Footbridge Vibrations and Modelling of Pedestrian Loads 73 Table 7 Acceleration quantile a95 Model for step frequency Bridge I (m/s2) II (m/s2) III (m/s2) A 0.3093 0.2879 0.1750 B 0.3904 0.4256 0.3442 C 0.2743 0.4715 0.5033 In terms of bridge response, and focusing on the response characteristic a95, Table 7 summarises the results computed for footbridge A, B, and C. Values of a95 are provided for the three different step frequency models. For bridge A there is a maximum difference of (0.3093–0.1750=) 0.1343 m/s2 between results obtained for the three stochastic models for step frequency. If this value is normalised by the minimum number 0.1750 m/s2, one obtains a 77% difference in results for bridge A. Doing the same calculations for bridge B and C results in 24% and 83% differences, respectively. Hence, the choice of step frequency model assumed for computing a95 has a relative high impact on the result. 4 Conclusion and Discussion In the paper the influence of decisions as regards settling on a framework for pedestrian load models for evaluating footbridge response at the design stage was examined. Focus was on estimation of the footbridge acceleration response occurring at midspan of footbridges. The acceleration quantile a95 (the acceleration level exceeded in 5% of the pedestrian crossings) was chosen for investigation. For the investigations, different artificial SDOF and pin-supported bridges were considered so as to widen the perspective of conclusions. One issue addressed was on ways for choosing the dynamic load amplification factor for a computational prediction of footbridge response. Another issue was on choosing parameters of a stochastic model for the step frequency of pedestrians for entering into the calculations. Both choices might potentially affect the outcome of the predicted stochastic nature of bridge response and hence serviceability-limit-state evaluations for footbridges. As for the dynamic load factor, different methods for extracting the main governing load amplification factor were examined. It turned out that a simplified technique not fully in accordance with the stochastic nature of the pedestrian traffic provided fairly reasonable results (errors in predictions of a95 of maximum 20% for the investigated bridges). Whereas the investigations in terms of the dynamic load factor focused on a technique for simpler processing of data, the investigations in terms of choosing parameters for a stochastic model for step frequency directly relate to actual uncertainties. Solutions to this challenge are not provided here but it is interesting to notice that the calculations of this paper suggest up to 83% deviations in estimates of a95 depending on which bridge is considered and which input parameters are chosen for modelling the stochastic nature of step frequencies. References 1. Dallard, P., Fitzpatrick, A.J., Flint, A., Le Bourva, S., Low, A., Ridsdill-Smith, R.M., Wilford, M.: The London millennium bridge. Struct. Eng. 79, 17–33 (2001) 2. Ellis, B.R.: On the response of long-span floors to walking loads generated by individuals and crowds. Struct. Eng. 78, 1–25 (2000) 3. Bachmann, H., Ammann, W.: Vibrations in Structures – Induced by Man and Machines. IABSE Structural Engineering Documents 3e, Zürich, Switzerland (1987) 4. Rainer, J.H., Pernica, G., Allen, D.E.: Dynamic loading and response of footbridges. Can. J. Civ. Eng. 15, 66–78 (1998) 5. Matsumoto, Y., Nishioka, T., Shiojiri, H., Matsuzaki, K.: Dynamic design of footbridges. In: IABSE Proceedings, No. P-17/78, pp. 1–15 (1978) 6. Živanovic, S.: Probability-based estimation of vibration for pedestrian structures due to walking. PhD Thesis, Department of Civil and Structural Engineering, University of Sheffield, UK (2006) 7. Kerr, S.C., Bishop, N.W.M.: Human induced loading on flexible staircases. Eng. Struct. 23, 37–45 (2001) 8. Pedersen, L., Frier, C.: Sensitivity of footbridge vibrations to stochastic walking parameters. J. Sound Vibr. (2009). https://doi.org/10.1016/ j.jsv.2009.12.022 9. Živanovic, S., Pavic, A., Reynolds, P.: Probability-based prediction of multi-mode vibration response to walking excitation. Eng. Struct. 29, 942–954 (2007). https://doi.org/10.1016/j.engstruct.2006.07.004
RkJQdWJsaXNoZXIy MTMzNzEzMQ==