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Research Papers

Finite Element Analysis of Pedestrian-Bridge Dynamic Interaction

[+] Author and Article Information
J. W. Qin

School of Civil Engineering,
Beijing Jiaotong University,
No. 3 Shang Yuan Cun,
Hai Dian District,
Beijing 100044, China

S. S. Law

Professor
Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Hunghom, Kowloon,
Hong Kong, China
e-mail: cesslaw@inet.polyu.edu.hk

Q. S. Yang

Professor

N. Yang

Professor
School of Civil Engineering,
Beijing Jiaotong University,
No. 3 Shang Yuan Cun,
Hai Dian District,
Beijing 100044, China

Manuscript received November 8, 2011; final manuscript received June 23, 2013; accepted manuscript posted July 16, 2013; published online September 23, 2013. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 81(4), 041001 (Sep 23, 2013) (15 pages) Paper No: JAM-11-1424; doi: 10.1115/1.4024991 History: Received November 08, 2011; Revised June 23, 2013; Accepted June 29, 2013

The pedestrian-bridge dynamic interaction problem in the vertical direction based on a bipedal walking model and damped compliant legs is presented in this work. The classical finite element method, combined with a moving finite element, represents the motion of the pedestrian in the dynamic analysis of a footbridge. A control force is provided by the pedestrian to compensate for the energy loss due to the system damping in walking and to regulate the walking performance of the pedestrian. The effects of leg stiffness, the landing angle of attack, the damping ratio of the leg and the mass ratio of the human and structure are investigated in the numerical studies. Simulation results show that the dynamic interaction will increase with a larger vibration level of the structure. More external energy must be input to maintain steady walking and uniform dynamic behavior of the pedestrian in the process. The simple bipedal walking model could well describe the human-structure dynamic interaction.

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References

Ellis, B. R., and Ji, T., 1997, “Human–Structure Interaction in Vertical Vibrations,” Proc. Inst. Civ. Eng., Struct. Build., 122(1), pp. 1–9. [CrossRef]
Brownjohn, J. M. W., 1999, “Energy Dissipation in One-Way Slabs With Human Participation,” Proceedings of the Asia-Pacific Vibration Conference, Nanyang Technological University, Singapore, December 13-15, pp. 155–160.
Brownjohn, J. M. W., 2001, “Energy Dissipation From Vibrating Floor Slabs Due to Human–Structure Interaction,” Shock Vib., 8(6), pp. 315–323.
Ji, T., 2003, “Understanding the Interactions Between People and Structures,” The Struct. Eng., July 15, pp. 12–13. Available at: http://personalpages.manchester.ac.uk/staff/tianjian.ji/research/papers/a3-understandingHSI.pdf
Sachse, R., Pavic, A., and Reynolds, P., 2003, “Human-Structure Dynamic Interaction in Civil Engineering Dynamics: A Literature Review,” Shock Vib. Dig., 35(1), pp. 3–18. [CrossRef]
Sachse, R., Pavic, A., and Reynolds, P., 2004, “Parametric Study of Modal Properties of Damped Two-Degree-of-Freedom Crowd-Structure Dynamic Systems,” J. Sound Vib., 274, pp. 461–480. [CrossRef]
Dougill, J. W., Wright, J. R., Parkhouse, J. G., and Harrison, R. E., 2006, “Human Structure Interaction During Rhythmic Bobbing,” The Struct. Eng., 84(22), pp. 32–39. Available at: http://www.istructe.org/journal/volumes/volume-84-(published-in-2006)/issues/issue-22/articles/human-structure-interaction-during-rhythmic-bobbin
Grundmann, H., Kreuzinger, H., and Schneider, M., 1993, “Dynamic Calculations of Footbridges,” Bauingenieur, 68, pp. 215–225.
Dallard, P., Fitzpatrick, A. J., Flint, A., Le Bourva, S., Low, A., Ridsdill-Smith, R. M., and Willford, M., 2001, “The London Millennium Footbridge,” The Struct. Eng., 79(22), pp. 17–33. Available at: http://www.istructe.org/journal/volumes/volume-79-(published-in-2001)/issues/issue-22/articles/the-london-millennium-footbridge
Dallard, P., Fitzpatrick, A. J., Flint, A., Le Bourva, S., Low, A., Ridsdill-Smith, R. M., and Willford, M., 2001, “London Millennium Bridge: Pedestrian-Induced Lateral Vibration,” J. Bridge Eng., 6(6), pp. 412–417. [CrossRef]
Mouring, S. E., and Ellingwood, B. R., 1994, “Guidelines to Minimize Floor Vibrations From Building Occupants,” J. Struct. Eng., 120(2), pp. 507–526. [CrossRef]
Brownjohn, J. M. W., Pavic, A., and Omenzetter, P., 2004, “A Spectral Density Approach for Modeling Continuous Vertical Forces on Pedestrian Structures Due to Walking,” Can. J. Civ. Eng., 31(1), pp. 65–77. [CrossRef]
Ricciardelli, F., and Pizzimenti, A. D., 2007, “Lateral Walking-Induced Forces on Footbridges,” J. Bridge Eng., 12(6), pp. 677–688. [CrossRef]
Sun, L., and Yuan, X., 2008, “Study on Pedestrian-Induced Vibration of Footbridge,” Proceedings of the Third International Conference on Footbridges 2008, Porto, Portugal, July 2-4.
Piccardo, G., and Tubino, F., 2008, “Parametric Resonance of Flexible Footbridges Under Crowd-Induced Lateral Excitation,” J. Sound Vib., 311, pp. 353–71. [CrossRef]
Ingolfsson, E. T., and Georgakis, C. T., 2011, “A Stochastic Load Model for Pedestrian-Induced Lateral Forces on Footbridges,” Eng. Struct., 33(12), pp. 3454–3470. [CrossRef]
Bruno, L., and Venuti, F., 2009, “Crowd-Structure Interaction in Footbridges: Modelling, Application to a Real Case-Study and Sensitivity Analyses,” J. Sound Vib., 323, pp. 475–493. [CrossRef]
Kim, S. H., Cho, K., Choi, M., Choi, M. S., and Lim, J. Y., 2008, “Development of Human Body Model for the Dynamic Analysis of Footbridges Under Pedestrian Induced Excitation,” J. Steel Struct., 8, pp. 333–345.
Archbold, P., Keogh, J., Caprani, C., and Fanning, P., 2011, “A Parametric Study of Pedestrian Vertical Force Models for Dynamic Analysis of Footbridges,” Proceedings of the 4th International Conference on Experimental Vibration Analysis for Civil Engineering Structures, Varenna, Italy, October 3-5.
Macdonald, J. H. G., 2009, “Lateral Excitation of Bridges by Balancing Pedestrians,” Proc. R. Soc. London, Ser. A, 465, pp. 1055–1073. [CrossRef]
Carroll, S. P., Owen, J. S., and Hussein, M. F. M., 2011, “Crowd-Bridge Interaction by Combining Biomechanical and Discrete Element Models,” Proceedings of the 8th International Conference on Structural Dynamics, Leuven, Belgium, July 4-6.
Geyer, H., Seyfarth, A., and Blickhan, R., 2006, “Compliant Leg Behavior Explains Basic Dynamics of Walking and Running,” Proc. R. Soc. London, Ser. B, 273, pp. 2861–2867. [CrossRef]
Whittington, B. R., and Thelen, D. G., 2009, “A Simple Mass-Spring Model With Roller Feet Can Induce the Ground Reactions Observed in Human Walking,” ASME J. Biomech. Eng., 131, p. 011013. [CrossRef]
Kim, S., and Park, S., 2011, “Leg Stiffness Increases With Speed to Modulate Gait Frequency and Propulsion Energy,” J. Biomech., 44, pp. 1253–1258. [CrossRef] [PubMed]
Yang, Y. B., Chang, C. H., and Yau, J. D., 1999, “An Element for Analyzing Vehicle Bridge System Considering Vehicle's Pitching Effect,” Int. J. Numer. Methods Eng., 46, pp. 1031–1047. [CrossRef]
Yang, Y. B., and Wu, Y. S., 2001, “A Versatile Element for Analyzing Vehicle–Bridge Interaction Response,” Eng. Struct., 23, pp. 452–469. [CrossRef]
Wu, J. J., 2008, “Transverse and Longitudinal Vibrations of a Frame Structure Due to a Moving Trolley and the Hoisted Object Using Moving Finite Element,” Int. J. Mech. Sci., 50, pp. 613–625. [CrossRef]
İsmail, E., 2011, “Dynamic Response of a Beam Due to an Accelerating Moving Mass Using Moving Finite Element Approximation,” Math. Comput. Appl., 16(1), pp. 171–182. Available at: http://mcajournal.cbu.edu.tr/specialissuevolume16_1/17.pdf
Clough, R. W., and Penzien, J., 1993, Dynamics of Structures, second ed., McGraw-Hill, New York.
Bathe, K. J., 1982, Finite Element Procedure in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Ellis, B. R., Ji, T., and Littler, J. D., 2000, “The Response of Grandstands to Dynamic Crowd Loads,” Proc. Inst. Civ. Eng., Struct. Build., 140, pp. 355–365. [CrossRef]
Ellis, B. R., 2000, “On the Response of Long-Span Floors to Walking Loads Generated by Individual and Crowds,” J. Struct. Eng., 78(10), pp. 17–25. Available at: http://www.istructe.org/journal/volumes/volume-78-(published-in-2000)/issues/issue-10/articles/on-the-response-of-long-span-floors-to-walking-loa
Yao, S., Wright, J. R., Pavic, A., and Reynolds, P., 2006, “Experimental Study of Human-Induced Dynamic Forces Due to Jumping on a Perceptibly Moving Structure,” J. Sound Vib., 296, pp. 150–165. [CrossRef]
Seyfarth, A., Geyer, H., Gunther, M., and Blickhan, R., 2002, “A Movement Criterion for Running,” J. Biomech., 35, pp. 649–655. [CrossRef] [PubMed]
Farley, C. T., and Gonzalez, O., 1996, “Leg Stiffness and Stride Frequency in Human Running,” J. Biomech., 29(2), pp. 181–186. [CrossRef] [PubMed]
Ferris, D. P., and Farley, C. T., 1997, “Interaction of Leg Stiffness and Surfaces Stiffness During Human Hopping,” J. Appl. Physiol., 82, pp. 15–22. Available at: http://www.ncbi.nlm.nih.gov/pubmed/9029193 [PubMed]
Farley, C. T., Houdijk, H. H., Van Strien, C., and Louie, M., 1998, “Mechanism of Leg Stiffness Adjustment for Hopping on Surfaces of Different Stiffnesses,” J. Appl. Physiol., 85, pp. 1044–1055. Available at: http://www.ncbi.nlm.nih.gov/pubmed/9729582 [PubMed]
Grimmer, S., Ernst, M., Guenther, M., and Blickhan, R., 2008, “Running on Uneven Ground: Leg Adjustment to Vertical Steps and Self-Stability,” J. Exp. Biol., 211(18), pp. 2989–3000. [CrossRef] [PubMed]
Mueller, R., Grimmer, S., and BlickhanmR., 2010, “Running on Uneven Ground: Leg Adjustments by Muscle Pre-Activation Control,” Hum. Mov. Sci., 29(2), pp. 299–310. [CrossRef] [PubMed]
Zivanovic, S., Pavic, A., and Ingolfsson, E. T., 2010, “Modeling Spatially Unrestricted Pedestrian Traffic on Footbridges,” J. Struct. Eng., 136(10), pp. 1296–1308. [CrossRef]
Brownjohn, J. M. W., Fok, P., Roche, M., and Omenzetter, P., 2004, “Long Span Steel Pedestrian Bridge at Singapore Changi Airport—Part 2: Crowd Loading Tests and Vibration Mitigation Measures,” Struct. Eng., 82(16), pp. 28–34.

Figures

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Fig. 1

Schematic of the biomechanical walking model (θ0 is the angle of attack)

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Fig. 2

Finite element discretization of a beam subjected to a pedestrian: (a) a beam subjected to a pedestrian, and (b) the nodal forces and displacements of the ith and jth beam elements

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Fig. 3

Free body diagrams for the components of the HSI system

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Fig. 4

Box-section girder structure

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Fig. 5

Reaction force on rigid ground

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Fig. 6

Acceleration at the midspan of the simply supported beam

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Fig. 7

Displacement of the CoM in walking

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Fig. 8

Acceleration of the CoM in walking

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Fig. 9

Beam reaction force generated in walking on a rigid beam

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Fig. 10

Acceleration spectrum at the midspan of the simply supported beam

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Fig. 11

Box-section girder structure

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Fig. 12

Acceleration at the midspan of the simply supported beam

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Fig. 13

Beam reaction force generated in walking on a flexible beam

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Fig. 14

Effect of leg stiffness on the dynamic response of the structure

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Fig. 15

Step frequencies in walking on a beam corresponding to the angle θ0 = 68 deg

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Fig. 16

Beam reaction force generated in the resonance case

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Fig. 17

Control force in walking in the resonance case

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Fig. 18

Effect of the mass ratio on the dynamic response of the beam

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Fig. 19

Effect of the damping ratio of the leg on the dynamic response of the beam

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