Technical Papers
Aug 1, 2022

Equivalent Dynamic Load Factor for Crowd Walking Loads

Publication: Journal of Structural Engineering
Volume 148, Issue 10

Abstract

Pedestrian-induced loads may cause vibration serviceability or safety issues in slender structures such as long-span floors and footbridges. Although some models for crowd walking loads have been established, the synchronization among pedestrians and interaction with the structure have not been fully expressed. This study proposes a Fourier series model with a series of equivalent dynamic load factors (EDLFs), which are adaptive to different crowd-dominant walking frequencies, structural damping ratios, crowd sizes, and pedestrian traffic conditions (unrestricted, restricted, and exceptionally restricted). Using the power spectral density for the crowd walking loads proposed in a previous study, the structural responses of different single-degree-of-freedom systems are calculated via numerical simulations of approximately 20 million variations, and the EDLF for crowd walking loads is obtained after back-calculating the structural responses. This modeling method weighted the energy around the dominant walking frequency. The results show that the EDLFs are stable for crowds of over 30 pedestrians. The proposed model was compared with three modeling methods for dynamic load factors and five codified models for crowd walking loads from different aspects, and the feasibility of the EDLF is verified based on a benchmark footbridge and an as-built floor structure. The EDLF is convenient for design purposes because it is compatible with the single-person model currently adopted in major design codes and software.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (52108158, 51778465, and U1711264). Moreover, the authors are thankful for the literature regarding the model verification on benchmark structures.

References

An, Q., Q. Ren, H. Liu, X. Liu, and Z. Chen. 2016. “Dynamic performance characteristics of an innovative cable supported beam structure–concrete slab composite floor system under human-induced loads.” Eng. Struct. 117 (Mar): 40–57. https://doi.org/10.1016/j.engstruct.2016.02.038.
Bachmann, H., and W. Ammann. 1987. “Vibrations in structures: Induced by man and machines.” In Structural Engineering Documents 3e. Zurich, Switzerland: International Association for Bridge and Structural Engineering.
Bassoli, E., K. van Nimmen, L. Vincenzi, and P. van den Broeck. 2018. “A spectral load model for pedestrian excitation including vertical human-structure interaction.” Eng. Struct. 156 (Feb): 537–547. https://doi.org/10.1016/j.engstruct.2017.11.050.
Bro. 2004. Vägverkets allmänna tekniska beskrivning för nybyggande och förbättring av broar. Stockholm, Sverige: Svensk Byggtjänst.
Brownjohn, J. M. W., A. Pavic, and P. Omenzetter. 2004. “A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking.” Can. J. Civ. Eng. 31 (1): 65–77. https://doi.org/10.1139/l03-072.
BSI (British Standards Institution). 2008. UK National Annex to Eurocode 1: Actions on structures—Part 2: Traffic loads on bridges. NA to BS EN 1991-2: 2003. London: BSI.
Chen, J., H. Q. Wang, and Y. X. Peng. 2014. “Experimental investigation on Fourier-series model of walking load and its coefficients.” [In Chinese.] J. Vib. Shock 33 (8): 11–15. https://doi.org/10.13465/j.cnki.jvs.2014.08.003.
Chen, J., J. P. Wang, and J. M. W. Brownjohn. 2019. “Power spectral density model for pedestrian walking load.” J. Struct. Eng. 145 (2): 04018239. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002248.
Chopra, A. K. 2005. Dynamics of structures: Theory and applications to earthquake engineering. Upper Saddle River, NJ: Prentice Hall.
Croce, P. 2010. Guidebook 2 design of bridges. Prague, Czechia: Czech Technical Univ.
Dallard, P., A. J. Fitzpatrick, A. Flint, S. Le Bourva, A. Low, R. M. Ridsdill Smith, and M. Willford. 2001. “The London millennium footbridge.” Struct. Eng. 79 (22): 17–33.
Donno, A. D., D. Powell, and A. Low. 2005. “Design and damping system for footbridges conceptual framework.” In Proc., 2nd Int. Footbridge Conf. Zurich, Switzerland: International Association for Bridge and Structural Engineering.
Ebrahimpour, A., A. Hamam, R. L. Sack, and W. N. Patten. 1996. “Measuring and modeling dynamic loads imposed by moving crowds.” J. Struct. Eng. 122 (12): 1468–1474. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:12(1468).
Ebrahimpour, A., and R. L. Sack. 2005. “A review of vibration serviceability criteria for floor structures.” Comput. Struct. 83 (28–30): 2488–2494. https://doi.org/10.1016/j.compstruc.2005.03.023.
Ellingwood, B., and A. Tallin. 1984. “Structural serviceability: Floor vibrations.” J. Struct. Eng. 110 (2): 401–418. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:2(401).
Feldmann, M., C. Heinemeyer, and M. Lukic. 2008. HiVoSS (human induced vibrations of steel structures): Design of footbridges. Brussels, Belgium: Office for Official Publications of the European Communities.
FIB (Fédération Internationale du Béton). 2005. Guidelines for the design of footbridges. Stuttgart, Germany: Sprint-Digital-Druck.
Ingólfsson, E. T., C. T. Georgakis, F. Ricciardelli, and J. Jönsson. 2011. “Experimental identification of pedestrian-induced lateral forces on footbridges.” J. Sound Vib. 330 (6): 1265–1284. https://doi.org/10.1016/j.jsv.2010.09.034.
Jones, C. A., P. Reynolds, and A. Pavic. 2011. “Vibration serviceability of stadia structures subjected to dynamic crowd loads: A literature review.” J. Sound Vib. 330 (8): 1531–1566. https://doi.org/10.1016/j.jsv.2010.10.032.
Kerr, S. C. 1998. “Human induced loading on staircases.” Ph.D. thesis, Dept. of Mechanical Engineering, Univ. College London.
Muhammad, Z., P. Reynolds, O. Avci, and M. Hussein. 2018. “Review of pedestrian load models for vibration serviceability assessment of floor structures.” Vibration 2 (1): 1–24. https://doi.org/10.3390/vibration2010001.
Murray, T. M., D. E. Allen, and E. E. Ungar. 2003. Steel design guide series 11: Floor vibrations due to human activity. Chicago: American Institute of Steel Construction.
Parkhouse, J. G., and D. J. Ewins. 2006. “Crowd-induced rhythmic loading.” Proc. Inst. Civ. Eng. Struct. Build. 159 (5): 247–259. https://doi.org/10.1680/stbu.2006.159.5.247.
Racic, V., A. Pavic, and J. M. W. Brownjohn. 2009. “Experimental identification and analytical modelling of human walking forces: Literature review.” J. Sound Vib. 326 (1–2): 1–49. https://doi.org/10.1016/j.jsv.2009.04.020.
Rainer, J. H., G. Pernica, and D. E. Allen. 1988. “Dynamic loading and response of footbridges.” Can. J. Civ. Eng. 15 (1): 66–71. https://doi.org/10.1139/l88-007.
Ricciardelli, F., and A. D. Pizzimenti. 2007. “Lateral walking-induced forces on footbridges.” J. Bridge Eng. 6 (12): 677–688. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(677).
Sétra (Service d’Étude Techniques des Routes et Autoroutes). 2006. Technical guide: Assessment of vibrational behavior of footbridges under pedestrian loading. Paris: Sétra.
Smith, A. L., S. J. Hicks, and P. J. Devine. 2009. Design of floors for vibration: A new approach. New Bedford, MA: Steel Construction Institute.
Van Nimmen, K., J. van Hauwermeiren, and P. van den Broeck. 2021. “Eeklo footbridge: Benchmark dataset on pedestrian-induced vibrations.” J. Bridge Eng. 26 (7): 05021007. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001707.
Wang, J. P., J. Chen, Y. Yokoyama, and J. C. Xiong. 2020. “Spectral model for crowd walking load.” J. Struct. Eng. 146 (3): 04019220. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002514.
Wirsching, P. H., T. L. Paez, and K. Ortiz. 2006. Random vibrations: Theory and practice. New York: Wiley.
Wolmuth, B., and J. Surtees. 2003. “Crowd-related failure of bridges.” Proc. Inst. Civ. Eng. Civ. Eng. 156 (3): 116–123. https://doi.org/10.1680/cien.2003.156.3.116.
Yang, X., Y. Li, G. Ma, X. Hu, J. Wang, Z. Cui, Z. Wang, W. Yu, Z. Yang, and F. Zhai. 2005. “Study on weight and height of the Chinese people and the differences between 1992 and 2002.” [In Chinese.] Chin. J. Epidemiol. 26 (7): 489–493.
Živanović, S. 2012. “Benchmark footbridge for vibration serviceability assessment under vertical component of pedestrian load.” J. Struct. Eng. 138 (10): 1193–1202. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000571.
Živanović, S., A. Pavic, and P. Reynolds. 2005. “Vibration serviceability of footbridges under human-induced excitation: A literature review.” J. Sound Vib. 279 (1–2): 1–74. https://doi.org/10.1016/j.jsv.2004.01.019.
Živanović, S., A. Pavic, and P. Reynolds. 2006. “Modal testing and FE model tuning of a lively footbridge structure.” Eng. Struct. 28 (6): 857–868. https://doi.org/10.1016/j.engstruct.2005.10.012.
Živanović, S., A. Pavić, and E. T. Ingólfsson. 2010. “Modeling spatially unrestricted pedestrian traffic on footbridges.” J. Struct. Eng. 136 (10): 1296–1308. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000226.
Živanović, S., A. Pavić, and P. Reynolds. 2007. “Probability-based prediction of multi-mode vibration response to walking excitation.” Eng. Struct. 29 (6): 942–954. https://doi.org/10.1016/j.engstruct.2006.07.004.
Żółtowski, K. 2008. “Pedestrian on footbridges, vertical loads and response.” In Proc., 3rd Int. Footbridge Conf. Zurich, Switzerland: International Association for Bridge and Structural Engineering.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 148Issue 10October 2022

History

Received: Apr 11, 2021
Accepted: May 16, 2022
Published online: Aug 1, 2022
Published in print: Oct 1, 2022
Discussion open until: Jan 1, 2023

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Authors

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Jinping Wang, Ph.D. [email protected]
Assistant Professor, Dept. of Civil Engineering, Shanghai Normal Univ., Shanghai 200233, PR China (corresponding author). Email: [email protected]
Jun Chen, Ph.D. [email protected]
Professor, Dept. of Structural Engineering, Tongji Univ., Shanghai 200092, PR China. Email: [email protected]

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