DOI QR코드

DOI QR Code

Numerical study on the walking load based on inverted-pendulum model

  • Cao, Liang (School of Civil Engineering, Chongqing University) ;
  • Liu, Jiepeng (School of Civil Engineering, Chongqing University) ;
  • Zhang, Xiaolin (School of Civil Engineering, Chongqing University) ;
  • Chen, Y. Frank (School of Civil Engineering, Chongqing University)
  • Received : 2018.11.26
  • Accepted : 2019.04.01
  • Published : 2019.08.10

Abstract

In this paper, an inverted-pendulum model consisting of a point supported by spring limbs with roller feet is adopted to simulate human walking load. To establish the kinematic motion of first and second single and double support phases, the Lagrangian variation method was used. Given a set of model parameters, desired walking speed and initial states, the Newmark-${\beta}$ method was used to solve the above kinematic motion for studying the effects of roller radius, stiffness, impact angle, walking speed, and step length on the ground reaction force, energy transfer, and height of center of mass transfer. The numerical simulation results show that the inverted-pendulum model for walking is conservative as there is no change in total energy and the duration time of double support phase is 50-70% of total time. Based on the numerical analysis, a dynamic load factor ${\alpha}_{wi}$ is proposed for the traditional walking load model.

Keywords

Acknowledgement

Supported by : Central Universities, National Natural Science Foundation of China

References

  1. Ahmadi, E., Caprani, C., Zivanovic S. and Heidarpour, A. (2018), "Vertical ground reaction forces on rigid and vibrating surfaces for vibration serviceability assessment of structures", Eng. Struct., 172, 723-738. https://doi.org/10.1016/j.engstruct.2018.06.059.
  2. Allen, D.E. and Murray, T.M. (1993), "Design criterion for vibrations due to walking", Eng. J. AISC, 30(4), 117-129.
  3. Avossa, A.M., Demartino, C. and Ricciardelli, F. (2017), "Design procedures for footbridges subjected to walking loads: comparison and remarks", Balt. J. Road Bridge E., 12(2), 94-105. https://doi.org/10.3846/bjrbe.2017.12
  4. Bachmann, H. and Ammann, W. (1987), Vibrations in Structures Induced by Man and Machines, International Association for Bridge and Structural Engineering, Zurich, Switzerland.
  5. Blanchard, J., Davies, B.L. and Smith, J.W. (1977), "Design criteria and analysis for dynamic loading of footbridges", Proceeding of a Symposium on Dynamic Behaviour of Bridges at the Transport and Road Research Laboratory, Berkshire, England, May.
  6. Bocian, M., Macdonald, J.H.G. and Burn, J.F. (2014), "Probabilistic criteria for lateral dynamic stability of bridges under crowd loading", Comput. Struct., 136, 108-119. https://doi.org/10.1016/j.compstruc.2014.02.003.
  7. Brownjohn, J.M.W., Chen, J., Bocian, M., Racic, V. and Shahabpoor, E. (2018), "Using inertial measurement units to identify medio-lateral ground reaction forces due to walking and swaying", J. Sound Vib., 426, 90-110. https://doi.org/10.1016/j.jsv.2018.04.019.
  8. Cao, L., Liu, J.P., Zhou, X.H. and Chen, Y.F. (2018), "Vibration performance characteristics of a long-span and light-weight concrete floor under human-induced loads", Struct. Eng. Mech., 65(3), 349-357. https://doi.org/10.12989/sem.2018.65.3.349.
  9. Chen, J., Peng, Y.X. and Ye, T. (2013), "On methods for extending a single footfall trace into a continuous force curve for floor vibration serviceability analysis", Struct. Eng. Mech., 46(3), 179-196. https://doi.org/10.12989/sem.2013.46.2.179.
  10. Chen, J., Wang, H.Q. and Peng, Y.X. (2014), "Experimental investigation on Fourier-series model of walking load and its coefficients", J. Vib. Shock, 33(8), 11-15.
  11. Davis, B. and Avci, O. (2015), "Simplified vibration serviceability evaluation of slender monumental stairs", J. Struct. Eng., 141(11), https://doi.org/10.1061/(ASCE)ST.1943-541X.0001256.
  12. Han, H.X., Zhou, D. and Ji, T.J. (2017), "Mechanical parameters of standing body and applications in human-structure interaction", Int. J. Appl. Mech., 9(2). https://doi.org/10.1142/S1758825117500211.
  13. Kerr, S.C. (1998), "Human induced loading on staircases", Ph.D. Dissertation, University College London, London.
  14. Kim, J.H. and Jeon, J.Y. (2014), "Effects of vibration characteristics on the walking discomfort of floating floors on concrete slabs", J. Acoust. Soc. AM., 136(4), 1702-1711. https://doi.org/10.1121/1.4894686.
  15. Liu, J.P., Cao, L. and Chen, Y. F. (2019), "Vibration performance of composite steel-bar truss slab with steel girder", Steel Compos. Struct., 30(6), 577-589. https://doi.org/10.12989/scs.2019.30.6.577.
  16. Mello, A.V.A., da Silva, J.G.S., da S. Vellasco, P.C.G., de Andrade, S.A.L. and de Lima, L.R.O. (2008), "Dynamic analysis of composite systems made of concrete slabs and steel beams", J. Constr. Steel Res., 64, 1142-1151. https://doi.org/10.1016/j.jcsr.2007.09.011.
  17. Murray, T.M., Allen, D.E. and Ungar, E.E. (1997), Floor Vibrations Due to Human Activity, American Institute of Steel Construction, Inc., Chicago, USA.
  18. Murray, T.M., Allen, D.E., Ungar, E.E. and Davis, D.B. (2016), Vibrations of Steel-Framed Structural Systems Due to Human Activity (2nd Edition), American Institute of Steel Construction, Inc., Chicago, USA.
  19. Peng, Y.X., Chen, J. and Ding, G. (2015), "Walking load model for single footfall trace in three dimensions based on gait experiment", Struct. Eng. Mech., 54(5), 937-953. https://doi.org/10.12989/sem.2015.54.5.937.
  20. Petrovic-Kotur, S.P. and Pavic, A.P. (2016), "Vibration analysis and FE model updating of lightweight steel floors in full-scale prefabricated building", Struct. Eng. Mech., 58(2), 277-300. https://doi.org/10.12989/sem.2016.58.2.277.
  21. Rainer, J.H., Pernica, G. and Allen, D.E. (1988), "Dynamic loading and response of footbridges", Can. J. Civil. Eng., 15(1), 66-71. https://doi.org/10.1139/l88-007.
  22. Setareh, M. (2016), "Vibration serviceability issues of slender footbridges", J. Bridge Eng., 21(11), https://doi.org/10.1061/(ASCE)BE.1943-5592.0000951.
  23. Setareh, M. and Gan, S.Q. (2018), "Vibration testing, analysis, and human-structure interaction studies of a slender footbridge", J. Perform. Constr. Fac., 32(5), https://doi.org/10.1061/(ASCE)CF.1943-5509.0001213.
  24. Smith, A.L., Hicks, S.J. and Devine, P.J. (2009), Design of Floors for Vibration: A New Approach, The Steel Construction Institute, Berkshire, United Kingdom.
  25. Van Nimmen, K., Lombaert, G., De Roeck, G. and Van den Broeck, P. (2017), "The impact of vertical human-structure interaction on the response of footbridges to pedestrian excitation", J. Sound Vib., 402, 104-121. https://doi.org/10.1016/j.jsv.2017.05.017.
  26. Wang, J. and Chen, J. (2017), "A comparative study on different walking load models", Struct. Eng. Mech., 63(6), 847-856. https://doi.org/10.12989/sem.2017.63.6.847.
  27. 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", J. Biomech. Eng., 131(1). https://doi.org/10.1115/1.3005147.
  28. Yin, S.H. (2017), "Pedestrian-induced vibration of a simplysupported beam", J. Mech., 33(5), 577-591. https://doi.org/10.1017/jmech.2016.94.
  29. Young, P. (2001), "Improved floor vibration prediction methodologies", Proceedings of Arup Vibration Seminar on Engineering for Structure Vibration-Current Developments in Research and Practice, London, October.
  30. Younis, A., Avci, O., Hussein, M., Davis, B. and Reynolds, P. (2017), "Dynamic forces induced by a single pedestrian: a literature review", Appl. Mech. Rev., 69(2). https://doi.org/10.1115/1.4036327.
  31. Zhou, X.H., Liu, J.P., Cao, L. and Li, J. (2017), "Vibration serviceability of pre-stressed concrete floor system under human activity", Struct. Infrastruct. E., 13(8), 967-977. https://doi.org/10.1080/15732479.2016.1229796.