PAT DALLARD was staring at the result of four years鈥� work鈥攁n 拢18
million footbridge spanning 328 metres across the river Thames in London. The
bridge was to be a symbol of the new millennium, a structure so sleek and
elegant that its designers called it a 鈥渂lade of light鈥�. But Dallard, an
engineer at the construction consultancy Arup, was feeling sick. The Millennium
Bridge鈥檚 opening was going badly wrong: the structure was swaying violently.
That was 10 June last year, and just two days later the bridge was closed.
During the intense scrutiny that followed, it emerged that engineers at Arup had
made a crucial error during its construction鈥攐ne they now admit made the
bridge dangerous. Nine months and several failed experiments later, they are
finally convinced they can fix it.
It seems ludicrous that at the start of the 21st century we can鈥檛 build a
footbridge that鈥檚 safe to walk across. Worse still, the Millennium Bridge may be
just the tip of a pretty wobbly iceberg. It turns out that other bridges around
the world suffer from the same problem. One of these is more than a century old.
How could such a fundamental flaw have been missed for so long, and what are the
consequences for other bridges out there? Is it time for civil engineers to
reassess the way they work, before someone is injured?
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The saga of London鈥檚 wobbly bridge began in 1996 when the Financial
Times newspaper and London鈥檚 Southwark Borough Council launched a
competition to design a new footbridge across the Thames. The winning design was
submitted by a consortium comprising consulting engineers Arup, the architects
Foster and Partners, and sculptor Anthony Caro. The bridge would cut straight
across the Thames, from a point near St Paul鈥檚 cathedral over to the south bank
outside the Tate Modern art gallery.
With a standard suspension bridge, the supporting cables would obscure the
views from the walkway. So the team hit upon an unusual, low-slung design. It
would consist of eight steel cables stretched across the river, four on each
side over two Y-shaped piers driven into the river bed (see Diagram, p 40).
Concrete anchors sunk 25 metres deep into each bank would take the huge strain
in the cables. Finally, an aluminium and steel walkway would be slung between
the two sets of cables. 鈥淲e had a minimal, simple and elegant design and that
was exactly what we were looking for in a bridge to represent the millennium,鈥�
says Roger Ridsdill Smith, the bridge鈥檚 project manager at Arup.
Construction began in April 1999, and the following June, crowds of thousands
lined the banks of the Thames, eager to try out the capital鈥檚 latest river
crossing. Ridsdill Smith arrived early to witness the opening. As the crowds
poured onto the bridge, the swaying started. Pedestrians were forced to grab the
handrail to keep their balance.
鈥淚 just asked myself what was going on,鈥� recalls Ridsdill Smith. Dallard,
Arup鈥檚 structural adviser for the bridge, arrived by noon. He too could see the
swaying immediately. 鈥淵ou feel, `Have I made a mistake, have I done something
wrong?'鈥� says Dallard.
By chance, Dallard had a stopwatch with him and he used it to time the
swaying of the bridge. It was moving from side to side about once a second.
鈥淰ery quickly we saw it was the natural frequency of the bridge,鈥� says Dallard.
Just like guitar strings, bridges have frequencies at which they鈥檒l happily
vibrate when given the right kick. These frequencies are determined by factors
such as the bridge鈥檚 length and stiffness. 鈥淲hat we didn鈥檛 know was what was
exciting it,鈥� says Dallard.
Then he noticed that the crowds appeared to be walking in step. Ridsdill
Smith saw it too, but before they could investigate further, they were called to
an emergency meeting.
The bridge closed two days later. While the media happily got their teeth
into Britain鈥檚 latest millennium fiasco, the engineers set to work on the
problem. They first went back to the scientific literature. Ridsdill Smith
insists extensive searches had already been made, but this time around they
uncovered a seven-year-old paper in the journal Earthquake Engineering and
Structural Dynamics.
It was written by an engineer called Yozo Fujino from the University of
Tokyo, and describes an effect seen on the Toda Park footbridge which spans a
river in Tokyo鈥檚 suburbs. The bridge is popular because of boat races on the
stretch of water. 鈥淢ore than 30,000 people came to enjoy the boat races and
crossed the bridge before and after the races,鈥� says Fujino. His report reveals
how the slight sideways vibrations of the bridge had made pedestrians walk in
step. And that wasn鈥檛 all. By synchronising their footfall, the pedestrians
reinforced the vibrations, sending the bridge into a lively lateral sway. The
paper was describing the exact phenomenon that struck the blade of light on its
opening day.
To help them understand the problem, the Arup engineers flew Fujino to
London. Together, they came to the conclusion that small vibrations induced in
the Millennium Bridge by wind and crowds made people alter their step slightly.
鈥淛ust like when you鈥檙e on a tube train, you steady yourself by placing your feet
further apart,鈥� says Dallard. 鈥淲hat that does when you鈥檙e walking is increase
the horizontal force you generate with each step,鈥� he says.
Crucially, because everyone was experiencing the same swaying motion as they
walked, they adjusted their gait in unison. The result was that large portions
of the crowd鈥擠allard estimates around 40 per cent鈥攆ell into step
with each other because of the bridge鈥檚 movement and 鈥渓ocked in鈥� to the
oscillations. The forces they produced made the bridge sway even more. And the
more the bridge swayed, the more people had to fight to keep their balance.
So why didn鈥檛 the engineers spot this at the design stage? It鈥檚 all down to
how the modelling is done. To study the effects of moving loads such as crowds
on bridges, civil engineers in Britain create computer simulations that conform
to a standard code drawn up by the British Standards Institution. But this only
requires simulations to test for the effect of any vertical vibrations produced
by a crowd walking out of step.
鈥淲hat you do is simulate the vertical force due to one person and then set
him off walking at one of the natural frequencies of the bridge,鈥� says Dallard.
So if the bridge vibrates vertically with a natural frequency of 2 cycles per
second, the simulated walker would be programmed to take two strides each
second. The computer calculates how much the bridge will oscillate as the person
walks across. The engineers had simulated this vertical force at 2 cycles per
second. What they had overlooked was the side-to-side force exerted by
pedestrians, which has a frequency of 1 cycle per second.
What鈥檚 more, the code assumes that the worst-case scenario is one person
walking at a natural frequency. It also assumes that crowds of people tend to
walk out of step, so the forces they exert cancel out. That鈥檚 the theory. But as
the engineers discovered, if you have a lot of people feeling the same
vibrations, they begin to walk in step, producing entirely different
results.
The team now set out to understand precisely what forces were at
work鈥攂ut to their dismay, every test they commissioned turned out to be
flawed. At Imperial College, London, engineer Roger Hobbs built a 7.2-metre
walkway and recorded the forces produced by a person walking on it. 鈥淲e wanted
to find out if the forces they produced increased as the bridge was shaken,鈥�
says Dallard. However, this model bridge was only long enough to allow people
about seven strides in which to synchronise their steps with the vibrations. And
that, they discovered, simply wasn鈥檛 enough.
Arup also commissioned Mike Griffin at Southampton University鈥檚 Institute of
Sound and Vibration Research to look into the problem. His approach was to
measure the forces people produced to keep their balance when shaken from side
to side as they walked on the spot. But this, too, turned out to be far from
ideal. 鈥淲alking on the spot removed the inherent balance requirement of
walking,鈥� says Dallard, 鈥渟o it removed part of the process going to drive this
迟丑颈苍驳.鈥�
Engineers from Arup also did their own tests. They fixed video cameras to the
bridge and got a crowd of people to walk up and down it. 鈥淭here were sensors in
people鈥檚 boots which recorded when their heels touched the ground,鈥� Dallard
explains. Signals from the sensors were relayed back to a computer via radio
mikes borrowed from theatres around London.
But again the experiments ran into difficulties. The cameras couldn鈥檛 see
enough people to give accurate results. The feedback from the boot sensors was
also flawed: people scuffed their feet on the ground, spoiling the signal.
鈥淎lmost half of it was unusable,鈥� says Dallard. It seemed Arup just couldn鈥檛 get
it right. 鈥淲e were beginning to feel a bit miffed at this stage,鈥� he says. So
they decided to bin the scientific tests. 鈥淚t was a case of, `Sorry guys,
there鈥檚 some really interesting science in here, but it鈥檚 not for us. We鈥檝e got
a bridge to open.'鈥�
The engineers changed tack and worked backwards from measurements taken on
the bridge itself. By looking at how much the bridge moved as the crowds walked
across it, they calculated the net sideways forces the pedestrians must be
exerting. Dallard and his colleagues quickly discovered that the average
sideways force from each person was proportional to the speed of the swaying
they were subjected to. The more the bridge wobbled, the more people had to
widen their stance to keep their balance as they walked, and the more they fell
in step with each other. The change of strategy had paid off.
Now that the engineers knew what they were up against, they could try to work
out how to fix it. They decided on a series of triangular steel frames called
chevrons slung beneath the walkway
(see Diagram). Where neighbouring chevrons
meet, sideways forces between the two are absorbed by a viscous
damper鈥攅ssentially a plunger encased in a cylinder full of thick
liquid.
After the opening fiasco, the engineers are taking no chances. Just in case
pedestrians set the bridge oscillating vertically as well, they propose adding
鈥渢uned mass dampers鈥� to absorb vertical vibrations. Tuned mass dampers contain
spring-mounted masses which counter the movement of any vertical oscillations
and absorb their energy. In total, Arup says around 35 viscous dampers and 50
tuned mass dampers should do the job. It will cost around 拢5 million and
Ridsdill Smith reckons the bridge could be fixed in a matter of months.
Could engineers make the same mistake again? 鈥淪tructural engineers have to
rely on design codes of practice because we don鈥檛 do prototypes,鈥� says Alex
Pavic, a structural engineer at the University of Sheffield. 鈥淲e have one
bullet, one shot.鈥� The Arup team is determined to see that the relevant design
codes are updated in the light of this experience. But it鈥檚 not just British
codes that should be changed, according to Pavic. 鈥淲hen the Millennium Bridge
saga started, I reviewed the key codes used in the UK, USA, Canada and
Switzerland, and none of them deals with the phenomenon,鈥� he says.
The publicity surrounding the Millennium Bridge fiasco has brought other
cases to light. In 1999, the Pont Solferino, a new footbridge over the Seine in
Paris, closed as soon as it had opened. The entourage walking behind the French
culture minister made the bridge start swaying violently, and the engineers in
charge were soon on the phone to Fujino. And it鈥檚 not just modern bridges that
can get the wobbles. For the past few years, Canada Day crowds surging onto the
100-year-old steel and concrete Alexandra Bridge in Ottawa have experienced the
same effect. In principle, says Pavic, any long, relatively lightweight bridge
could oscillate like this if there are enough pedestrians on it.
So should engineers worry that an unexpected wobble could cause a devastating
collapse? 鈥淓veryone鈥檚 heard stories about bridges collapsing when soldiers march
over them,鈥� says Pavic. 鈥淎nything can collapse if there鈥檚 sufficient force on
it, but I鈥檓 not aware of any case where lateral forces by pedestrians have
brought a bridge down.鈥�
That doesn鈥檛 mean unwanted wobbles are harmless. They could knock pedestrians
off their feet or damage the structure of the bridge. In retrospect, the
Millennium Bridge may not have been safe the day it opened, Dallard admits.
There was no risk of structural failure, he says, 鈥渂ut old people could have
fallen over and hurt themselves. It wasn鈥檛 safe for that reason.鈥�
Engineers can blame their design codes, but are these mistakes the symptoms
of a wider problem? Perhaps it鈥檚 time engineers stopped sticking blindly to
their models and started thinking more carefully about the way their structures
are used in the real world.
One lesson from London鈥檚 bridge is clear. The problem could have been avoided
if the engineering community had got wind of Fujino鈥檚 work sooner. Dallard
contrasts the way engineers work with what happens when an aircraft crashes:
every plane manufacturer is informed about the problem. 鈥淏ut it seems in our
world there are certain pressures not to disseminate knowledge,鈥� he says. Bridge
builders don鈥檛 like to publicise their failures. Perhaps if it had been tucked
away in some rural backwater, we would never have heard the tale of the wobbling
Millennium Bridge. 鈥淢aybe that鈥檚 true,鈥� says Ridsdill Smith. 鈥淲e鈥檒l never know,
will we?鈥�