Investigation Of The Lateral Vibration Of Flexible Footbridges

The excessive lateral resonance problem of the London Millennium Bridge in 2000 attracted great public and professional attention. It is currently accepted that flexible footbridges with lateral natural frequencies below 1.3 Hz are potentially the most vulnerable to exhibit excessive lateral vibration, when excited by large crowds. There exist three solutions to this problem. The first is to increase the lateral stiffness of the bridge to move all the lateral frequencies out of the sensitive frequency range, but it would significantly affect the aesthetics of the bridge, and usually it is not feasible in practice for especially flexible footbridge; the second option is to increase the damping of the structure to reduce the resonant response, but this would be a very costly work, such as the retrofit work of the Millennium Bridge, 7 million dollar were added; another way is to restrict the number of pedestrians across the footbridge. Because the excessive lateral resonance are induced only when the walker number on the bridge is large enough, it is necessary to study the critical number of pedestrians likely to induce the lateral resonance of flexible footbridges.For this purpose, an analytical theory on the pedestrian-induced lateral vibration of footbridges was developed. Based on the principle of the same motion of pedestrian and bridge in modal space, the critical number of pedestrians likely to induce the lateral resonance of footbridge was derived, and influential factors on the critical walker number were discussed.Subsequently, the above theory was verified through the comparison with the results of the full scale vibration test of the Millennium Bridge. The procedure is as follows: an elaborate FE model was built for the Millennium Bridge, and the results of modal analysis revealed that there is less than 2% difference of the analytical value and the measured value for the lateral natural frequencies of the bridge; then the critical walker number of the bridge was calculated, and all the walker were uniformed distributed over the deck, and then the maximum of peak acceleration of the bridge was calculated, which fitted well with the results of the pedestrian-comfort-related acceleration limit obtained from the vibration test of the bridge. All the results demonstrated that the proposed analysis quite well predicted the lateral vibration problem occurred in the Millennium Bridge.