The Millennium Bridge, London
What Happened and Consequences:
In 1996 a unique collaboration was formed between Arup Engineers,
Foster and Partners Architects and Sir Anthony Caro, sculptor. They
came together to design a pedestrian bridge with a span of 325m over
the river Thames in London. They came up with a modern innovative
design. It was a very shallow suspension bridge, with a 4m wide
aluminum deck, supported by cables at each side.
When the bridge opened on 10 June 2000, up to 100,000 people crossed
it. Suspension bridges are always vulnerable to some slight movement,
as could be seen with the London Millennium Bridge when people began
crossing it. However as the amount of people crossing the bridge grew
quite large, the swaying movements began to exceed those predicted by
the designers. As a consequence of these large movements, the
decision was taken to close the bridge only two days after opening to
fully investigate the causes of this behaviour.
Technical Factors Contributing to the Disaster:
Since the bridge was so light and flexible, it had a very low natural
frequency. The force generated by people as they walk was the main
cause of the problem. During the design of the bridge, pedestrian
loads were applied and analysed assuming that people walked in a
totally random manner. However, due to the slight movement of the
bridge when it was first opened, people began to walk in
synchronization with the bridge movement to steady themselves as they
walked. This tendency caused the motion of the bridge to increase,
which in turn compelled more people to walk in time with the bridge.
As the movement increased, people widened their stance to keep their
balance, thus increasing the lateral force exerted on the bridge
deck.
This behaviour ensured that the frequency of the sideways oscillating
force caused by the pedestrians matched the low resonant frequency of
the bridge. This resonance led to a further increase in motion. This
phenomenon became known as Synchronous Lateral Excitation. Because
this was an unforeseen problem, no dampeners were included as part of
the original design. Therefore, it was necessary to close the bridge
until the problem was fully understood and reparative measures could
be taken.
Following much investigation, engineers created a formula to
calculate the size of the crowd that would cause Synchronous Lateral
Excitation to occur.
F=k x v
F= the average sideways force exerted by pedestrians on the bridge
when walking on the deck.
k = a mathematical constant
v = the sideways velocity of the bridge
The effect is sudden rather than gradual (i.e. it takes a critical
number of people for the bridge to sway noticeably)
Human and Managerial Factors Contributing to the
Disaster:
When designing the bridge, Arup designed it assuming that groups of
people walk in a random manner. This inaccurate assumption proved to
be the main cause of the disaster. It wasn’t until after the closure
of the bridge that Arup discovered that other bridges in the past had
behaved in a similar manner when large crows passed over them. These
cases were not widely published; therefore, not many practicing
engineers were aware of this phenomenon.
However, the engineers were very quick to take the appropriate action
and close the bridge until the cause of the problem was fully
understood. They were then faced with two options to limit the
motion. The first option was to stiffen the structure so the natural
frequency of the bridge could no longer match pedestrians’ footsteps.
It was calculated that the bridge would have to be made ten times
stiffer to increase the frequency enough to move it out of the
excitation range. Therefore the second option of introducing dampers
was chosen. It wasn’t until the dampers were fitted and proved to be
successful that the bridge was reopened.
This structure acts as a brace. At the centre points of
the "xxx" shaped skeleton there are damping
mechanisms to counter lateral movement
Lessons To Be Learned From the Disaster:
This disaster emphasised the fact that the British Standard codes are
just a guideline to designing structures. It is hard to predict how
each new structure will behave, therefore it is necessary to think of
all the possible combinations of forces that could act on a
structure. It’s not good enough to simply follow the codes.
The Millennium Bridge was designed in accordance with the codes, and
the analysis that was carried out was correct. The problem arose
because the designers failed to see that their assumptions were not
justified. They failed to see that even a slight movement of the
slender bridge would cause people crossing the bridge to follow a
walking pattern in accordance with the movement of the bridge,
therefore making their assumption invalid. Following Arup’s
investigation, the BS codes are currently being modified to cover
this particular phenomenon so that the same situation can be avoided
in the future.
Finally, another lesson which can be learned from this disaster is
how to prevent this phenomenon from occurring in the future. There
are two ways of preventing this kind of behaviour. The deck can be
stiffened, a method which was not chosen in this case as it was
considered to be too expensive and not suitable for the project.
Conversely, the bridge can be damped. The millennium bridge was
modified to include dampers in both the horizontal and vertical
directions.
References:
1.
2.
Arup – www .ar up .c om/M ill enn ium Br id ge
BBC –
http :// new s .b bc .c o.uk /hi /en gli sh /s tati c/i n_ d ept h/ uk /2
000/ mil len niu m_ br idge