PEDESTRIAN INDUCED sway is now seen as the most likely cause of the excessive movement which alarmed many of the thousands who crossed London's Millennium footbridge on its opening day.
Computer analyses by structural engineer Ove Arup are understood to have shown that with unusually large numbers of pedestrians on the structure a pattern of lateral movement could develop which would produce the alarming deflections observed. With the bridge now closed, a team from building research body BRE is carrying out live dynamic tests to validate Arup's model (see box).
Specialist vibration consultant Dr John Parker confirmed that pedestrian behaviour could be at the root of the problem. 'A pedestrian's centre of gravity is about 1m above his feet and as he walks normally he puts his feet alternately about 100mm each side of a centre line.
'Thus each pedestrian exerts a cyclic lateral force of about 8% of body weight at a frequency of around 1Hz.'
NCE understands that bridge oscillations on the June 10 opening day were measured at 1Hz.
Parker explained: 'If a large number of people walk - not in step - across a bridge, the resultant mean lateral force would be the force from one pedestrian multiplied by the square root of the total number.
'This would probably be enough to start the bridge swaying at the critical frequency. At this point more and more pedestrians would find it more comfortable to walk in phase with the movement, feeding more and more lateral energy into the structure.'
If the theory is correct it points to a simple solution to the problem. Tuned mass dampers have been used for years on structures as diverse as ultra tall buildings and the main cantilever of the Arup-designed Mind Zone in the Millennium Dome. They are relatively cheap and quick to design and manufacture. A steel or concrete mass free to slide or swing horizontally could be fixed beneath the bridge deck at a location suggested by the dynamic analysis.
A system of springs and hydraulic dampers would restrain the mass's motion and transmit forces from the mass into the deck. Essentially the mass would move horizontally out of phase with the deck's sway, largely cancelling it out.
Advantages over the more sophisticated active damper alternative include lower cost, shorter lead time and no need for outside power supplies. TMDs would also probably be less visually intrusive as well.
However, TMDs only work over a limited frequency range, which may reduce their effectiveness if a structure has more than one critical frequency. But if Arup's investigation confirms that oscillations at around 1Hz are the only real problem, TMDs would be an efficient solution.
The main alternative to damping would be to change the frequency of the deck structure by adding mass or stiffness.
Maunsell's plastic composite 63m span Aberfeldy footbridge in Perthshire had extra mass added down the centre of the deck to change the natural frequency of its vertical oscillation.
Maunsell chief executive Peter Head said last week that he believed it 'would not be easy' to add similar masses to the Arup bridge. He added that TMDs were 'too large and complex.'
Parker suggested cross bracing with steel cables might be an alternative way of adding stiffness more quickly and cheaply.
'Raising the natural frequency of the deck to more than 1.4Hz would eliminate the problem, ' he predicted. Bridge architect Lord Foster is likely to have a major say in any solution that would impact directly on the aesthetics of the landmark structure.