202 L. Pedersen and C. Frier Table 24.5 Acceleration quantiles Bridge A B Load model I (m/s2) II (m/s2) I (m/s2) II (m/s2) a95 0.3537 0.3421 0.0257 0.0754 a90 0.2770 0.2674 0.0212 0.0670 a75 0.1095 0.1296 0.0152 0.0559 Step length deterministic 24.5.2 Influence of Approach for Modelling Step Length Table 24.5 presents acceleration quantiles derived having applied load models I and II for the two bridges (bridges A and B). Values for the similar acceleration quantiles were presented in Table 24.4. The only difference is that for the results given in Table 24.5, the step length, ls, was handled as a deterministic property (and not as a random variable as was the case for the results presented in Table 24.4). For the calculations, the step length was set to the mean value, 0.071 m. A comparison of values of the acceleration quantiles listed in Tables 24.4 and 24.5 reveals that there is a marginal difference in the values. This is the case for both bridges and for both load models. This suggests that it is not of importance whether the step length is modelled as random parameter or a deterministic property. 24.6 Conclusion Two walking load models have been employed for examining of the stochastic nature of bridge response of two different SDOF bridges in order to compare outcome of results. One bridge was a 1.9 Hz-bridge and the other was a 2.85 Hz-bridge. One of the load models is capable of reproducing forces generated by a pedestrian to a high level of detail. The other load model is not able to replicate the action of pedestrians to a similar level of detail. It was found that for the 1.9 Hz-bridge, the simple load model provided estimates of bridge acceleration quantiles that where very close to those found when applying a pedestrian load generated by the advanced load model. For the 2.85 Hzbridge, the estimates of bridge acceleration quantiles did not compare well. This is a result of the fact that the simple load model fails to model energy of pedestrian action correctly at all frequencies, especially in frequency ranges between the main harmonics of the action. Hence, in some cases the simple load model would not be an appropriate choice. It was found that even though both load models are capable of accounting for stochastic nature of characteristics such as step frequency, dynamic load factor, step length etc., the computed bridge acceleration quantiles are insensitive to whether step length was modelled as a random parameter or as a deterministic property. This was observed for both load models. It would be of interest to examine whether the conclusions are also valid for other footbridges than those considered for the studies of this paper. Acknowledgements This research was carried out in the framework of the project “UrbanTranquility” under the Intereg V program and the authors of this work gratefully acknowledge the European Regional Development Fund for the financial support. 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. Ontario Highway Bridge Design Code, Highway Engineering Division; Ministry of Transportation and Communication, Ontario, Canada, 1983 3. British Standard Institution: Steel, concrete and composite bridges. Specification for loads, BS 5400: Part 2, 1978 4. Matsumoto, Y., Nishioka, T., Shiojiri, H., Matsuzaki, K.: Dynamic design of footbridges, IABSE Proceedings, No. P-17/78, pp. 1–15, 1978 5. 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 6. Kerr, S.C., Bishop, N.W.M.: Human induced loading on flexible staircases. Eng. Struct. 23, 37–45 (2001) 7. Pedersen, L., Frier, C.: Sensitivity of footbridge vibrations to stochastic walking parameters. J. Sound Vib. 329, 2683–2701 (2009). doi:10.1016/j.jsv.2009.12.022 8. Ellis, B.R.: On the response of long-span floors to walking loads generated by individuals and crowds. Struct. Eng. 78, 1–25 (2000)
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