Footbridge Vibrations and Their Sensitivity to Pedestrian Load Modelling
Pedestrians may cause vibrations in footbridges, and these vibrations may potentially be problematic from a footbridge serviceability point-of-view. Foreseeing (already at the design stage) unfit conditions is useful, and the present paper employs a proba
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Footbridge Vibrations and Their Sensitivity to Pedestrian Load Modelling Lars Pedersen and Christian Frier
Abstract Pedestrians may cause vibrations in footbridges, and these vibrations may potentially be problematic from a footbridge serviceability point-of-view. Foreseeing (already at the design stage) unfit conditions is useful, and the present paper employs a probability-based methodology for predicting vibrational performance of a bridge. The methodology and the walking load model employed for calculation of bridge response accounts for the stochastic nature of the walking parameters of pedestrians (step frequency, step length etc.) and the end result is central statistical parameters of bridge response (quantiles of bridge acceleration) to the action of a pedestrian. The paper explores the impact that selected decisions made by the engineer in charge of computations have on the statistical parameters of the dynamic response of the bridge. The investigations involve Monte Carlo simulation runs as walking parameters are modelled as random variables and not as deterministic properties. Single-person pedestrian traffic is the load scenario considered for the investigations of the paper and numerical simulations of bridge accelerations are made for artificial but realistic footbridges. Keywords Footbridge vibrations · Walking loads · Walking parameters · Stochastic load models · Serviceability-limit-state
Nomenclature a f1 fs i ls m1 t v F L Q W α ζ1 μ σ Θ Φ
Bridge acceleration Bridge fundamental frequency Step frequency Integer Step length Bridge modal mass Time Pacing speed Walking load Bridge length Modal load Weight of pedestrian Dynamic load factor Bridge damping ratio Mean value Standard deviation Phase Mode shape
L. Pedersen () · C. Frier Department of Civil Engineering, Aalborg University, Aalborg, Denmark e-mail: [email protected] © Society for Experimental Mechanics, Inc. 2020 S. Pakzad (ed.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12115-0_31
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L. Pedersen and C. Frier
31.1 Introduction Footbridges may become so slender that excessive vibrations may occur as a result of loads on the bridge generated by pedestrians. The Millennium Bridge in London [1] is an example of a footbridge for which the engineers in charge of design had overlooked that the bridge would be unfit for its intended use, namely carrying people in locomotion. Maybe based on tradition, walking load models specified in some codes of practice (such as [2, 3]) are deterministic in the sense that they do not account for intersubject variability in walking forces. Variability is known to exist (for instance variability in step frequency, step length and dynamic load factors). Variability in these parameters is documented in [4–7]. It is considered useful to employ a load model that accounts for uncertainty related to these parameters. The load model used in this paper (developed and described in [8]) models parameters such
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