|Dr. N. Subramanian
Joined: 21 Feb 2008
Location: Gaithersburg, MD, U.S.A.
|Posted: Thu Nov 12, 2009 3:45 pm Post subject: The London Millennium Footbridge-it's vibration problems and
|The London Millennium Footbridge-it's vibration problems and solution
The London Millennium Footbridge is a pedestrian-only steel suspension bridge crossing the River Thames in London, England, linking Bankside with the City. It is located between Southwark Bridge (downstream) and Blackfriars Railway Bridge (upstream). The bridge is owned and maintained by the Bridge House Estates, a charitable trust overseen by the City of London Corporation. Construction of the bridge began in 1998, with the opening on 10th June 2000.
Londoners nicknamed the bridge the Wobbly Bridge after participants in a special event to open the bridge (a charity walk on behalf of Save the Children) felt an unexpected (and, for some, uncomfortable) swaying motion on the first two days after the bridge opened. The bridge was closed later that day, and after two days of limited access the bridge was closed for almost two years while modifications were made to eliminate the wobble entirely. It was reopened in 2002.
The southern end of the bridge is near Globe Theatre, the Bankside Gallery and Tate Modern, the north end next to the City of London School below St Paul's Cathedral. The bridge alignment is such that a clear view of St Paul's south facade is presented from across the river, framed by the bridge supports.
The nearest London Underground station is Mansion House.
See the the following videos which shows the vibrations in the London Millennium Bridge on the opening day on 10th June 2000.
The bridge's movements were caused by a 'positive feedback' phenomenon, known as Synchronous Lateral Excitation. The natural sway motion of people walking caused small sideways oscillations in the bridge, which in turn caused people on the bridge to sway in step, increasing the amplitude of the bridge oscillations and continually reinforcing the effect.
The bridge opened on an exceptionally fine day, and it was included on the route of a major charity walk. On the day of opening the bridge was crossed by 90,000 people, with up to 2,000 on the bridge at any one time.DesignThe design of the bridge was the subject of a competition organized in 1996 by Southwark council. The winning entry was an innovative "blade of light" effort from Arup, Foster and Partners and Sir Anthony Caro. Due to height restrictions, and to improve the view, the bridge's suspension design had the supporting cables below the deck level, giving a very shallow profile. The bridge has two river piers and is made of three main sections of 81 m , 144 m and 108 m (North to South) with a total structure length of 325 m ; the aluminium deck is 4 m wide. The eight suspension cables are tensioned to pull with a force of 2,000 tons against the piers set into each bank — enough to support a working load of 5,000 people on the bridge at one time.
Construction began in late 1998 with the main works beginning on 28 April 1999 by Monberg Thorsen and Sir Robert McAlpine. The bridge was completed at a cost of £18.2m (£2.2m over budget) and opened on 10 June 2000 (2 months late). Unexpected lateral vibration (resonant structural response) caused the bridge to be closed on 12 June for modifications.
Attempts were made to limit the number of people crossing the bridge: this led to long queues, but dampened neither public enthusiasm for what was something of a white-knuckle ride, nor the vibrations themselves. The closure of the bridge only three days after opening attracted public criticism, as another high-profile British millennium project suffered an embarrassing setback, akin to how many saw the Millennium Dome.
Further modifications to the bridge successfully eliminated the wobble, which has not recurred since the bridge reopened in February 2002.
The bridge was temporarily closed on 18 January 2007, during the Kyrill storm due to strong winds and a risk of pedestrians being blown off the bridge. Resonance
Resonant vibrational modes due to vertical loads (such as trains, traffic, pedestrians) and wind loads are well understood in bridge design. In the case of the Millennium Bridge, because the lateral motion caused the pedestrians loading the bridge to directly participate with the bridge, the vibrational modes had not been anticipated by the designers.
The lateral vibration problems of the Millennium Bridge are very unusual, but not entirely unique. Any bridge with lateral frequency modes of less than 1.3 Hz, and sufficiently low mass, could witness the same phenomenon with sufficient pedestrian loading. The greater the number of people, the greater the amplitude of the vibrations. Other bridges which have seen similar problems are:
* Birmingham NEC Link bridge, with a lateral frequency of 0.7 Hz
* Groves Suspension Bridge, Chester, in 1977 during the Jubilee River Regatta
* Auckland Harbour Road Bridge, with a lateral frequency of 0.67 Hz, during a 1975 demonstration
After extensive analysis by the engineers, the problem was fixed by the retrofitting of 37 fluid-viscous dampers (energy dissipating) to control horizontal movement and 52 tuned mass dampers (inertial) to control vertical movement. This took from May 2001 to January 2002 and cost £5m. After a period of testing, the bridge was successfully re-opened on 22 February 2002. The bridge has not been subject to significant vibration since.
The Millennium Bridge, located in London, was used to represent the Brockdale Bridge in the film adaptation of Harry Potter and the Half-Blood Prince. Despite representing it, the collapse shown is not to be confused with Brockdale Bridge's collapse, since the bridge that collapses on the film is stated to be the Millennium Bridge. This creates a error in the film's timeline, seen as the film decurs in 1996-1997 and the actual Millennium Bridge was built in 2000.
The Millennium Bridge twisting and buckling before finally collapsing, as seen in Harry Potter and the Half-Blood Prince.
2. Reaney, Patricia. (Nov. 6, 2005). "Why the Millennium Bridge wobbled". New Sunday Times, p. F20
3. Strogatz, Steven et al. (2005). "Theoretical mechanics: Crowd synchrony on the Millennium Bridge," Nature, Vol. 438, pp, 43-44.
4. Dallard, P. et al. (2001)"The London Millennium Footbridge," Structural Engineer. November 20, 2001. 79:22, pp.17-35.
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