WHEN THE decision was taken to close the Millennium footbridge across the Thames in London two days after it opened, Arup engineers already had a strong suspicion about what had caused the excessive sway.
Many of the bridge's designers had been there on the Saturday and had spotted large sections of the crowd marching in step and in phase with the alarming lateral movement of the deck.
But there were other possibilities which had to be investigated.
'Basically there were some fundamental questions to be answered, ' says Arup director Pat Dallard. 'First: was our computer model of the structure reliable? Had we got all the numbers right? Did it satisfy all the requirements of the codes?
'And if the answer to those questions was yes, then we had to ask if the loading figures we had entered covered the behaviour we had seen on the Saturday.'
One team went back through the model 'with a fine-tooth comb', checking 'all masses, section properties, foundation springs, joints'. Another searched the literature for any reference to similar problems with unusually large pedestrianonly crossings. This eventually struck gold in a 1993 edition of Earthquake Engineering & Structural Dynamics - 'not widely read in bridge engineering circles', Dallard comments.
This paper describes a similar horizontal movement problem on the opening day of a large cable stay footbridge in Japan.
'This happened to have a lateral mode of oscillation with a frequency of 0.9Hz, which is comparable to the centre span of our bridge, ' says Dallard. 'The problem was that the client had done his best to suppress publication of the results of the subsequent analysis, to avoid embarrassment.'
Professor Fujino Yozo of Tokyo University, who had carried out the investigation and developed the solution, was promptly retained by Arup to advise the design teams.
Dallard admits the design team had never ruled out the possibility of unexpected dynamic problems with such an unusual structure. But early suspicions that the line of flagpoles erected for the opening day had fed abnormal forces into the bridge were soon discounted.
'The flags could be shown to increase the wind response by well under 10%, 'says Dallard.
'Wind conditions on the day were Force 2 gusting Force 5 at midspan, not enough to cause this scale of movement.'
While the cause was being found, stabilisation options were also being examined.
Proven ways to keep movements in check included tuned mass dampers, tuned slosh dampers - tanks partially filled with liquid and fitted with internal baffles, or 'shock absorbers' - viscous and visco-elastic dampers.
But until there was more data on how the bridge was moving the design of a solution could not begin. By the Wednesday morning teams from the TRL and BRE had joined Arup engineers on the bridge.
TRL installed an array of triaxial accelerometers, the BRE deployed its Grandstand Shaker and the Arup team solemnly marched in step until the bridge began to replicate its movement of Saturday.
'BS5400 and other bridge codes are all about vertical input from pedestrians at 2Hz, ' Dallard points out. 'Observations at the time and analysis of the videotapes showed the frequency of lateral movement to range between 0.77Hz on the southern span and 0.99Hz at the centre. At the design stage we had considered lateral movement caused by off-centre vertical input producing torsional oscillation.'
But Dallard points out that the movement seen on the bridge, especially on the centre span, was large lateral movement with virtually no vertical component.
Technically, Mott MacDonald's role as independent design checker ended when the design was signed off. Arup nevertheless invited Mott to attend the first meeting at which it was retasked with approving whatever solution was developed.
Flint & Neill was also invited on board: 'we felt we would prefer to be externally reviewed during the development process, ' Dallard explains. Also asked to assist were Professor Heinrich Kreuzinger from Munich and Professor Hugo Bachmann from Zurich, established experts in dynamic problems.
As the response of the real bridge to lateral inputs became clearer, faith in the original model was reinforced. Both the frequency and mode of movement predicted by the model fitted very closely to the observations made on opening day and the data recorded during the joint TRL/BRE investigation.
Any differences could be accounted for by a number of factors, not least that even the larger BRE shaker was really not up to the task. The real questions that still remained, however, would not be easy to answer.
'It's really a crowd behaviour problem, ' says Dallard. 'We need to know at what level of lateral movement people start walking in phase and what forces they exert when this 'lock-in' happens.
'And is there a visual factor:
do they see others in the crowd walking in step and just copy them?' But the test results on the bridge's inherent damping does give the Arup team working on solutions a very good clue as to what the best route may be.
'Stiffening the deck to increase its natural frequency to more than 1.5Hz just isn't an option, ' says Dallard. 'It would have to be four times stiffer than it is now - and this could only be achieved by propping the spans - which simply isn't possible on the centre span.
'But we are convinced that increasing the damping by a factor of 10 would work, and at this point it looks like there will be a very effective solution.'
Slosh dampers were ruled out because there is only one Japanese supplier with expertise in their design and construction.
Mass dampers are more widely available, but the biggest unit Arup would accept hanging under the deck would weigh 2.5t, and would work only over a limited frequency range. 'So we are looking at off the shelf viscous dampers - basically giant shockabsorbers - acting as diagonal braces beneath the deck.
'We calculate that this way we could easily increase damping by 20 times, which should solve all our dynamic problems.'
Arup has 20 engineers devoted to this project, but even so, the best estimate of the time the landmark structure will stay closed is 'months rather than weeks'.
Best foot forward
AN ARMY of volunteer pedestrians could be marched across the controversial Millennium footbridge in London shortly in an attempt to replicate the alarming sway which led to its premature closure.
Structural engineer Ove Arup confirmed that its engineers were considering the experiment, which would measure the volunteers' reactions to a range of lateral movements generated by a BRE shaking machine. This would supplement two emergency research programmes it commissioned at British universities this week.
One, at London's Imperial College, involves building and instrumenting a 10m long test bridge.
'But this may not be long enough to allow the sort of behaviour we saw on the opening Saturday to develop, ' said Arup director Pat Dallard.
'Similar research carried out at Tokyo University in the early 1990s used a test bridge only 7.2m long, and no useful data was obtained.'
Arup is desperate to obtain 'hard numbers' on the forces involved when large numbers of pedestrians start walking in phase with the lateral movements of the bridge deck. It has given Imperial and Southampton Universities just six weeks to come up with reliable data, which would allow the design of a cost-effective 'damped deck' solution.
This would involve fitting large viscous dampers diagonally under the deck. Without reliable data the only option would be to fit so many dampers that the natural damping of the deck would be increased by a factor of 20 - well above the range suggested by tests so far.
However, Arup is still not sure the BRE shaker would produce enough movement to stimulate the synchronised walking phenomenon.
A final decision is expected shortly.