Análisis por condición de servicio causado por vibración vertical inducida por peatones en estructuras
Publicado 2022-10-01
Palabras clave
- interacción vertical humano-estructura,
- análisis de vibraciones verticales en condición de servicio,
- carga inducida por peatones,
- códigos de diseño,
- puentes peatonales
- evaluación de la vibración estructural,
- modelos de carga para peatones,
- respuesta dinámica vertical,
- interacción multitud-estructura,
- vibración a baja frecuencia ...Más
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Derechos de autor 2022 Revista UIS Ingenierías
Esta obra está bajo una licencia internacional Creative Commons Atribución-SinDerivadas 4.0.
Resumen
Estructuras civiles tales como tribunas, losas, puentes peatonales y escaleras están presentando vibraciones verticales inaceptables cuando se ven afectadas por actividades humanas. Por lo tanto, todavía no se tiene claridad sobre los efectos producidos por la interacción entre el ser humano y la estructura que, en algunos casos, pueden llegar a aumentar la respuesta estructural comprometiendo el desempeño para condiciones de servicio. Un examen a las normas y códigos de diseño existentes, arroja una amplia gama de resultados, lo que demuestra que no son consistentes cuando las estructuras están expuestas a cargas inducidas por peatones. Este estudio tiene como objetivo identificar los mecanismos de vibración, los modelos matemáticos y los métodos para abordar la vibración vertical excesiva en las estructuras peatonales. Este análisis establece un conjunto de recomendaciones sobre las cargas que producen los peatones y las respuestas estructurales que pueden producir, lo que genera el potencial para futuros enfoques más racionales que mejoren el análisis y el diseño de estructuras peatonales.
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Referencias
- A. Cunha, C. Moutinho, “Active control of vibrations in pedestrian bridges,” in Conference of the European Association for Structural Dynamics (Eurodyn’99), vol. 2, 1999, pp. 783–788.
- R. Sachse, A. Pavic, P. Reynolds, “Humanstructure dynamic interaction in civil engineering dynamics: A literature review,” Shock and Vibration Digest, vol. 35, no. 1, pp. 3–18, 2003, doi: https://doi.org/10.1177/0583102403035001624
- D. Gomez, S. J. Dyke, S. Rietdyk, “Experimental verification of a substructure-based model to describe pedestrian-bridge interaction,” Journal of Bridge Engineering, vol. 23, no. 4, pp. 1–19, 2018, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0001204
- B. Wolmuth and J. Surtees, “Crowd-related failure of bridges,” Proceedings of the ICE: Civil Engineering, vol. 156, no. 3, pp. 116–123, 2003, doi: https://doi.org/10.1680/cien.2003.156.3.116
- B. Ellingwood, A. Tallin, “Structural service ability: floor vibrations,” J. Struct. Eng., vol. 110, no. 2, pp. 401–418, 1984.
- H. Bachmann, W. J. Ammann, F. Deischl, J. Eisenmann, I. Floegl, G. H. Hirsch, G. K. Klein, G. J. Lande, O. Mahrenholtz, H. G. Natke et al., Vibration problems in structures: practical guidelines. Birkhäuser, 1995.
- A. R. Ortiz, J. M. Caicedo, “Modeling the effects of a human standing on a structure using a closed loop–control system,” Journal of Engineering Mechanics, vol. 145, no. 5, p. 04019025, 2019.
- F. Danion, E. Varraine, M. Bonnard, J. Pailhous, “Stride variability in human gait: The effect of stride frequency and stride length,” Gait and Posture, vol. 18, no. 1, pp. 69–77, 2003, doi: https://doi.org/10.1016/S0966-6362(03)00030-4
- H. V. Dang and S. Živanović, “Experimental characterisation of walking locomotion on rigid level surfaces using motion capture system,” Engineering Structures, vol. 91, pp. 141–154, 2015, doi: https://doi.org/10.1016/j.engstruct.2015.03.003
- M. García-diéguez, J. L. Zapico-Valle, “Sensitivity of the vertical response of footbridges to the frequency variability of crossing pedestrians,” Vibration, pp. 290–311, 2018, doi: https://doi.org/10.3390/vibration1020020
- D. Gomez, S. Rietdyk, S. J. Dyke, “Spatio-temporal assessment of gait kinematics in vertical pedestrian-structure interaction,” Structures, vol. 31, no. February, pp. 1199–1206, 2021, doi: https://doi.org/10.1016/j.istruc.2021.02.024
- AASHTO, LRFD Guide Specifications for the Design of Pedestrian Bridges, 2009, no. T-5 (WAI 31).
- NSR-10, Norma Colombianas de Diseño y Construcción Sismo Resistente. Asociación Colombiana de Ingeniería Sísmica, 2010.
- CCP-14, Norma Colombiana de Diseño de Puentes. Asociación Colombiana de Ingeniería Sísmica, 2014.
- R. Stevenson, “Description of bridges of suspension,” The Edinburgh Philosophical Journal, vol. 5, no. 10, pp. 237–256, 1821.
- C. J. Tilden, “Kinetic effects of crowds,” Transactions of the American Society of Civil Engineers, vol. 76, no. 1, pp. 2107–2126, 1913.
- A. N. Blekherman, “Swaying of pedestrian bridges,” Journal of Bridge Engineering, vol. 10, no. 2, pp. 142–150, 2005, doi: https://doi.org/10.1061/(ASCE)1084-0702(2005)10:2(142)
- Y. Fujino, L. Sun, B. M. Pacheco, A. Member, P. Chaiseri, “Tuned liquid damper (TLD) for suppressing horizontal motion of structures,” Journal of Engineering Mechanics, vol. 118, no. 10, pp. 2017–2030, 1992, doi: https://doi.org/10.1061/(ASCE)0733-9399(1992)118:10(2017)
- Y. Fujino, B. Pacheco, S. I. Nakamura, P. Warnitchai, “Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge,” Earthquake Engineering & Structural Dynamics, vol. 22, no. December 1993, pp. 741–758, 1993, doi: https://doi.org/10.1002/eqe.4290220902
- S. I. Nakamura, Y. Fujino, “Lateral vibration on a pedestrian cable-stayed bridge,” Structural Engineering International: Journal of the International Association for Bridge and Structural Engineering (IABSE), vol. 12, no. 4, pp. 295–300, 2002.
- N. Poovarodom, S. Kanchanosot, P. Warnitchai, “Application of non-linear multiple tuned mass dampers to suppress man-induced vibrations of a pedestrian bridge,” Earthquake Engineering and Structural Dynamics, vol. 32, no. 7, pp. 1117–1131, 2003, doi: https://doi.org/10.1002/eqe.265
- M. Brand, J. Sanjayan, A. Sudbury, “Dynamic response of pedestrian bridges for random crowdloading,” Australian Journal of Civil Engineering, vol. 3, no. 1, pp. 27–38, 2017, doi: https://doi.org/10.1080/14488353.2007.11463918
- F. Ricciardelli, C. Demartino, “Design of footbridges against pedestrian-induced vibrations,” Journal of Bridge Engineering, vol. 21, no. 8, pp. 1–13, 2016, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000825
- Skyscrapercity, “Solférino bridge,” 2021, https://www.skyscrapercity.com/
- LondonTown, “Millennium bridge,” 2021, http://www.londontown.com/
- S. Živanović, A. Pavić, E. Ingólfsson, “Modelling spatially unrestricted pedestrian traffic on footbridges,” ASCE Journal of Structural Engineering, vol. 136, no. 10, pp. 1296–1308, 2010, doi: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000226
- G. Piccardo, F. Tubino, “Equivalent spectral model and maximum dynamic response for the serviceability analysis of footbridges,” Engineering Structures, vol. 40, pp. 445–456, 2012, doi: https://doi.org/10.1016/j.engstruct.2012.03.005
- P. Dallard, T. Fitzpatrick, A. Flint, A. Low, R. Smith, M. Willford, M. Roche, “London Millennium bridge: pedestrian-induced lateral vibration,” Journal of Bridge Engineering, vol. 6, no. 6, pp. 412–417, 2001, doi: https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(412)
- T. M. Roberts, “Synchronised pedestrian excitation of footbridges,” Proceedings of ICE, Bridge Engineering, vol. 156, no. 4, pp. 155–160, 2003, doi: https://doi.org/10.1680/bren.2003.156.4.155
- F. Ricciardelli, A. D. Pizzimenti, “Lateral walking-induced forces on footbridges,” Journal of Bridge Engineering, vol. 12, no. 6, pp. 677–688, 2007, doi: https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(677)
- B. Eckhardt, E. Ott, S. H. Strogatz, D. M. Abrams, A. McRobie, “Modeling walker synchronization on the Millennium bridge,” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 75, no. 2, pp. 1–10, 2007, doi: https://doi.org/10.1103/PhysRevE.75.021110
- F. Venuti, L. Bruno, N. Bellomo, “Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges,” Mathematical and Computer Modelling, vol. 45, no. 3-4, pp. 252–269, 2007, doi: https://doi.org/10.1016/j.mcm.2006.04.007
- J. Macdonald, “Lateral excitation of bridges by balancing pedestrians,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 465, no. 2104, pp. 1055–1073, 2009, doi: https://doi.org/10.1098/rspa.2008.0367
- S. Živanović, A. Pavić, P. Reynolds, “Vibration serviceability of footbridges under human-induced excitation: A literature review,” Journal of Sound and Vibration, vol. 279, no. 1-2, pp. 1–74, 2005, doi: https://doi.org/10.1016/j.jsv.2004.01.019
- E. C. f. S. EN 1991-2, Eurocode 1 - Actions on structures – Part 2: General actions -Traffic loads on bridges, European Committee for Standardization CEN,Brussels, Belgium, 2002.
- ONT95, Ontario Highway Bridge Design Code ONT95, Ontario Government, Ontario, Canada, 1995.
- E. C. f. S. EN 1995-2, Eurocode 5 - Design of timber structures – Part 2: bridges, Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC,Brussels, Belgium, 2004.
- Sétra, “Footbridges, assessment of vibrational behavior of footbridges under pedestrian loading,” in Technical guide, Service d’Etudes Techniques des Routes et Autoroutes, Paris, France, 2006.
- ISO-10137, Bases for design of structures – Serviceability of buildings and walkways against vibrations, International standard, Switzerland, 2007.
- HIVOSS, Human induced Vibrations of Steel Structures Design of Footbridges (HIVOSS), 2007.
- P. Archbold, J. Keogh, C. Caprani, P. Fanning, “A parametric study of pedestrian vertical force models for dynamic analysis of footbridges,” in EVACES – Experimental Vibration Analysis for Civil Engineering Structures, Varenna, Italy, 2011, pp. 35–44.
- C. Caprani, J. Keogh, P. Archbold, and P. Fanning, “Characteristic vertical response of a footbridge due to crowd loading,” in Proceedings of the 8th international conference on structural dynamics (Eurodyn 2011), Leuven, Belgium, 2011, pp. 90–106.
- C. Caprani, E. Ahmadi, “Formulation of human-structure system models for vertical vibration,” Journal of Sound and Vibration, vol. 377, pp. 346–367, 2016, doi: https://doi.org/10.1016/j.jsv.2016.05.015
- P. Fanning, P. Archbold, A. Pavic, “A novel interactive pedestrian load model for flexible footbridges,” in Proceeding of the 2005 Society for Experimental Mechanics Annual Conference on Experimental and Applied Mechanics, Portland, OR, 2005, pp. 7–9.
- M. A. Toso, H. M. Gomes, F. T. Silva, R. L. Pimentel, “A biodynamic model fit for vibration serviceability in footbridges using experimental measurements in a designed force platform for vertical load gait analysis,” in Icem15: 15Th International Conference on Experimental Mechanics, vol. 22, Porto, Portugal, 2013, pp. 23–33.
- M. Pfeil, N. Amador, R. Pimentel, R. Vasconcelos, “Analytic – numerical model for walking person – footbridge structure interaction,” in Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014, Porto, Portugal, 2014, pp. 1079–1086.
- M. Zhang, Georgakis, W. Qu, J. Chen, “SMD model parameters of pedestrians for vertical human structure interaction,” IMAC XXXIII A Conference and Exposition on Structural Dynamics, 2015.
- J. F. Jimenez-Alonso, A. Saez, E. Caetano, F. Magalhaes, “Vertical crowd-structure interaction model to analyze the change of the modal properties of a footbridge,” Journal of Bridge Engineering, pp. 1–19, 2016, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000828
- M. A. Toso, H. M. Gomes, F. T. Da Silva, R. L. Pimentel, “Experimentally fitted biodynamic models for pedestrian-structure interaction in walking situations,” Mechanical Systems and Signal Processing, vol. 72-73, pp. 590–606, 2016, doi: https://doi.org/10.1016/j.ymssp.2015.10.029
- S. Mochon, T. McMahon, “Ballistic walking: an improved model,” Mathematical Biosciences, vol. 52, pp. 241–260, 1980. [Online]. Available: https://doi.org/10.1016/0025-5564(80)90070-X
- S. Onyshko, D. Winter, “A mathematical model for the dynamics of human locomotion,” Journal of Biomechanics, vol. 13, no. 4, pp. 361–368, 1980, doi: https://doi.org/10.1016/0021-9290(80)90016-0
- S. Siegler, R. Seliktar, and W. Hyman, “Simulation of human gait with the aid of a simple mechanical model,” Journal of Biomechanics, vol. 15, no. 6, pp. 415–425, 1982, doi: https://doi.org/10.1016/0021-9290(82)90078-1
- R. Alexander, “Simple models of human movement,” Applied Mechanics Reviews, vol. 48, no. 8, p. 461, 1995, doi: https://doi.org/10.1115/1.3005107
- H. Geyer, A. Seyfarth, R. Blickhan, “Compliant leg behaviour explains basic dynamics of walking and running,” Proceeding of the royal society of London: Biological science, vol. 1603, no. 273, pp. 2861–2867, 2006, doi: https://doi.org/10.1098/rspb.2006.3637
- B. R. Whittington, D. G. Thelen, “A Simple mass-spring model with roller feet can induce the ground reactions observed in human walking,” Journal of Biomechanical Engineering, vol. 131, no. 1, p. 011013, 2009, doi: https://doi.org/10.1115/1.3005147
- M. Bocian, J. H. G. Macdonald, J. F. Burn, “Biomechanically inspired modeling of pedestrian-induced vertical self-excited forces,” Journal of Bridge Engineering, vol. 18, no. 12, pp. 1336–1346, 2013, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000490
- J. W. Qin, S. S. Law, Q. S. Yang, N. Yang, “Finite element analysis of pedestrian bridge dynamic interaction,” Journal of Applied Mechanics, vol. 81, no. 4, p. 041001, 2013.
- R. Sachse, A. Pavic, P. Reynolds, “Pedestrian-bridge dynamic interaction, including human participation,” Journal of Sound and Vibration, vol. 332, no. 4, pp. 1107–1124, 2013, doi: https://doi.org/10.1016/j.jsv.2012.09.02
- E. Shahabpoor, A. Pavic, V. Racic, “Identification of mass-spring-damper model of walking humans,” Structures, vol. 5, pp. 233–246, 2016, https://doi.org/10.1016/j.istruc.2015.12.001
- S. Živanović, A. Pavic, P. Reynolds, “Probability-based prediction of multi-mode vibration response to walking excitation,” Engineering Structures, vol. 29, no. 6, pp. 942–954, 2007, doi: https://doi.org/10.1016/j.engstruct.2006.07.004
- V. Racic, A. Pavić, J. Brownjohn, “Experimental identification and analytical modelling of human walking forces: Literature review,” Journal of Sound and Vibration, vol. 326, no. 1-2, pp. 1–49, 2009, doi: https://doi.org/10.1016/j.jsv.2009.04.020
- D. Gomez, S. J. Dyke, S. Rietdyk “Structured uncertainty for a pedestrian-structure interaction model,” Journal of Sound and Vibration, vol. 474, p. 115237, 2020, doi: https://doi.org/10.1016/j.jsv.2020.115237
- G. Piccardo, F. Tubino, “Simplified procedures for vibration serviceability analysis of footbridges subjected to realistic walking loads,” Computers and Structures, vol. 87, no. 13-14, pp. 890–903, 2009, doi: https://doi.org/10.1016/j.compstruc.2009.04.006
- L. Pedersen and C. Frier, “Sensitivity of footbridge vibrations to stochastic walking parameters,” Journal of Sound and Vibration, vol. 329, no. 13, pp. 2683–2701, 2010, doi: https://doi.org/10.1016/j.jsv.2009.12.022
- C. C. Caprani, J. Keogh, P. Archbold, P. Fanning, “Enhancement factors for the vertical response of footbridges subjected to stochastic crowd loading,” Computers and Structures, vol. 102-103, pp. 87–96, 2012, doi: https://doi.org/10.1016/j.compstruc.2012.03.006
- S. Krenk, “Dynamic response to pedestrian loads with statistical frequency distribution,” Journal of Engineering Mechanics, vol. 138, no. 10, pp. 1275–1281, 2012, doi: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000425
- M. Zhang, C. T. Georgakis, J. Chen, “Biomechanically excited SMD model of a walking pedestrian,” Journal of Bridge Engineering, vol. 21, no. 8, p. C4016003, 2016, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000910
- L. Bruno and A. Corbetta, “Uncertainties in crowd dynamic loading of footbridges: A novel multi-scale model of pedestrian traffic,” Engineering Structures, vol. 147, pp. 545–566, 2017, doi: https://doi.org/10.1016/j.engstruct.2017.05.066
- S. Živanović, “Probability-based estimation of vibration for pedestrian structures due to walking,” Ph.D. dissertation, University of Sheffield, 2006.
- E. Ingólfsson, C. Georgakis, “A stochastic load model for pedestrian-induced lateral forces on footbridges,” Engineering Structures, vol. 33, no. 12, pp. 3454–3470, 2011, doi: https://doi.org/10.1016/j.engstruct.2011.07.009
- E. Ingólfsson, C. Georgakis, J. Jönsson, “Pedestrian-induced lateral vibrations of footbridges: A literature review,” Engineering Structures, vol. 45, pp. 21–52, 2012, doi: https://doi.org/10.1016/j.engstruct.2012.05.038
- Z. O. Muhammad and P. Reynolds, “Probabilistic multiple pedestrian walking force model including pedestrian inter-and intrasubject variabilities,” Advances in Civil Engineering, vol. 2020, 2020, doi: https://doi.org/10.1155/2020/9093037
- H. Wang, J. Chen, J. M. Brownjohn, “Parameter identification of pedestrian’s springmass-damper model by ground reaction force records through a particle filter approach,” Journal of Sound and Vibration, vol. 411, pp. 409–421, 2017, doi: https://doi.org/10.1016/j.jsv.2017.09.020
- F. Tubino, “Human-structure interaction in pedestrian bridges: A probabilistic approach,” Procedia Engineering, vol. 199, pp. 2883–2888, 2017, doi: https://doi.org/10.1016/j.proeng.2017.09.584
- A. Younis, O. Avci, M. Hussein, B. Davis, P. Reynolds, “Dynamic forces induced by a single pedestrian: a literature review,” Applied Mechanics Reviews, vol. 69, no. 2, 2017, doi: https://doi.org/10.1115/1.4036327
- J. Brownjohn, A. Pavic, P. Omenzetter, “A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking,” Canadian Journal of Civil Engineering, vol. 31, no. 1, pp. 65–77, 2004, doi: https://doi.org/10.1139/l03-072
- A. Ferrarotti, F. Tubino, “Generalized equivalent spectral model for serviceability analysis of footbridges,” Journal of Bridge Engineering, vol. 21, no. 12, pp. 942–954, 2016, doi: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000963
- J. Brownjohn, V. Racic, J. Chen, “Universal response spectrum procedure for predicting walking-induced floor vibration,” Mechanical Systems and Signal Processing, vol. 70-71, pp. 1–15, 2015, doi: https://doi.org/10.1016/j.ymssp.2015.09.010
- Z. Muhammad, P. Reynolds, O. Avci, M. Hussein, “Review of pedestrian load models for vibration serviceability assessment of floor structures,” Vibration, vol. 2, no. 1, pp. 1–24, 2019, doi: https://doi.org/10.3390/vibration2010001
- C. Demartino, G. Quaranta, C. Maruccio, and V. Pakrashi, “Feasibility of energy harvesting from vertical pedestrian-induced vibrations of footbridges for smart monitoring applications,” Computer-Aided Civil and Infrastructure Engineering, no. 2011, pp. 1–22, 2021, doi: https://doi.org/10.1111/mice.12777
- S. Villamizar, D. Gomez, P. Thomson, “Effects of human-structure interaction in slabs,” Dyna, vol. 81, no. 184, pp. 129–137, 2014, doi: https://doi.org/10.15446/dyna.v81n184.39622
- H. V. Dang, S. Živanović, “Influence of low-frequency vertical vibration on walking locomotion,” Journal of Structural Engineering, vol. 142, no. 04016120, pp. 1–12, 2016, doi: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001599
- S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature, vol. 438, no. 7064, pp. 43–44, 2005, doi: https://doi.org/10.1038/438043a
- V. Joshi, M. Srinivasan, “Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal,” Mathematical, physical and engineering science, vol. 471, no. 2174, pp. 1–19, 2015, doi: https://doi.org/10.1098/rspa.2014.0662
- V. Joshi, M. Srinivasan, “Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony,” Biol. Lett., vol. 14, no. 10, p. 20180564, Oct. 2018, doi: https://doi.org/10.1098/rsbl.2018.0564
- S. Živanović, A. Pavic, P. Reynolds, “Humanstructure dynamic interaction in footbridges,” Proceedings of ICE, Bridge Engineering, vol. 158, no. 4, pp. 165–177, 2005, doi: https://doi.org/10.1680/bren.2005.158.4.165
- M. G. Pandy and N. Berme, “Synthesis of human walking: A planar model for single support,” Journal of Biomechanics, vol. 21, no. 12, pp. 1053–1060, 1988, doi: https://doi.org/10.1016/0021-9290(88)90251-5
- C. R. Lee, C. T. Farley, “Determinants of the center of mass trajectory in human walking and running,” The Journal of Experimental Biology, vol. 201, pp. 2935–2944, doi: https://doi.org/10.1242/jeb.201.21.2935
- S. Kim, S. Park, “Leg stiffness increases with speed to modulate gait frequency and propulsion energy,” Journal of Biomechanics, vol. 44, no. 7, pp. 1253–1258, 2011, doi: https://doi.org/10.1016/j.jbiomech.2011.02.072
- F. T. da Silva, H. M. B. F. Brito, R. L. Pimentel, “Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges,” Canadian Journal of Civil Engineering, vol. 40, pp. 1196–1204, 2013, doi: https://doi.org/10.1139/cjce-2011-0587
- A. Jakkula, A history of suspension bridges in bibliographical form. USA: Cooperative investigation of bridges types by the public roads administration and the agricultural and mechanical college of Texas, 1941.
- R. Hatfield, Theory of transverse strains and its applications in the construction of buildings. USA: Association of Engineering Societies, 1877.
- L. J. Johnson, New Data on the Weight of a Crowd of People. Association of Engineering Societies, 1905.
- E. Chaussé, Code of Building Laws and Regulations of the City of Montreal. Guertin printing Company, 1906.
- A. S. Nowak, K. R. Collins, Reliability of structures. CRC Press, 2012.
- I. Roos, “Human induced vibration on footbridges: Application and comparison of pedestrian load models,” Master’s thesis, Delft University of Technology, Netherlands, 2009.
- D. Zuo, J. Hua, D. Van Landuyt, “A model of pedestrian-induced bridge vibration based on full-scale measurement,” Engineering Structures, pp. 117–126, 2012, doi: https://doi.org/10.1016/j.engstruct.2012.06.015
- K. Van Nimmen, G. Lombaert, G. De Roeck, and P. Van den Broeck, “Vibration serviceability of footbridges: Evaluation of the current codes of practice,” Engineering Structures, vol. 59, no. 0, pp. 448–461, 2014, doi: https://doi.org/10.1016/j.engstruct.2013.11.006
- D. Gomez, “Human-induced vertical vibration on pedestrian structures: numerical and experimental assessment,” Ph.D. dissertation, Purdue University, 2019.
- A. M. Avossa, C. Demartino, F. Ricciardelli, “Design procedures for footbridges subjected to walking loads: comparison and remarks,” Baltic Journal of Road and Bridge Engineering, vol. 12, no. 2, pp. 94–105, 2017, doi: https://bjrbe-journals.rtu.lv/article/view/bjrbe.2017.12
- S. Živanović, I. M. Diaz, A. Pavić, “Influence of walking and standing crowds on structural dynamic properties,” in Proceedings of the 27th IMAC Conference, Orlando, Florida USA, 2009.
- E. Shahabpoor, A. Pavic, V. Racic, “Using MSD model to simulate human-structure interaction during walking,” in Topics in Dynamics of Civil Structures, Volume 4: Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013, vol. 4, 2013, pp. 357–364.
- B. S. A. BS5400, Steel, Concrete and Composite Bridges—Part 2: Specification for Loads; Appendix C: Vibration Serviceability Requirements for Foot and Cycle Track Bridges. Great Britain, 1978.
- DIN-Fachbericht, DIN-Fachbericht 102, Deutsches Instiut für Normung, Betonbrücken, 2003.
- Bro2004, Vägverkets allmänna tekniska beskrivning för nybyggande och förbättring av broar, Svensk Byggtjänst, Stockholm, Sverige, 2004.