Chapter 24 Predicting Footbridge Vibrations Using a Probability-Based Approach Lars Pedersen and Christian Frier Abstract Vibrations in footbridges may be problematic as excessive vibrations may occur as a result of actions of pedestrians. Design-stage predictions of levels of footbridge vibration to the action of a pedestrian are useful and have been employed for many years based on a deterministic approach to modeling the action of a pedestrian. The paper employs a probability-based approach to modeling the action of a pedestrian by considering randomness in the behavior of the pedestrian crossing the footbridge. The paper describes the approach and studies implications (sensitivity) of selected decisions made when setting up the probabilistic framework for the predictions of footbridge response. Keywords Footbridge vibrations • Walking loads • Numerical prediction • Serviceability-limit-state • Response prediction Nomenclature a Bridge acceleration fs Step frequency m1 Bridge modal mass ˛ Dynamic load factor Standard deviation f1 Bridge fundamental frequency F Walking load L Bridge length 1 Bridge damping ratio Phase i Integer ls Step length W Weight of pedestrian Mean value ˆ Mode shape 24.1 Introduction Pedestrians are known to be capable of causing problematic vibrations in footbridges. The London Millennium Bridge incident [1] is well-known and it resulted in increased focus on the modelling of loads generated by pedestrians. Modelling of walking loads is also the topic of this paper. Deterministic models for walking loads are available in design guides and codes of practise (such as in [2, 3]). However it is known that the locomotion of a pedestrian is not deterministic. Parameters of walking load models (such as step frequency, step length and dynamic load factors) are fundamentally stochastic by nature [4–7] and different pedestrians generate different dynamic forces. This paper will respect this and therefore it will respect that the response of a footbridge L. Pedersen ( ) •C. Frier Department of Civil Engineering, Aalborg University, Sofiendalsvej 9-11, DK-9200, Aalborg SV, Denmark e-mail: lp@civil.aau.dk © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_24 197
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