introduction
oscillation
test programme
results
solution
modifications

video

The sideways force exerted by the pedestrians on the structure was calculated using the results from the crowd tests on the bridge in July 2000. The test results showed a clear relationship between the movement of the bridge and the force exerted by the crowds:

F = k x V

Where:
F is the average sideways force we exert on the bridge when walking on the deck
k is a mathematical constant
V is the sideways velocity of the bridge.

Using this formula, it is possible to calculate the size of crowd which will cause Synchronous Lateral Excitation to occur. The graph below indicates the results of one of the December 2000 crowd tests, the video footage shows the test in process on the north span of the bridge.

The time is plotted along the horizontal axis – with the test starting at around time=300 seconds and finishing at around time=1400 seconds, when excessive movements occurred. The test lasted around 20 minutes.

Two lines are shown on the vertical axis.

The stepped line is the number of people walking on the bridge. This starts with around 50 walkers, further walkers are added to the span in groups of around 10 people. The time between each group was to allow time for any movements to occur.

The red line shows the bridge’s movements (measured as lateral acceleration and not shown to scale). It can be seen that the north span is stable with 156 people but with just 10 more people the movements increase suddenly and the test is stopped – Synchronous Lateral Excitation occurred, at the crowd size predicted by the above formula.

As can be seen, the effect is sudden rather than gradual. It does not show as small movements with a few people, gradually building up as more people are added. Instead, it takes a critical number of people for a bridge to sway. Until that critical number is reached there is no evidence of the effect.

As well as enabling the calculation of the number of people required to cause Synchronous Lateral Excitation, the Arup research also allows calculation of the amount of damping necessary to prevent this from occurring. In the future bridge designers will be able to design against Synchronous Lateral Excitation occurring, making reference to the research carried out on the Millennium Bridge.