EXCESSIVE SWAY caused closure of London's Millennium footbridge across the Thames just two days after it opened.
But engineers from designer Ove Arup & Partners already had a strong suspicion about what had caused the problem.
Many had been there on the opening day 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. 'Was our computer model of the structure reliable? Had we got all the numbers right? Did it satisfy all the requirements of the codes?
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 pedestrian-only crossings. This eventually struck gold in a 1993 edition of Earthquake Engineering & Structural Dynamics - 'not w idely read in br idge 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 its best to suppress publication of the results of the 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.
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 the movement, the design of a solution could not begin.
'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. But there was virtually no vertical movement - which rules out torsional oscillation caused by off-centre loading.'
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 opening day observations and the data recorded during the Transport Research Laboratory/Building Research Establishment investigation. Any differences could be accounted for, not least by the fact 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 do 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.
'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 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 on the project, but even so, the best estimate of the time the landmark structure will stay closed is 'months rather than weeks'.