Millennium Bridge, London#Mitigation

{{Unreferenced section|date=December 2019}}

An architectural design competition was organised in 1996 by Southwark council and RIBA Competitions. The winning entry was an innovative "blade of light" effort from Arup Group, Foster + Partners and Anthony Caro.{{cite book |editor1-last=Cole |editor-first1=Ina |title=“From the Sculptor’s Studio”, conversation with Anthony Caro, held in 2006 |year=2021 |publisher=Laurence King Publishing Ltd |page=34-47 |isbn=9781913947590 |oclc=1420954826}} 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 consists of three main sections of {{convert|81|m|0|abbr=on}}, {{convert|144|m|0|abbr=on}}, {{convert|108|m|0|abbr=on}} (north to south) with a total structure length of {{convert|325|m|0|abbr=on}}; the aluminium deck is {{convert|4|m|0|abbr=on}} 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.

thumb

File:Millennium Bridge, 2018.jpg

File:St Pauls and Millennium Bridge at night.jpg

Ordinarily, bridges across the River Thames require an Act of Parliament. For this bridge, that was avoided by the Port of London Authority granting a licence for the structure, and the City of London and London Borough of Southwark granting planning permission.Thames Bridges – Neil Davenport{{Page needed|date=May 2020}} Construction began in late 1998, and the main works were started on 28 April 1999 by Monberg & Thorsen and Sir Robert McAlpine.[http://thames.me.uk/s00080.htm Where Thames Smooth Waters Glide] The eventual cost was £18.2 million (£2.2m over budget), primarily paid for by the Millennium Commission and the London Bridge Trust.Life: The Observer Magazine – A celebration of 500 years of British Art – 19 March 2000

The bridge opened on 10 June 2000, one month late.{{cite news|title=Queen dedicates Millennium Bridge|url=http://news.bbc.co.uk/2/hi/uk_news/741512.stm|publisher=BBC News|date=9 May 2000|access-date=1 February 2023}} Unexpected lateral vibration due to resonant structural response caused the bridge to be closed on 12 June for modifications. Attempts had been made to limit the number of people crossing the bridge, which led to long queues but were ineffective to dampen the vibrations. Closure of the bridge only two days after opening attracted public criticism as another high-profile British Millennium project that suffered an embarrassing setback, akin to how many saw the Millennium Dome.

The vibration was attributed to a then under researched phenomenon"Before the Millennium Bridge, the math of "synchronous lateral excitation" from pedestrians was not at all well-understood. Once the bridge had been fixed, it was a well-investigated area." -- Humble Pi: When Math Goes Wrong In The Real World, by Matt Parker, page 274 whereby pedestrians crossing a bridge that has a lateral sway have an unconscious tendency to match their footsteps to the sway, exacerbating it. This is different from the well-understood problem of vertical sway, which is why troops stop marching in stride together as a unit when crossing such a bridge.{{cite book|last=Jeans|first=James|author-link=James Jeans|title=Science and Music|url=https://archive.org/details/in.ernet.dli.2015.459051|publisher=Cambridge University Press|year=1923|page=[https://archive.org/details/in.ernet.dli.2015.459051/page/n67 56]}} An example is London's Albert Bridge, which has a sign dating from 1873 warning marching ranks of soldiers to break step while crossing.{{cite web|title=All troops must break step on Albert Bridge|url=https://www.flickr.com/photos/31505964@N08/6817075683/|url-status=dead|archive-url=https://web.archive.org/web/20140125215409/https://www.flickr.com/photos/31505964@N08/6817075683/|archive-date=25 January 2014}}

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;{{cite news|last=Josephson|first=Brian|title=Out of step on the bridge|url=https://www.theguardian.com/theguardian/2000/jun/14/guardianletters3|work=The Guardian|date=14 June 2000|access-date=22 March 2018}}Strogatz, Steven et al. (2005). [http://www.nature.com/nature/journal/v438/n7064/abs/438043a.html "Theoretical mechanics: Crowd synchrony on the Millennium Bridge"], Nature, Vol. 438, pp. 43–44. the maximum sway was around {{convert|70|mm|inch}}.{{cite web|url=http://www.arup.com/MillenniumBridge/challenge/index.html|title=The Millennium Bridge: Challenge|website=Arup|url-status=dead|archive-url=https://web.archive.org/web/20081231211303/http://www.arup.com/MillenniumBridge/challenge/index.html|archive-date=31 December 2008}} On the day of opening, the bridge was crossed by 90,000 people, with up to 2,000 on the bridge at a time.

Resonant vibrational modes due to vertical loads (such as trains, traffic or pedestrians) and wind loads are well understood in bridge design. In the case of the Millennium Bridge, because the lateral motion caused pedestrians to directly participate with the bridge, the vibrational modes had not been anticipated by the designers. When the bridge lurches to one side, the pedestrians must adjust to keep from falling over, and they all do this at the same time. The effect is similar to soldiers marching in lockstep, but horizontal instead of vertical.

The risks of lateral vibration in lightweight bridges are well known.Julavitz, Robert. [http://www.villagevoice.com/news/0335,julavits,46559,1.html "Point of Collapse"], {{webarchive |url=https://web.archive.org/web/20080617054919/http://www.villagevoice.com/news/0335,julavits,46559,1.html|date=17 June 2008}} Village Voice, 26 August 2003. 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:

• Auckland Harbour Bridge, with a lateral frequency of 0.67 Hz during a 1975 demonstration.Dallard, P. et al. [http://www.arup.com/MillenniumBridge/indepth/pdf/IStructE.pdf "The London Millennium Footbridge,"] {{webarchive|url=https://web.archive.org/web/20110927001537/http://www.arup.com/MillenniumBridge/indepth/pdf/IStructE.pdf|date=27 September 2011}} Structural Engineer, 20 November 2001. 79:22, pp. 17–35.
• Birmingham NEC Link bridge, with a lateral frequency of 0.7 Hz.

Engineers at Arup, the company that designed the bridge, conducted research into the unexpected oscillation, which they called 'synchronous lateral excitation'. The first laboratory studies used pedestrians on moving platforms at the University of Southampton and Imperial College London. Later in 2000, one span of the bridge was instrumented and tested with crowds of up to 275 people.

They concluded that making the bridge stiffer, to move its resonant frequency out of the excitation range, was not feasible as it would greatly change its appearance. Instead, the resonance was controlled by retrofitting 37 viscous fluid dampers to dissipate energy. These include 17 chevron dampers – long V-shaped braces under the deck panels – to control lateral movement, 4 vertical to ground dampers to control lateral and vertical movements, and 16 pier dampers to control lateral and torsional movements.{{cite book|last=Taylor|first=Douglas P.|title=Damper Retrofit of the London Millennium Footbridge - A Case Study in Biodynamic Design|url=https://www.taylordevices.com/custom/pdf/tech-papers/66-DamperRetrofit-London.pdf|publisher=Taylor Devices, Inc.|access-date=14 March 2019}}{{cite book|last=Klembczyk|first=Alan R.|title=A Study in the Long-Term Performance of Specialized Low Friction Hermetically Sealed Fluid Viscous Dampers Under Nearly Continuous Operation on a Pedestrian Bridge|publisher=Taylor Devices, Inc.|url=http://www.teratec.ca/wp-content/uploads/Millennium-Bridge-Dampers-long-term-study-2.pdf|access-date=14 March 2019}} Additionally, 52 tuned mass dampers add inertia to control vertical movement. The work took from May 2001 to January 2002 and cost £5 million. After a period of testing, the bridge was reopened on 22 February 2002 and, since that date, has not been subject to significant vibration. In spite of the successful cure, the "wobbly bridge" (sometimes "wibbly-wobbly"E.g., "[https://www.youtube.com/watch?v=y2FaOJxWqLE The Wibbly Wobbly Millennium Bridge in London]", YouTube; accessed 20 August 2021) epithet remains in common usage among Londoners.{{cite web|url=http://www.urban75.org/london/millennium.html|title=Millennium Bridge over the River Thames, joining the Tate Modern and St Paul's London – photos, history and background|publisher=Urban75.org|access-date=26 March 2013}}{{cite web|last=Lydall|first=Ross|url=http://www.thisislondon.co.uk/standard/article-23761203-second-wobbly-bridge-for-london.do|title=Second wobbly bridge for London|publisher=Evening Standard|date=27 October 2009|access-date=26 March 2013|url-status=dead|archive-url=https://web.archive.org/web/20091030004102/http://www.thisislondon.co.uk/standard/article-23761203-second-wobbly-bridge-for-london.do|archive-date=30 October 2009}}

File:Millennium Bridge decking underside.jpg|Chevron dampers

File:Bridge vert mode shock.jpg|Vertical to ground dampers

File:Bridge_horiz_mode_shock.jpg|Pier dampers

File:Moving End of Pier Damper of Millennium Bridge, London.jpg|Moving end of pier damper

File:London Millennium Bridge - Damper beneath deck, north side - 240404.jpg|Tuned mass damper

An artistic expression of the higher-frequency resonances within the cables of the bridge were explored by Bill Fontana's Harmonic Bridge exhibition at the Tate Modern in mid-2006. This used acoustic transducers placed at strategic locations on the cabling of the Millennium Bridge and the signals from those transducers were amplified and dynamically distributed throughout the Turbine Hall of the Tate by a programme which Fontana entered into the sound diffusion engine of the Richmond Sound Design AudioBox.[http://www.resoundings.org/ The sound sculptures and ideas of Bill Fontana] Resoundings

In October 2023, the bridge was closed for three weeks to allow repairs to its surface, undertaken by FM Conway.{{cite news|last1=Dale|first1=Sarah|title=Catch net installed to soffit of Millennium Bridge to facilitate planned maintenance work|url=http://www.infrastructure-intelligence.com/article/oct-2023/catch-net-installed-soffit-millennium-bridge-facilitate-planned-maintenance-work|access-date=26 October 2023|work=Infrastructure Intelligence|date=25 October 2023}} The bridge closed on Saturday 14 October{{cite news|title=Millennium Bridge: 'Wobbly' pedestrian crossing to close for repairs|url=https://www.bbc.co.uk/news/uk-england-london-67018260|access-date=6 October 2023|work=BBC News|date=5 October 2023}} and reopened late on 5 November.{{cite web|url=https://www.citybridgefoundation.org.uk/news-and-blog/millennium-bridge-reopens-after-three-week-closure#:~:text=The%20bridge%20opened%20on%20Sunday,old%20structure%20a%20deep%20clean.|title=Millennium Bridge Reopens after Three-week Closure|publisher=City Bridge Foundation|date=November 2023|access-date=5 March 2024}}

File:City of London, London, UK - panoramio - IIya Kuzhekin (37).jpg

A short inclined lift, known as the Millennium Inclinator, is next to the northern end of the Millennium Bridge. It was opened in December 2003 to allow pedestrians to surmount the steep slope (13.6°) of Peter's Hill from the riverside to the entrance to the Millennium Bridge without using the alternative flight of steps.{{cite web|title=Ride the London Millennium Funicular|url=http://www.tiredoflondontiredoflife.com/2010/10/ride-london-millennium-funicular.html|website= Tired of London, Tired of Life|access-date=12 April 2013|date=4 October 2010}}{{cite web|last1=Hows|first1=Mark|title=London Millennium Funicular|url= http://www.hows.org.uk/personal/rail/lon.htm |website=Hows.org.uk|access-date=5 April 2013|date=5 December 2003}} The lower end of the lift is on Paul's Walk next to the Thames, and the top end is {{convert|26.85|m|ft}} further up Peter's Hill on the terrace which is level with the deck of the bridge. It was primarily installed for use by those who cannot easily manage the steep steps, such as people with disabilities and parents with push chairs.{{cite news|last1=Bloomfield|first1=Ruth|title=Millennium Bridge throws another wobbly as 'erratic' disabled lift must have £750,000 replacement|newspaper=Evening Standard|url= https://www.standard.co.uk/news/millennium-bridge-throws-another-wobbly-as-erratic-disabled-lift-must-have-750000-replacement-6538042.html|access-date=12 April 2013|date=19 November 2010}}

The lift carriage was originally powered by an electric traction motor, manufactured in Italy by Maspero Elevatori, with a speed of {{convert|0.5|m/s|ft/s}} and a maximum capacity of {{convert|0.7|MT|ST LT|lk=on}}. However, by 2010 the City of London Planning and Transportation Committee decided that the level of service was unacceptable, because the inclinator was frequently out of service due to mechanical breakdowns and vandalism. So the Committee agreed it would be replaced at a cost of up to £750,000 in time for the 2012 Summer Paralympics.

A major renovation project was undertaken in 2012, and the lift was reopened in time for the Thames Diamond Jubilee Pageant of 3 June 2012, which took place about a month before the 2012 Summer Olympics. The new lift was manufactured by Hütter Aufzüge of Glinde, Schleswig-Holstein, Germany, a lift manufacturer which was taken over by Otis in 2013.{{cite news|last1=Stürmlinger|first1=Daniela|title=Hütter-Aufzüge in Glinde droht das Aus|url=https://www.abendblatt.de/wirtschaft/article206695281/Huetter-Aufzuege-in-Glinde-droht-das-Aus.html|access-date=25 June 2020|publisher=Hamburger Abendblatt|date=20 November 2015|language=de}} Axis Elevators installed the new equipment.{{cite web|title=The Millennium Bridge Inclined Lift|url=http://dunbarandboardman.blogspot.co.uk/2012/10/the-millennium-bridge-inclined-lift.html|website=Dunbar and Boardman|access-date=12 April 2013|date=18 October 2012}}

Following a redevelopment of the area in 2021 the lift was closed and will be replaced by a platform lift.

File:Underneath Millennium Bridge.JPG

File:Under the Millennium Bridge, London (geograph 4907090).jpg

File:London Millenium Bridge.jpg

File:View from Millenium bridge 04 Panorama.jpg

• The bridge is featured in the opening scenes of the film version of Harry Potter and the Half-Blood Prince, where the bridge collapses following an attack by Death Eaters.{{cite web|url=http://golondon.about.com/od/londonpictures/ig/Harry-Potter-Film-Locations/Millennium-Bridge.htm|title=Harry Potter Film Locations in London – Millennium Bridge|publisher=Golondon.about.com|date=5 March 2014|access-date=10 July 2014}}
• The bridge appears in the 2014 Marvel Cinematic Universe film Guardians of the Galaxy during the climactic battle on Xandar.{{cite web|date=11 August 2013 |first=Sharnaz |last=Shahid|title=Guardians Of The Galaxy Cast Get Physical In London Shoot|publisher=Entertainmentwise|url=http://www.entertainmentwise.com/photos/123327/1/PHOTOS-Guardians-Of-The-Galaxy-Cast-Get-Physical-In-London-Shoot|access-date=11 August 2013|archive-date=2 December 2014|archive-url=https://web.archive.org/web/20141202065302/http://www.entertainmentwise.com/photos/123327/1/PHOTOS-Guardians-Of-The-Galaxy-Cast-Get-Physical-In-London-Shoot|url-status=dead}}
• The bridge appears in the 2017 Taylor Swift music video for "End Game" from her sixth studio album, Reputation (2017).

• Angers Bridge
• Brooklyn Bridge—Pedestrian access
• Broughton Suspension Bridge, which collapsed in 1831 partly due to resonant swaying
• List of bridges in London
• List of crossings of the River Thames
• Tacoma Narrows Bridge (1940), original Tacoma Narrows Bridge that collapsed in 1940
• Tay Bridge disaster

File:Millennium Bridge London uk.jpg

;Notes

{{Reflist}}

;Bibliography

{{refbegin}}

• Reaney, Patricia. (6 November 2005). "Why the Millennium Bridge wobbled". New Sunday Times, p. F20.
• Strogatz, Steven. (2003). Sync: The Emerging Science of Spontaneous Order. New York: Hyperion Books. {{ISBN|978-0-7868-6844-5}} (cloth) [2nd ed., Hyperion, 2004. {{ISBN|978-0-7868-8721-7}} (paper)]

{{refend}}

{{commons}}

• {{Structurae|id=20000603|title=Millennium Bridge}}
• [https://web.archive.org/web/20111102072050/http://www.arup.com/millenniumbridge/ Arup's Millennium Bridge site]
• A [https://web.archive.org/web/20110926235714/http://www.arup.com/MillenniumBridge/indepth/pdf/linking_london.pdf PDF paper] from Arup, discussing the engineering and resonance of the bridge.
• A [https://web.archive.org/web/20041031072113/http://www.taylordevices.com/papers/damper/damper.html paper] from Taylor Devices Inc on the dampers retrofitted to the bridge
• Information about the [http://gerb.com/en/arbeitsgebiete/projektbeispiele/show_projektbeispiel.php?rubrik=tilger&projekt=millen_bridge GERB TMDs] retrofitted to the bridge.
• [https://web.archive.org/web/20080617054919/http://www.villagevoice.com/news/0335,julavits,46559,1.html Brooklyn Bridge: lateral S-shaped vibration = pedestrian oscillations or "sway"]
• [http://www-g.eng.cam.ac.uk/125/now/millennium_bridge.html A Cambridge University Engineering Department account of the Millennium Bridge problem.] (January 2002)
• [https://web.archive.org/web/20200610193039/https://www.bing.com/ Bing's Image of the Day for 2020-06-10]. The Millennium Bridge is featured.
• [https://www.youtube.com/watch?v=xP7gcWUV37s title=London Millennium Funicular Modernized - video of a descent and an ascent using the Millennium Inclinator]

{{ThamesCrossings | west=Blackfriars Railway Bridge | east=Southwark Bridge }}

{{Bridges of Central London}}

{{London Borough of Southwark}}

{{London landmarks}}

{{Authority control}}

Category:2000 establishments in England

Category:Bridges completed in 2000

Category:Bridges in the City of London

Category:Buildings and structures in the London Borough of Southwark

Category:Buildings and structures celebrating the third millennium

Category:Foster and Partners buildings

Category:Pedestrian bridges across the River Thames

Category:Pedestrian bridges in London

Category:Suspension bridges in London

Category:Tourist attractions in the London Borough of Southwark

Category:Tourist attractions in the City of London

Category:Tourist attractions in London

Category:Transport in the City of London