Biomechanically Inspired Modeling of Pedestrian-Induced Vertical Self-Excited Forces
Publication: Journal of Bridge Engineering
Volume 18, Issue 12
Abstract
Although many models of pedestrian dynamic loading have been proposed, possible bidirectional interactions between the walker and the excited structure are generally ignored, particularly for vertical vibrations. This shortcoming has arisen from scarcity of data on gait-adaptation strategies used in the presence of structural motion and, as a consequence, the absence of a credible fundamental pedestrian model capable of capturing the underlying relations between the two dynamic systems. To address this inadequacy of current approaches, a biomechanically inspired inverted-pendulum pedestrian model has been applied to the human-structure interaction problem. The behavior of the model is studied when subjected to vertical motion of the supporting structure, in particular, in relation to potential self-excited forces that can be generated. A mechanism has been identified by which the timing of pedestrian footsteps can be altered subtly, giving a net damping effect on the structure, without necessarily involving full synchronization. It has been found that depending on the ratio between the bridge vibration frequency and pedestrian pacing frequency, walkers can effectively act as positive or negative dampers to the structural motion, but it is expected that for a group of pedestrians with distributed parameters, their action is, on average, to add damping and mass.
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Acknowledgments
This work was supported by an Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Account studentship for Mateusz Bocian and an EPSRC Advanced Research Fellowship for John H. G. Macdonald.
References
Alexander, N. A. (2006). “Theoretical treatment of crowd-str–ucture interaction dynamics.” Proc., ICE Struct. Build., 159(6), 329–338.
Alexander, R. M. (1989). “Optimization and gaits in the locomotion of vertebrates.” Physiol. Rev., 69(4), 1199–1227.
Alexander, R. M. (1992). “A model of bipedal locomotion on compliant legs.” Phil. Trans. R. Soc. Lond. B, 338(1284), 189–198.
Alexander, R. M. (1995). “Simple models of human movement.” Appl. Mech. Rev., 48(8), 461–469.
Alexander, R. M. (2003). Principles of animal locomotion, Princeton University Press, Woodstock, U.K.
Bachmann, H., and Ammann, W. (1987). Vibrations in structures induced by man and machines, 3rd Ed., International Association for Bridge and Structural Engineering (IABSE), Zurich, Switzerland.
Barker, C. (2002). “Some observations on the nature of the mechanism that drives the self-excited lateral response of footbridges.” Proc., Footbridge 2002: 1st Int. Conf., Paris.
Bertram, J. A. E., and Ruina, A. (2001). “Multiple walking speed-frequency relations are predicted by constraint optimization.” J. Theor. Biol., 209(4), 445–453.
Bocian, M., Macdonald, J. H. G., and Burn, J. F. (2012). “Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures.” J. Sound Vibrat., 331(16), 3914–3929.
British Standards Institution (BSI). (2003). UK national annex to Eurocode 1: Actions on structures. 2: Traffic loads on bridges, London.
Brownjohn, J. M. W., Fok, P., Roche, M., and Omenzetter, P. (2004). “Long span steel pedestrian bridge at Singapore Changi Airport. 2: Crowd loading tests and vibration mitigation measures.” Struct. Eng., 82(16), 28–34.
Butz, C., et al. (2008). “Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges.” RFSR-CT-2003-00019, European Commission, Brussels, Belgium.
Caprani, C. C., Keogh, J., Archbold, P., and Fanning, P. (2011). “Characteristic vertical response of a footbridge due to crowd loading.” Proc., Eurodyn 2011: 8th Int. Conf. on Structural Dynamics, 978–985.
Collins, S., Ruina, A., Tedrake, R., and Wisse, M. (2005). “Efficient bipedal robots based on passive-dynamic walkers.” Science, 307(5712), 1082–1085.
Dallard, P., et al. (2001). “The London Millennium Footbridge.” Struct. Eng., 79(22), 17–33.
Danbon, F., and Grillaud, G. (2005). “Dynamic behaviour of a steel footbridge: Characterisation and modelling of the dynamic loading induced by a moving crowd on the Solferino Footbridge in Paris.” Proc., Footbridge 2008: 2nd Int. Conf., Porto, Portugal.
Griffin, M. J. (1990). Handbook of human vibration, Academic Press, London.
Grundmann, H., Kreuzinger, H., and Schneider, M. (1993). “Schwingungsuntersuchungen für Fußgängerbrücken [Vibration tests of pedestrian bridges].” Der Bauingenieur, 68, 215–225 (in German).
Hof, A. L. (2008). “The ‘extrapolated center of mass’ concept suggests a simple control of balance in walking.” Hum. Mov. Sci., 27(1), 112–125.
Hof, A. L., Gazendam, M. G. J., and Sinke, W. E. (2005). “The condition for dynamic stability.” J. Biomech., 38(1), 1–8.
Ingólfsson, E. T., Georgakis, C. T., Ricciardelli, F., and Jönsson, J. (2011). “Experimental identification of pedestrian-induced lateral forces on footbridges.” J. Sound Vibrat. 330(6), 1265–1284.
Ingólfsson, E. T., Georgakis, C. T., and Svendsen, M. N. (2008). “Vertical footbridge vibrations: Details regarding and experimental validation of the response spectrum methodology.” Proc., Footbridge 2008: 3rd Int. Conf., Porto, Portugal.
Inman, V. T., Ralston, H. J., and Todd, F. (1981). Human walking, Williams & Wilkins, Baltimore.
Institution of Structural Engineers (ISE). (2008). Dynamic performance requirements for permanent grandstands subject to crowd action: Recommendations for management, design and assessment, London.
International Federation for Structural Concrete (fib). (2005). “Guidelines for the design of footbridges.” fib Bull. 32, Lausanne, Switzerland.
International Organization for Standardization (ISO). (1981). “Vibration and shock: Mechanical driving point impedance of the human body.” ISO 5982-1981, Geneva.
International Organization for Standardization (ISO). (2007). “Bases for design of structures: Serviceability of buildings and walkways against vibrations.” ISO 10137:2007, Geneva.
Kim, S. H., Cho, K. I., Choi, M. S., and Lim, J. Y. (2008). “Development of human body model for the dynamic analysis of footbridges under pedestrian induced excitation.” Int. J. Steel Struct., 8(4), 333–345.
Kuo, A. D. (2007). “The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective.” Hum. Mov. Sci., 26(4), 617–656.
Lee, C. R., and Farley, C. T. (1998). “Determinants of the center of mass trajectory in human walking and running.” J. Exp. Biol., 201(21), 2935–2944.
Macdonald, J. H. G. (2008). “Pedestrian-induced vibrations of the Clifton Suspension Bridge, UK.” Proc. ICE Bridge Eng., 161(2), 69–77.
Macdonald, J. H. G. (2009). “Lateral excitation of bridges by balancing pedestrians.” Proc. R. Soc. A, 465(2104), 1055–1073.
Masani, K., Kouzaki, M., and Fukunaga, T. (2002). “Variability of ground reaction forces during treadmill walking.” J. Appl. Physiol., 92(5), 1885–1890.
MATLAB 7.8.0.347 [Computer software]. Natick, MA, MathWorks.
Matsumoto, Y., and Griffin, M. J. (1998). “Dynamic response of the standing human body exposed to vertical vibration: Influence of posture and vibration magnitude.” J. Sound Vibrat., 212(1), 85–107.
Matsumoto, Y., and Griffin, M. J. (2003). “Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration.” J. Sound Vibrat., 260(3), 431–451.
McGeer, T. (1990). “Passive dynamic walking.” Int. J. Robot. Res., 9(2), 62–82.
Mochon, S., and McMahon, T. A. (1980). “Ballistic walking.” J. Biomech., 13(1), 49–57.
National Health Service (NHS). (2009). Health survey for England: 2008 trend tables, London.
O’Connor, S. M., and Kuo, A. D. (2009). “Direction-dependent control of balance during walking and standing.” J. Neurophysiol., 102(3), 1411–1419.
Pachi, A., and Ji, T. (2005). “Frequency and velocity of people walking.” Struct. Eng., 83(3), 36–40.
Pandy, M. G. (2003). “Simple and complex models for studying muscle function in walking.” Phil. Trans. R. Soc. Lond. B, 358(1437), 1501–1509.
Pheasant, S. T. (1982). “Anthropometric estimates for British civilian adults.” Ergonomics, 25(11), 993–1001.
Pizzimenti, A. D., and Ricciardelli, F. (2005). “Experimental evaluation of the dynamic lateral loading of footbridges by walking pedestrians.” Proc., Footbridge 2005: 2nd Int. Conf., Venice, Italy.
Racic, V., Pavic, A., and Brownjohn, J. M. W. (2009). “Experimental identification and analytical modelling of human walking forces: Literature review.” J. Sound Vibrat., 326(1–2), 1–49.
Tavares da Silva, F., and Pimentel, R. L. (2011). “Biodynamic walking model for vibration serviceability of footbridges in vertical direction.” Proc., Eurodyn 2011: 8th Int. Conf. on Structural Dynamics, 1090–1096.
Technical Department for Transport, Roads and Bridges Engineering and Road Safety/French Association of Civil Engineering (SETRA/AFGC). (2006) “Footbridges: Assessment of vibrational behaviour of footbridges under pedestrian loading.” Technical Guide 0611, Paris.
Willford, M. (2002). “Dynamic actions and reactions of pedestrians.” Proc., Footbridge 2002: 1st Int. Conf., Paris.
Živanović, S. (2012). “Benchmark footbridge for vibration serviceability assessment under the vertical component of pedestrian load.” J. Struct. Eng., 138(10), 1193–1202.
Živanović, S., Díaz, I. M., and Pavić, A. (2009). “Influence of walking and standing crowds on structural dynamic properties.” Proc., IMAC-XXVII: Conf. and Exposition on Structural Dynamics: Model Verification and Validation, Society for Experimental Mechanics, Bethel, CT.
Živanović, S., Pavić, A., and Ingólfsson, E. T. (2010). “Modeling spatially unrestricted pedestrian traffic on footbridges.” J. Struct. Eng., 136(10), 1296–1308.
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Published In
Journal of Bridge Engineering
Volume 18 • Issue 12 • December 2013
Pages: 1336 - 1346
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 26, 2012
Accepted: Mar 20, 2013
Published online: Mar 22, 2013
Published in print: Dec 1, 2013
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