Skip to main content
SpringerLink
Log in

Framework for Calculating the Vertical Human-Induced Vibration of the Suspension Footbridge Under the Random Pedestrian Flow

  • Published:
International Journal of Steel Structures Aims and scope Submit manuscript

Abstract

Currently, the problem of human-induced vibration of suspension footbridges is a research hotspot in bridge engineering. Moreover, on the suspension footbridge deck, the walking parameters of pedestrians, the simulation of random pedestrian flow, and the calculation method of human-induced vibration are the keys to solving the above problem. Therefore, in this paper, the following three studies have been carried out: (1) Firstly, the Jiufengshan suspension footbridge was taken as the observation site, and the statistical values of the step frequency (f), step length (l), and walking velocity (v) of pedestrians on the suspension footbridge deck were investigated and obtained. (2) Secondly, by combining the “social force model” with the obtained f, l, and v, a Matlab program was compiled to simulate the random pedestrian flow on the suspension footbridge deck. (3) Finally, by combining the above program with the vertical vibration equations of the human–footbridge coupling system, a Matlab program was compiled to calculate the vertical human-induced vibration of the suspension footbridge deck, which then was used to study the influence of the random pedestrian flow and human–footbridge coupling effect on the vertical human-induced vibration of the suspension footbridge deck. So, the above studies can provide a meaningful reference for the design of suspension footbridges.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data Availability

All data, models, and code generated or used during the study appear in the submitted article.

References

  • Bruno, L., Corbetta, A., & Tosin, A. (2016). From individual behaviour to an evaluation of the collective evolution of crowds along footbridges. Journal of Engineering Mathematics, 101(1), 153–173. https://doi.org/10.1007/s10665-016-9852-z

    Article  MathSciNet  MATH  Google Scholar 

  • Buchmueller, S., & Weidmann., U. (2006). Parameters of pedestrians, pedestrian traffic and walking facilities. ETH, Zürich.

  • Caprani, C. C., & Ahmadi, E. (2016). Formulation of human–structure interaction system models for vertical vibration. Journal of Sound and Vibration, 377, 346–367. https://doi.org/10.1016/j.jsv.2016.05.015

    Article  Google Scholar 

  • Caprani, C. C., Keogh, J., Archbold, P., & Fanning, P. (2011) Characteristic vertical response of a footbridge due to crowd loading. In Proceedings of the 8th international conference on structural dynamics (pp. 978–985).

  • Chraibi, M., Seyfried, A., & Schadschneider, A. (2010). Generalized centrifugal-force model for pedestrian dynamics. Physical Review E, 82(4), 046111. https://doi.org/10.1103/PhysRevE.82.046111

    Article  Google Scholar 

  • Cristiani, E., Piccoli, B., & Tosin, A. (2011). Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Modeling and Simulation, 9(1), 155–182. https://doi.org/10.1137/100797515

    Article  MathSciNet  MATH  Google Scholar 

  • Ellis, B. R. (2000). On the response of long-span floors to walking loads generated by individuals and crowds. The Structural Engineer, 78(10), 17–25.

    Google Scholar 

  • EN03-08. (2008). Human induced vibrations of steel structures. Design of footbridges guidelines, Research fund for coal and steel, German.

  • Fruin, J. J. (1971). Pedestrian planning and design. Metropolitan Association of Urban Designers and Environment Planners, New York.

  • Gallup, A. C., Hale, J. J., Sumpter, D. J. T., Garnier, S., Kacelnik, A., Krebs, J. R., & Couzin, I. D. (2012). Visual attention and the acquisition of information in human crowds. Proceedings of National Academy of Science of the United States of America, 109(19), 7245–7250. https://doi.org/10.1073/pnas.1116141109

    Article  Google Scholar 

  • Gaspar, C., Caetano, E., Moutinho, C., & Silva, J. GSd. (2017). Biodynamic modelling of human rhythmic activities. Procedia Engineering, 199(12), 2802–2807. https://doi.org/10.1016/j.proeng.2017.09.556

    Article  Google Scholar 

  • Ingólfsson, E. T., Georgakis, C. T., & Jönsson, J. (2015). Pedestrian-induced lateral vibrations of footbridges: A literature review. Engineering Structures, 45, 21–52. https://doi.org/10.1016/j.engstruct.2012.05.038

    Article  Google Scholar 

  • Jiménez-Alonso, J. F., & Sáez, A. (2014). A direct pedestrian–structure interaction model to characterize the human induced vibrations on slender footbridges. Informes De La Construccion, 66, 1–9. https://doi.org/10.1007/978-3-319-15248-6_34

    Article  Google Scholar 

  • Jiménez-Alonso, J. F., Sáez, A., Caetano, E., & Magalhães, F. (2016). Vertical crowd-structure interaction model to analyze the change of the modal properties of a footbridge. Journal of Bridge Engineering. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000828

    Article  Google Scholar 

  • Kasperski, M., & Sahnaci, C. (2007). Service ability of pedestrian structures. In Proceedings of the 25th international modal analysis conference.

  • Kerr, S. C. (1998). Human induced loading of staircases. University College: London, UK.

    Google Scholar 

  • Kerr, S. C., & Bishop, N. W. M. (2001). Human induced loadingon flexible staircases. Engineering Structures, 23(1), 37–45. https://doi.org/10.1016/S0141-0296(00)00020-1

    Article  Google Scholar 

  • Li, H. L., & Chen, Z. Q. (2013). A calculation method for footbridge vibration under stochastic pedestrian loading. Journal of Hunan University (Natural Sciences) [In Chinese], 40(10), 22–31. https://doi.org/10.3969/j.issn.1674-2974.2013.10.004

    Article  Google Scholar 

  • Li, Y., Chen, Z., Dong, S. J., & Li, J. W. (2021a). Study on the effects of pedestrians on the aerostatic response of a long-span pedestrian suspension bridge. KSCE Journal of Civil Engineering, 25(10), 1–13. https://doi.org/10.1007/s12205-021-2127-x

    Article  Google Scholar 

  • Li, Y., & Li, C. (2020). Experimental investigations on the flutter derivatives of the pedestrian–bridge section models. KSCE Journal of Civil Engineering, 24(11), 3416–3434. https://doi.org/10.1007/s12205-020-0243-7

    Article  Google Scholar 

  • Li, Y., Li, C., Liang, Y. D., & Li, J. W. (2022). Flutter derivative prediction of flat box girder based on integrated neural network. Journal of Wind Engineering & Industrial Aerodynamics, 222, 104939. https://doi.org/10.1016/j.jweia.2022.104939

    Article  Google Scholar 

  • Li, Y., Li, C., Wang, F., & Li, J. W. (2021b). Study on the mechanism of the vortex-induced vibration of a bluff double-side box section. Steel and Composite Structures, 41(2), 293–315. https://doi.org/10.12989/scs.2021.41.2.293

    Article  Google Scholar 

  • Matsumoto, Y., & Griffin, M. J. (2003). Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration. Journal of Sound and Vibration, 260(3), 431–451. https://doi.org/10.1016/S0022-460X(02)00941-0

    Article  MATH  Google Scholar 

  • Matsumoto, Y., Nishioka, T., Shiojiri, H., & Matsuzaki, K. (1978). Dynamic design of footbridges. In Proceedings of international association for bridge and structural engineering (pp. 1–15).

  • Matsumoto, Y., Sato, S., Nishioka, T., & Shiojiri, H. (1972). A study on design of pedestrian over-bridges. Transactions of the Japan Society of Civil Engineers, 4, 50–51.

    Google Scholar 

  • Morbiato, T., Vitaliani, R., & Saetta, A. (2011). Numerical analysis of a synchronization phenomenon: Pedestrian–structure interaction. Computers & Structures, 89(12), 1649–1663. https://doi.org/10.1016/j.compstruc.2011.04.013

    Article  Google Scholar 

  • Nimmen, K. V., Maes, K., Živanović, S., Lombaert, G., Roeck, G. D., & Broeck, P. V. d. (2015). Identification and modelling of vertical human–structure interaction. In Proceedings of the 33rd conference of the society of experimental mechanics (pp. 319–330). https://doi.org/10.1007/978-3-319-15248-6_34.

  • Older, S. J. (1964). Pedestrian. No. LN275/SJ0, Berkshire: Department of Scientific and Industrial Research, Road Research Laboratory, Crowthorne.

  • Pachi, A., & Ji, T. (2005). Frequency and velocity of people walking. The Structural Engineer, 83(3), 36–40.

    Google Scholar 

  • Pedersen, L., & Frier, C. (2010). Sensitivity of footbridge vibrations to stochastic walking parameters. Journal of Sound and Vibration, 329, 2683–2701. https://doi.org/10.1016/j.jsv.2009.12.022

    Article  Google Scholar 

  • Predtechenskii, V. M., & Milinskii, A. I. (1978). Planning for foot traffic flow in buildings. National Bureau of Standardsm, Amerind Publishing Co. Pvt. Ltd., New Delhi.

  • Rainer, J. H., Pernica, G., & Allen, D. E. (1988). Dynamic loading and response of footbridges. Canadian Journal of Civil Engineering, 15(1), 66–71. https://doi.org/10.1139/l88-007

    Article  Google Scholar 

  • Sarkar, S. (1993). Determination of service levels for pedestrians, with European Examples." No. 1405, Transportation Research, Washington DC, pp. 35–42.

  • Shahabpoor, E. (2014). Dynamic interaction of walking humans with pedestrian structures in vertical direction experimentally based probabilistic modelling. Sheffield: University of Sheiffield.

    Google Scholar 

  • Silva, F. T., & Pimentel, R. L. (2013). Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges. Canadian Journal of Civil Engineering, 40(12), 1196–1204. https://doi.org/10.1139/cjce-2011-0587

    Article  Google Scholar 

  • Tanaboriboon, Y., Hwa, S. S., & Chor, C. H. (1986). Pedestrian characteristics study in Singapore. Journal of Transportation Engineering, 112(3), 229–235. https://doi.org/10.1061/(ASCE)0733-947X(1986)112:3(229)

    Article  Google Scholar 

  • Toso, M. A., Gomes, H. M., da Silva, F. T., & Pimentel, R. L. (2016). Experimentally fitted biodynamic models for pedestrian–structure interaction in walking situations. Mechanical Systems and Signal Processing, 72–73, 590–606. https://doi.org/10.1016/j.ymssp.2015.10.029

    Article  Google Scholar 

  • Tubino, F. (2018). Probabilistic assessment of the dynamic interaction between multiple pedestrians and vertical vibrations of footbridges. Journal of Sound and Vibration, 417, 80–96. https://doi.org/10.1016/j.jsv.2017.11.057

    Article  Google Scholar 

  • Venuti, F., & Bruno, L. (2007). The synchronous lateral excitation phenomenon: Modelling framework and an application. Comptes Rendus Mécanique, 335(12), 739–745. https://doi.org/10.1016/j.crme.2007.10.007

    Article  Google Scholar 

  • Venuti, F., Racic, V., & Corbetta, A. (2016). Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges. Journal of Sound and Vibration, 379, 245–263. https://doi.org/10.1016/j.jsv.2016.05.047

    Article  Google Scholar 

  • Wang, C. F., Gao, S. Q., Niu, S. H., & Liu, H. P. (2018). Influences of pedestrian SMD model parameters on dynamic characteristics of crowd–structure interaction. Journal of Vibration and Shock [in Chinese], 37(3), 91–97. https://doi.org/10.13465/j.cnki.jvs.2018.03.015

    Article  Google Scholar 

  • Wheeler, J. E. (1982). Prediction and control of pedestrian induced vibration in footbridges. Journal of the Structural Division, 108(ST9), 2045–2065. https://doi.org/10.1016/0022-1694(82)90165-2

    Article  Google Scholar 

  • Young, P. (2001) Improved floor vibration prediction methodologies. In Proceedings of arup vibration seminar on engineering for structure vibration-current developments in research and practice, London.

  • Zanlungo, F., Ikeda, T., & Kanda, T. (2011). Social force model with explicit collision prediction. Europhysics Letters, 93(6), 68005. https://doi.org/10.1209/0295-5075/93/68005

    Article  Google Scholar 

  • Zhang, M. S., Chen, J., & Xu, R. T. (2016). MD and SMD model parameters of pedestrians for vertical humarrstructure interaction. Journal of Vibration Engineering [in Chinese], 29(5), 814–821. https://doi.org/10.1007/978-3-319-15248-6_33

    Article  Google Scholar 

  • Zhang, M. S., Georgakis, C. T., Qu, W. J., & Chen, J. (2015). SMD model parameters of pedestrians for vertical human–structure interaction. Proceedings of the Society for Experimental Mechanics Series,. https://doi.org/10.1007/978-3-319-15248-6_33

    Article  Google Scholar 

  • Zhang, P. B., Lu, T., Chen, B. Z., & Lu, S. M. (2005). Observation and analysis of pedestrian flow under time pressure. Chinese Journal of Ergonomics [in Chinese], 11(1), 8–10. https://doi.org/10.3969/j.issn.1006-8309.2005.01.003

    Article  Google Scholar 

  • Živanović, S. (2006). Probability-based estimation of vibration for pedestrian structures due to walking. Ph.D, University of Sheffield, UK.

  • Zivanovic, S., Pavic, A., & Inuolfsson, E. T. (2010). Modelling spatially unrestricted pedestrian traffic on footbridges. Journal of Structural Engineering, 136(10), 1296–1308. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000226

    Article  Google Scholar 

  • Živanović, S., Pavić, A., & Reynolds, P. (2007) Probability-based estimation of footbridge vibration due to walking. In Proceedings of the 25th international modal analysis conference.

Download references

Acknowledgements

The research in this paper was supported by the National Natural Science Foundation of China (No. 51978077) and the Natural Science Basic Research Program of Shaanxi (Program No. 2022JQ-507). The authors wish to express their gratitude to the sponsors.

Author information

Authors and Affiliations

  1. School of Highway, Chang’an University, Xi’an, 710064, China

    Yu Li, Dong-Shuo Yin, Jia-Hao Wang & Jia-Wu Li

Authors
  1. Yu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dong-Shuo Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-Hao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jia-Wu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Li.

Ethics declarations

Competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. All data, models, and code generated or used during the study appear in the submitted article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Yin, DS., Wang, JH. et al. Framework for Calculating the Vertical Human-Induced Vibration of the Suspension Footbridge Under the Random Pedestrian Flow. Int J Steel Struct 22, 1322–1340 (2022). https://doi.org/10.1007/s13296-022-00640-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13296-022-00640-z

Keywords

Search

Navigation