Millennium Bridge
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Structure: Millennium Bridge
Location: London, England
Year of Failure: 2000
Type of Failure: Synchronous Lateral Excitation
Architect: Foster and Partners
Structural Engineer: ARUP
Construction Firm: Monberg & Thorsen and Sir Robert McAlpine

On June 10, 2000, the Millennium Bridge opened as the first pedestrian bridge in London in over 100 years. Designed by Foster and Partners and engineered by Arup, the Millennium Bridge was proclaimed as an engineering feat in its slender profile and expressed structure. On the day of it’s opening, nearly 100,000 people passed over the bridge, spanning across the River Thames from the Tate Modern to St. Paul’s cathedral. [a]

Almost immediately the bridge began to wobble from side to side. The oscillations increased to a magnitude of nearly 70 mm near the middle, large enough to force people to cling to the banisters. The engineers were immediately notified and attempted to mitigate the bridge sway by controlling the number of pedestrians. However, even smaller crowds, well under the bridge’s 2,000 person operational capacity induced lateral movement in the bridge. The Millennium Bridge was closed 2 days later in order to diagnose and remedy the failure. [b]

wobble
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Several factors played into the unforeseen behavior of the bridge under pedestrian load. Arup engineers understood that the normal gait of humans generates a small lateral force for balancing purposes. However, engineers expected the random step of the pedestrians to largely offset this lateral force, and focused more on the vertical force caused by walking that has been understood and documented in design code and specifications. [c]

What caused this underestimation to manifest itself in the Millennium Bridge more so than many other pedestrian bridges around the world had to do with the natural frequency of the bridge itself. Due to the sleek design of the bridge, the suspension cables run along side instead of well above the bridge as in the Golden Gate Bridge and other traditional suspension bridges. These suspension cables, therefore, were pulled more tightly between supports, increasing their tension and decreasing their length. These properties of the suspension cables along with the relatively light aluminum decking of the walkway, acted to raise the natural frequency of the bridge to very closely match the frequency of the human walk. [b]

The Arup engineers were correct in their assumption that people walk in a random fashion, but failed to understand that even in a random model, a portion of the people are destined to “match step.” In the case of the Millennium Bridge, the unintentional matching of step by a fraction of the crowd was able to induce lateral motion in the bridge. As the motion manifested itself, more and more people began to match step with the motion in order to balance themselves, therefore, magnifying the oscillation of the bridge. [a]

There were two options available to correct the failure. One option was to stiffen the bridge considerably to move the frequency outside of the excitation zone. The other option was to add a system of dampers to absorb and dissipate the lateral energy applied by the pedestrians. It was decided that stiffening the bridge would cause too serious a change to its physical appearance, and therefore, an extensive dampening system was designed. Arup underwent a $8.9 million dollar renovation installing 91 dampers in the bridge in order to disrupt the natural frequency and absorb the energy of the lateral movement. The Millennium Bridge reopened 18 months later. [c]

viscous damper3d_mods_06
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