Vibration serviceability of footbridges: Evaluation of the current codes of practice
Introduction
Slender footbridges are often highly susceptible to human induced vibrations, due to their low stiffness, damping and modal mass [1]. During the last decade, numerous problems with vibration serviceability have been reported, none of which as widely discussed as London’s Millennium [2], [3] and Paris’ Solférino footbridge [4]. In order to ensure user comfort and safety, many footbridges today are equipped with tuned mass dampers, e.g. the Pedro e Inês footbridge [5], [6], the Changi Mezzanine Bridge [7], [8], the Van Beethoven footbridge [9], the footbridge of VW Autostadt [10], the Kurilpa footbridge [11] and the Northshore footbridge [12].
Predicting the dynamic response of these civil engineering structures under crowd induced loading has therefore become an important aspect of the structural design [13]. Because the walking behaviour is unique for each individual and is influenced by interaction with the structure and synchronisation with other persons present on the structure [14], [15], [16], it is not straightforward to formulate a general model for crowd induced loading [17]. A clear need for practical design procedures exists given the large number of footbridges under construction and in design [1]. Multiple simplified design methodologies have been developed but their evaluation and validation have been given little attention so far. In order to evaluate and further develop these guidelines, applications on real case studies are needed.
The objective of this paper is to review and evaluate the methodology of two current codes of practice, the French Sétra guideline [18] and the European guideline HiVoSS [19], [20], both widely applied in engineering practice. In the evaluation procedures, it is assumed that the dynamical characteristics of the structure, e.g. the natural frequencies and mode shapes, are known. Furthermore, a simplified force model is proposed for the loads due to various densities of the pedestrian traffic on the bridge.
The methodology of the design guides is evaluated for application in design stage, using a finite element model based on structural drawings, and at completion when the footbridge is built and the dynamic characteristics of the structure can be identified in situ. In total, eight lively footbridges are considered in this study. For each case, a finite element model is developed, the modal characteristics are identified and the vibration serviceability is assessed.
The outline of this paper is as follows. First, the methodology of the current codes of practice is discussed. Second, the different case studies are presented, including a description of the finite element model and the modal parameters as identified from the operational modal analysis. In the final section, the vibration serviceability assessment is performed according to the guidelines in design stage and at completion enabling the evaluation of the design procedures.
Section snippets
Current codes of practice
This section gives a brief summary of the footbridge vibration serviceability design procedures as described by the French Sétra guideline [18] and the European HiVoSS guideline [19], [20]. The Sétra guideline was developed within the framework of the Sétra/AFGC working group on “Dynamic behaviour of footbridges”. The HiVoSS guideline is based on the results obtained within the research project RFS-CR-03019 “Advanced Load Models for Synchronous Pedestrian Excitation and Optimised Design
Case studies
A total of 8 footbridges has been studied (Fig. 2), all of which were built within the last 10 years. For each case, a finite element (FE) model is developed to simulate the physical behaviour of the structure and to enable the prediction of the response under human induced loading. The main characteristics of these footbridges and the finite element models are listed in Table 5. Fig. 3 presents the elevation and cross section of the tested structures on a uniform scale.
For all cases, an
Vibration serviceability assessment
In this section, the vibration serviceability of the considered footbridges is assessed according to the guidelines. First, an evaluation is performed in design stage based on the available finite element model. Second, the assessment is performed at completion based on in situ identified modal characteristics. For reasons of conciseness, the assessment is presented in detail for two cases, the Eeklo and the Anderlecht footbridge, and is followed by a brief summary of the results for all eight
Conclusions
Pedestrian bridges are very often lively structures prone to human induced vibrations, necessitating the vibration serviceability assessment in design stage. The current codes of practice (Sétra and HiVoSS) enable the designer to check the vibration serviceability of the footbridge based on a prediction of the maximum acceleration levels. The guides present a selection of pedestrian densities and apply a simplified equivalent load model to represent crowd induced loading.
The methodology of
Acknowledgements
The results of this paper were partly obtained within the framework of the research project, TRICON “Prediction and control of human-induced vibrations of civil engineering structures”, financed by the Flemish government (IWT, agency for Innovation by Science and Technology).
The authors would like to thank the engineering offices and parties concerned for their cooperation and providing information on the investigated footbridges.
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