Dynamic Analysis of Long Span Footbridges

University essay from KTH/Bro- och stålbyggnad; KTH/Bro- och stålbyggnad


A footbridge in Slussen is planned to be built and will connect the area of Gamla Stan with Sodermalm. As an increasing number of footbridges with large span tend to become more flexible and light these days, the corresponding dynamic problems due to decreased stiffness and mass draw much more attention. Specifically speaking, reduced stiffness and mass lead to smaller natural frequencies, which make the structure more sensitive to pedestrian-induced loading, especially in lateral direction.

Fortunately, in this master thesis, only the vibration in vertical direction is focused due to that the footbridge in Slussen project uses enough lateral bracings to make sure that the safety of lateral vibration is kept at an acceptable level.

In order to analyze dynamic response of the footbridge, the real footbridge structure is converted into a FE model by the commercial software LUSAS. In this thesis, four different kinds of critical standards are introduced, which are Sétra [8], Swedish standard Bro 2004 [9], ISO 10137 [5] and Eurocode respectively. By comparing these four criteria, Sétra and Eurocode are finally chosen to be the standard and guidelines for this project. They give the basic theories about how to model the pedestrian loading and provide critical values to check the accelerations in both vertical and lateral direction.

By using FE software LUSAS, natural frequencies of the footbridge and the corresponding mode shapes can be calculated directly. Then, according to these results and relevant theories introduced by Sétra, the pedestrian loading can be modeled and the acceleration response of any specific mode can be obtained as well.

Finally, based on the worst case with excessive acceleration, the methods to reduce dynamic response will be presented. Commonly, there are two ways to reduce acceleration response. One method is to increase the stiffness of the structure. However, the increased stiffness is always accompanied with increased mass of the structure. Because of this reason, the other way that installing dampers is widely used in recent years. In this thesis, the tuned mass dampers (TMDs) are introduced in detail as well as the information about the design principles of it. With important parameters known, TMDs can be added to the model to check how the accelerations can be reduced.

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