could cause
“lock-in”, as synchronous walking is called? One reason might be industry
secrecy, says Bill Harvey, a civil engineer at the University of Exeter.
“Engineers are very, very sensitive about these things,” he says. “The only
reason anybody knows about the Millennium Bridge is because it’s so public. If
it had been somewhere small, then I imagine it would have been kept quiet.” Even
when problems are aired in civil engineering journals, they rarely identify the
projects under discussion.
Pavic, too, isn’t surprised that Arup did not know about the effect. He says
it took a Sheffield PhD student four years to track down three cases of
horizontal wobbling on footbridges. “What chance have practising engineers got,
when they’re working on several projects at the same time?” Pavic asks. Arup has
now called in Yozo Fujino, who worked on one of the previous cases in 1992.
Arup is now working on a new computer simulation that will account for
lock-in—which should be cured with dampers. “I’m embarrassed for my
industry,” says Fitzpatrick. “But if you’re not going to do new things, you
might as well put a bin liner over your head and sit in the corner.”
