Structural Engineering and Mechanics

  • 제83권6호
  • /
  • Pages.729-744
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Practical formula for determining peak acceleration of footbridge under walking considering human-structure interaction

  • Cao, Liang (College of Civil Engineering, Hunan University) ;
  • Zhou, Hailei (College of Civil Engineering, Hunan University) ;
  • Chen, Y. Frank (Department of Civil Engineering, The Pennsylvania State University)
  • 투고 : 2021.01.22
  • 심사 : 2022.07.24
  • 발행 : 2022.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, an analytical formulation is proposed to predict the vertical vibration response due to the pedestrian walking on a footbridge considering the human-structure interaction, where the footbridge and pedestrian are represented by the Euler beam and linear oscillator model, respectively. The derived coupled equation of motion is a nonlinear fourth-order partial differential equation. An uncoupled solution strategy based on the combined weighted residual and perturbation method) is proposed to reduce the tedious computation, which allows the separate integration between the bridge and pedestrian subsystems. The theoretical study demonstrates that the pedestrian subsystem can be treated as a structural system with added mass, damping, and stiffness. The analysis procedure is then applied to a case study under the conditions of single pedestrian and multi pedestrians, and the results are validated and compared numerically. For convenient vibration design of a footbridge, the simplified peak acceleration formula and the idea of decoupling problem are thus proposed.

키워드

과제정보

The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant No. 51908084, 52278175), and the Fundamental Research Funds for the Central Universities (Grant No. 531118010784).

참고문헌

  1. Ahmadi, E., Caprani, C.C. and Heidarpour, A. (2017), "An equivalent moving force model for consideration of humanstructure interaction", Appl. Math. Model., 51, 526-545. https://doi.org/10.1016/j.apm.2017.06.042.
  2. Al-Foqaha'a, A.A. (1997), "Design criterion for wood floor vibrations via finite element and reliability analyses", Washington State University, Washington.
  3. Allen, D.E. and Murray, T.M. (1993), "Design criterion for vibrations due to walking", Eng. J. AISC, 30(4), 117-129.
  4. Ali, A., Mankad, H., Pereira, F. and Sousa, F.S. (2020), "The multiscale perturbation method for second order elliptic equations", Appl. Math. Comput., 387, 125023. https://doi.org/10.1016/j.amc.2019.125023.
  5. Bachmann, H. and Ammann, W. (1987), Vibrations in Structures: Induced by Man and Machines, International Association for Bridge and Structural Engineering, Switzerland.
  6. Bedon, C. (2020), "Experimental investigation on vibration sensitivity of an indoor glass footbridge to walking conditions", J. Build. Eng., 29, 101195. https://doi.org/10.1016/j.jobe.2020.101195.
  7. Berardengo, M., Drago, L., Manzoni, S. and Vanali, M. (2019), "An approach to predict human-structure interaction in the case of staircases", Arch. Appl. Mech., 89(10), 2167-2191. https://doi.org/10.1007/s00419-019-01569-2.
  8. 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.
  9. Cao, L., Liu, J.P. and Chen, Y.F. (2020), "Experimental study on vibration serviceability of steel-concrete composite floor", Struct. Eng. Mech., 74(5), 711-722. http://doi.org/10.12989/sem.2020.74.5.711.
  10. Cao, L. and Chen, Y.F. (2021), "Formulation of human-structure interaction for vibration serviceability of steel-concrete composite floors", Struct. Control Hlth. Monit., 28(3), e2679. http://doi.org/10.1002/stc.2679.
  11. Caprani, C.C. and Ahmadi, E. (2016), "Formulation of humanstructure interaction system models for vertical vibration", J. Sound Vib., 377, 346-367. https://doi.org/10.1016/j.jsv.2016.05.015.
  12. Caprani, C.C., Keogh, J., Archbold, P. and Fanning, P. (2012), "Enhancement factors for the vertical response of footbridges subjected to stochastic crowd loading", Comput. Struct., 102-103, 87-96. https://doi.org/10.1016/j.compstruc.2012.03.006.
  13. Casciati, S., Casciati, F. and Faravelli, L. (2015), "Pedestrian bridges monitoring data for stochastic modelling of humaninduced loads", International Conference on Applications of Statistics and Probability in Civil Engineering.
  14. Chan, C.K., Loh, W.P. and Abd Rahim, I. (2016), "Human motion classification using 2D stick-model matching regression coefficients", Appl. Math. Comput., 283, 70-89. https://doi.org/10.1016/j.amc.2016.02.032.
  15. 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. https://doi.org/10.13465/j.cnki.jvs.2014.08.003.
  16. Chopra, A.K. (2015), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Fourth Edition, Prentice Hall, New York.
  17. Fanning, P.J., Archbold, P. and Pavic, A. (2005), "A novel interactive pedestrian load model for flexible footbridges", Proceedings of the SEM Annual Conference & Exposition on Experimental and Applied Mechanics.
  18. Jimenez-Alonso, J.F., Saez, A., Caetano, E. and Cunha, A. (2014), "Proposal and calibration of an human-structure interaction biomechanical model by the resolution of the inverse dynamic problem", Proceedings of the 9th International Conference on Structural Dynamic, EURODYN, Porto.
  19. Kerr, S.C. (1998), "Human induced loading on staircases", PhD Dissertation, University College London, London.
  20. Li, D.J., Li, T., Li, Q.G., Liu, T. and Yi, J.G. (2016), "A simple model for predicting walking energetics with elasticallysuspended backpack", J. Biomech., 49(16), 4150-4153. https://doi.org/10.1016/j.jbiomech.2016.10.037.
  21. Ling, Y.H., Gu, J.X., Yang, T.Y., Liu, R. and Huang, Y.M. (2019), "Serviceability assessment of subway induced vibration of a frame structure using FEM", Struct. Eng. Mech., 71(2), 131-138. http://doi.org/10.12989/sem.2019.71.2.131.
  22. Liu, J.P., Cao, L. and Chen, Y.F. (2020) "Theoretical analysis of human-structure interaction on steel-concrete composite floors", J. Eng. Mech., 146(4), 04020007. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001740.
  23. Luca, F., Berardengo, M., Manzoni, S., Vanali, M. and Drago, L. (2022), "Human-structure interaction: convolution-based estimation of human-induced vibrations using experimental data", Mech. Syst. Signal Pr., 167, 108511. https://doi.org/10.1016/j.ymssp.2021.108511.
  24. Matsumoto, Y. and Griffin, M.J. (2003), "Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration", J. Sound Vib., 260, 431-451. https://doi.org/10.1016/S0022-460X(02)00941-0.
  25. Mohammed, A. and Pavic, A. (2021), "Human-structure dynamic interaction between building floors and walking occupants in vertical direction", Mech. Syst. Signal Pr., 147, 107036. https://doi.org/10.1016/j.ymssp.2020.107036.
  26. Mulas, M.G., Lai, E. and Lastrico, G. (2018), "Coupled analysis of footbridge-pedestrian dynamic interaction", Eng. Struct., 176, 127-142. https://doi.org/10.1016/j.engstruct.2018.08.055.
  27. Murray, T.M., Allen, D.E., Ungar, E.E. and Davis, D.B. (2016), Vibrations of Steel-Framed Structural Systems Due to Human Activity, 2 nd Edition, American Institute of Steel Construction, Inc., Chicago, USA.
  28. O'Sullivan, D., Caprani, C.C. and Keogh, J. (2012), "The response of a footbridge to pedestrians carrying additional mass", Bridge and Concrete Research Ireland Conference, Dublin.
  29. 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.
  30. Smith, A.L., Hicks, S.J. and Devine, P. J. (2009), Design of Floors for Vibration: A New Approach, The Steel Construction Institute, Berkshire.
  31. Svacek, P. and Horacek, J. (2018), "Finite element approximation of flow induced vibrations of human vocal folds model: Effects of inflow boundary conditions and the length of subglottal and supraglottal channel on phonation onset", Appl. Math. Comput., 319, 178-194. https://doi.org/10.1016/j.amc.2017.02.026.
  32. Van Nimmen, K., Lombaert, G., De Roeck, G. and Van den Broeck, P. (2014), "Vibration serviceability of footbridges: evaluation of the current codes of practice", Eng. Struct., 59, 448-61. https://doi.org/10.1016/j.engstruct.2013.11.006.
  33. 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.
  34. Venuti, F., Racic, V. and Corbetta, A. (2016), "Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges", J. Sound Vib., 379, 245-263. https://doi.org/10.1016/j.jsv.2016.05.047.
  35. Wu, C.P. and Lin, C.C. (2020), "Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium", Struct. Eng. Mech., 75(1), 109-122. http://doi.org/10.12989/sem.2020.75.1.109.
  36. Zhu, Q.K., Hui, X.L., Nan, N.N. and Du, Y.F. (2019a), "Study on the vertical dynamic coupled effects of the crowd-structure system based on the social force model", KSCE J. Civil Eng., 23(5), 2243-2253. https://doi.org/10.1007/s12205-019-1232-6.
  37. Zhu, Q.K., Hui, X.L., Du, Y.F. and Zhang, Q. (2019b), "A full path assessment approach for vibration serviceability and vibration control of footbridges", Struct. Eng. Mech., 70(6), 765-779. http://doi.org/10.12989/sem.2019.70.6.765.
  38. Zivanovic, S. (2012), "Benchmark footbridges for vibration serviceability assessment under the vertical component of pedestrian load", J. Struct. Eng., 138(10), 1193-1202. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000571