0
Review Article

Dynamic Forces Induced by a Single Pedestrian: A Literature Review

[+] Author and Article Information
Adel Younis

Department of Civil and
Architectural Engineering,
Qatar University,
P.O. Box 2713,
Doha, Qatar
e-mail: adel.younis@qu.edu.qa

Onur Avci

Department of Civil and
Architectural Engineering,
Qatar University,
P.O. Box 2713,
Doha, Qatar
e-mail: oavci@vt.edu

Mohammed Hussein

Department of Civil and
Architectural Engineering,
Qatar University,
P.O. Box 2713,
Doha, Qatar
e-mail: mhussein@qu.edu.qa

Brad Davis

Department of Civil Engineering,
University of Kentucky,
373 Raymond Building,
Lexington, KY 40506
e-mail: dbraddavis@uky.edu

Paul Reynolds

Professor of Structural Dynamics and
Control, Mathematics, and Physical Sciences
College of Engineering,
University of Exeter,
North Park Road,
Exeter EX4 4QF, UK
e-mail: p.reynolds@exeter.ac.uk

1Corresponding author.

Manuscript received August 24, 2016; final manuscript received March 22, 2017; published online April 10, 2017. Assoc. Editor: Francois Barthelat.

Appl. Mech. Rev 69(2), 020802 (Apr 10, 2017) (17 pages) Paper No: AMR-16-1066; doi: 10.1115/1.4036327 History: Received August 24, 2016; Revised March 22, 2017

With the use of lighter construction materials, more slender architectural designs, and open floor plans resulting in low damping, vibration serviceability has become a dominant design criterion for structural engineers worldwide. In principle, assessment of floor vibration serviceability requires a proper consideration of three key issues: excitation source, system, and receiver. Walking is usually the dominant human excitation for building floors. This paper provides a comprehensive review of a considerable number of references dealing with experimental measurement and mathematical modeling of dynamic forces induced by a single pedestrian. The historical development of walking force modeling—from single harmonic loads to extremely complex stochastic processes—is discussed. As a conclusion to this effort, it is suggested that less reliance should be made by the industry on the deterministic force models, since they have been shown to be overly conservative. Alternatively, due to the random nature of human walking, probabilistic force models seem to be more realistic, while more research is needed to achieve enough confidence to implement in design practice.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Jones, C. A. , Reynolds, P. , and Pavic, A. , 2011, “ Vibration Serviceability of Stadia Structures Subjected to Dynamic Crowd Loads: A Literature Review,” J. Sound Vib., 330(8), pp. 1531–1566. [CrossRef]
Xie, W. , Chang, L. , and Du, Y. , 2007, “ Analysis on Vibration Isolation of Zhongnan Theater,” Chin. J. Geotech. Eng., 29(11), pp. 1720–1725.
Davis, B. , Liu, D. , and Murray, T. M. , 2014, “ Simplified Experimental Evaluation of Floors Subject to Walking-Induced Vibration,” J. Performance Constr. Facil., 28(5), p. 4014023. [CrossRef]
Hudson, E. J. , 2016, “ Active Control of Concert-Induced Vibrations,” Geotechnical and Structural Engineering Congress, Phoenix, AZ, Feb. 14–17, pp. 1729–1741.
Brownjohn, J. M. W. , and Pavic, A. , 2015, “ Human-Induced Vibrations on Footbridges,” Advances in Bridge Maintenance, Safety Management, and Life-Cycle Performance: Proceedings of the Third International Conference on Bridge Maintenance, Safety and Management (IABMAS), Porto, Portugal, July 16–19, CRC Press, Boca Raton, FL, pp. 263–264.
Dallard, P. , Fitzpatrick, A. J. , Flint, A. , Le Bourva, S. , Low, A. , Ridsdill Smith, R. M. , and Willford, M. , 2001, “ The London Millennium Footbridge,” Struct. Eng., 79(22), pp. 17–21.
Davis, B. , and Avci, O. , 2015, “ Simplified Vibration Serviceability Evaluation of Slender Monumental Stairs,” J. Struct. Eng., 141(11), pp. 1–9. [CrossRef]
Avci, O. , 2014, “ Modal Parameter Variations Due to Joist Bottom Chord Extension Installations on Laboratory Footbridges,” J. Performance Constr. Facil., 29(5).
Avci, O. , 2016, “ Amplitude-Dependent Damping in Vibration Serviceability: Case of a Laboratory Footbridge,” J. Archit. Eng., 22(3).
Avci, O. , Setareh, M. , and Murray, T. M. , 2010, “ Vibration Testing of Joist Supported Footbridges,” Structures Congress, Orlando, FL, May 12–15, pp. 878–889.
Willford, M. R. , and Young, P. , 2006, A Design Guide for Footfall Induced Vibration of Structures, The Concrete Centre, London.
Smith, A. L. , Hicks, S. J. , and Devine, P. J. , 2007, Design of Floors for Vibration: A New Approach, Steel Construction Institute Ascot, Berkshire, UK.
Murray, T. M. , Allen, D. E. , and Ungar, E. E. , 2003, “Design Guide 11, Floor Vibrations Due to Human Activities,” American Institute of Steel Construction (AISC), Chicago, IL.
Pavic, A. , and Willford, M. R. , 2005, “ Appendix G: Vibration Serviceability of Post-Tensioned Concrete Floors,” Post-Tensioned Concrete Floors Design Handbook, Concrete Society, Slough, UK, pp. 99–107.
Tredgold, T. , 1890, Elementary Principles of Carpentry, E. & F.N. Spon, New York.
Pavic, A. , and Reynolds, P. , 2002, “ Vibration Serviceability of Long-Span Concrete Building Floors. Part 1: Review of Background Information,” Shock Vib. Dig., 34(3), pp. 191–211.
Pavic, A. , and Reynolds, P. , 2002, “ Vibration Serviceability of Long-Span Concrete Building Floors. Part 2: Review of Mathematical Modelling Approaches,” Shock Vib. Dig., 34(4), pp. 279–297.
Pavic, A. , Reynolds, P. , Waldron, P. , and Bennett, K. J. , 2001, “ Critical Review of Guidelines for Checking Vibration Serviceability of Post-Tensioned Concrete Floors,” Cem. Concr. Compos., 23(1), pp. 21–31. [CrossRef]
Racic, V. , Pavic, A. , and Brownjohn, J. M. W. , 2009, “ Experimental Identification and Analytical Modelling of Human Walking Forces: Literature Review,” J. Sound Vib., 326(1), pp. 1–49. [CrossRef]
Živanović, S. , Pavic, A. , and Reynolds, P. , 2005, “ Vibration Serviceability of Footbridges Under Human-Induced Excitation: A Literature Review,” J. Sound Vib., 279(1), pp. 1–74. [CrossRef]
Brownjohn, J. , Racic, V. , and Chen, J. , 2016, “ Universal Response Spectrum Procedure for Predicting Walking-Induced Floor Vibration,” Mech. Syst. Signal Process., 70–71, pp. 741–755. [CrossRef]
Racic, V. , Brownjohn, J. M. W. , and Pavic, A. , 2013, “ Dynamic Loading Factors of Individual Jogging Forces,” 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN), Kos Island, Greece, June 12–14, pp. 2619–2627.
Racic, V. , and Pavic, A. , 2010, “ Mathematical Model to Generate Near-Periodic Human Jumping Force Signals,” Mech. Syst. Signal Process., 24(1), pp. 138–152. [CrossRef]
Occhiuzzi, A. , Spizzuoco, M. , and Ricciardelli, F. , 2008, “ Loading Models and Response Control of Footbridges Excited by Running Pedestrians,” Struct. Control Health Monit., 15(3), pp. 349–368. [CrossRef]
Craig, R. R. , and Kurdila, A. J. , 2006, Fundamentals of Structural Dynamics, Wiley, Hoboken, NJ.
Ebrahimpour, A. , and Sack, R. L. , 2005, “ A Review of Vibration Serviceability Criteria for Floor Structures,” Comput. Struct., 83(28), pp. 2488–2494. [CrossRef]
Van Nimmen, K. , Gezels, B. , De Roeck, G. , and Van Den Broeck, P. , 2014, “ The Effect of Modelling Uncertainties on the Vibration Serviceability Assessment of Floors,” 9th International Conference on Structural Dynamics (EURODYN), Porto, Portugal, June 30–July 2, pp. 959–966.
Griffin, M. J. , 2012, Handbook of Human Vibration, Academic Press, London.
Reynolds, P. , 2000, “ The Effects of Raised Access Flooring on the Vibrational Performance of Long-Span Concrete Floors,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
Middleton, C. J. , and Brownjohn, J. M. W. , 2010, “ Response of High Frequency Floors: A Literature Review,” Eng. Struct., 32(2), pp. 337–352. [CrossRef]
Ayyappa, E. , 1997, “ Normal Human Locomotion, Part 1: Basic Concepts and Terminology,” J. Prosthetics Orthotics, 9(1), pp. 10–17. [CrossRef]
Messenger, N. , 1994, “ Moving the Human Machine: Understanding the Mechanical Characteristics of Normal Human Walking,” Phys. Educ., 29(6), pp. 352–357. [CrossRef]
Whittle, M. W. , 2014, Gait Analysis: An Introduction, Butterworth-Heinemann, Oxford, UK.
Galbraith, F. W. , and Barton, M. V. , 1970, “ Ground Loading From Footsteps,” J. Acoust. Soc. Am., 48(5B), pp. 1288–1292. [CrossRef]
Inman, V. T. , Ralston, H. J. , and Todd, F. , 1981, Human Walking, Williams & Wilkins, Philadelphia, PA.
Hausdorff, J. M. , 2007, “ Gait Dynamics, Fractals and Falls: Finding Meaning in the Stride-to-Stride Fluctuations of Human Walking,” Hum. Mov. Sci., 26(4), pp. 555–589. [CrossRef] [PubMed]
Vaughan, C. L. , Davis, B. L. , and Jeremy, C. O. , 1992, Dynamics of Human Gait, Kiboho Publishers, Cape Town, South Africa.
Perc, M. , 2005, “ The Dynamics of Human Gait,” Eur. J. Phys., 26(3), pp. 525–534. [CrossRef]
Rose, J. , Gamble, J. G. , and Adams, J. M. , 2006, Human Walking, Lippincott Williams & Wilkins, Philadelphia, PA.
Newell, K. M. , and Slifkin, A. B. , 1998, “ The Nature of Movement Variability,” Motor Behavior and Human Skill, Human Kinetics Publishers, Champaign, IL, pp. 143–160.
Pavia, A. , 2009, “ Probabilistic Assessment of Human Response to Footbridge Vibration,” J. Low Freq. Noise Vib. Act. Control, 28(4), pp. 255–268. [CrossRef]
Živanović, S. , Pavic, A. , and Racic, V. , 2012, “ Towards Modelling In-Service Pedestrian Loading of Floor Structures,” Topics on the Dynamics of Civil Structures, Vol. 1, Springer, New York, pp. 85–94.
Bachmann, H. , and Ammann, W. , 1987, Vibrations in Structures: Induced by Man and Machines, IABSE, Zurich, Switzerland.
Harper, F. C. , 1962, “ The Mechanics of Walking,” Res. Appl. Ind., 15(1), pp. 23–28.
Blanchard, J. , Davies, B. L. , and Smith, J. W. , 1977, “ Design Criteria and Analysis for Dynamic Loading of Footbridges,” Symposium on Dynamic Behaviour of Bridges at the Transport and Road Research Laboratory, Crowthorne, Berkshire, UK, May 19, pp. 90–106.
Ohlsson, S. V. , 1982, “ Floor Vibration and Human Discomfort,” Ph.D. thesis, Chalmers University of Technology, Göteborg, Sweden.
Andriacchi, T. P. , Ogle, J. A. , and Galante, J. O. , 1977, “ Walking Speed as a Basis for Normal and Abnormal Gait Measurements,” J. Biomech., 10(4), pp. 261–268. [CrossRef] [PubMed]
Kerr, S. C. , 1998, “ Human Induced Loading on Staircases,” Ph.D. thesis, University of London, London.
Rainer, J. H. , Pernica, G. , and Allen, D. E. , 1988, “ Dynamic Loading and Response of Footbridges,” Can. J. Civ. Eng., 15(1), pp. 66–71. [CrossRef]
Ebrahimpour, A. , Sack, R. L. , Patten, W. N. , and Hamam, A. , 1994, “ Experimental Measurements of Dynamic Loads Imposed by Moving Crowds,” Structures Congress XII, ASCE, Atlanta, GA, Apr. 24–28, pp. 1385–1390.
Wheeler, J. E. , 1980, “ Pedestrian Induced Vibrations in Footbridges,” 10th Australian Road Research Board Conference (ARRB), Sydney, Australia, Aug. 25–29, pp. 21–35.
Wheeler, J. E. , 1982, “ Prediction and Control of Pedestrian-Induced Vibration in Footbridges,” J. Struct. Div., 108(9), pp. 2045–2065.
Pavic, A. , 1999, “ Vibration Serviceability of Long-Span Cast In-Situ Concrete Floors,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
Pedersen, L. , and Frier, C. , 2010, “ Sensitivity of Footbridge Vibrations to Stochastic Walking Parameters,” J. Sound Vib., 329(13), pp. 2683–2701. [CrossRef]
Brownjohn, J. M. W. , Pavic, A. , and Omenzetter, P. , 2004, “ A Spectral Density Approach for Modelling Continuous Vertical Forces on Pedestrian Structures Due to Walking,” Can. J. Civ. Eng., 31(1), pp. 65–77. [CrossRef]
Mercier, H. , Ammann, W. J. , Deischl, F. , Eisenmann, J. , Floegl, I. , Hirsch, G. H. , Klein, G. K. , Lande, G. J. , Mahrenholtz, O. , and Natke, H. G. , 2012, Vibration Problems in Structures: Practical Guidelines, Birkhäuser, Basel, Switzerland.
Živanović, S. , and Pavic, A. , 2007, “ Probabilistic Approach to Subjective Assessment of Footbridge Vibration,” 42nd UK Conference on Human Responses to Vibration, Southampton, UK, Sept. 10–12.
Hanagan, L. M. , 2005, “ Walking-Induced Floor Vibration Case Studies,” J. Archit. Eng., 11(1), pp. 14–18. [CrossRef]
Yoneda, M. , 2002, “ A Simplified Method to Evaluate Pedestrian-Induced Maximum Response of Cable-Supported Pedestrian Bridges,” International Conference on the Design and Dynamic Behaviour of Footbridges, Paris, France, Nov. 20–22, pp. 255–256.
Young, P. , 2001, “ Improved Floor Vibration Prediction Methodologies,” Arup Vibration Seminar on Engineering Structural Vibration, Current Developments in Research and Practice, London, Oct. 1.
Willford, M. , Young, P. , and Field, C. , 2007, “ Predicting Footfall-Induced Vibration: Part 1,” Proc. Inst. Civ. Eng. Build., 160(2), pp. 65–72. [CrossRef]
Bachmann, H. , Pretlove, A. J. , and Rainer, J. H. , 1995, “ Vibrations Induced by People,” Vibration Problems in Structures, Birkhäuser, Basel, Switzerland, pp. 1–28.
Baumann, K. , and Bachmann, H. , 1988, Dynamic Loads Caused by Humans and Their Effect on Beam Structures, Institute of Structural Engineering (IBK), Zurich, Switzerland.
Pimentel, R. L. , 1997, “ Vibrational Performance of Pedestrian Bridges Due to Human-Induced Loads,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
Bocian, M. , Macdonald, J. H. G. , and Burn, J. F. , 2013, “ Biomechanically Inspired Modeling of Pedestrian-Induced Vertical Self-Excited Forces,” J. Bridge Eng., 18(12), pp. 1336–1346. [CrossRef]
Liu, D. , and Davis, B. , 2015, “ Walking Vibration Response of High-Frequency Floors Supporting Sensitive Equipment,” J. Struct. Eng., 141(8), p. 4014199. [CrossRef]
Willford, M. , Young, P. , and Field, C. , 2005, “ Improved Methodologies for the Prediction of Footfall-Induced Vibration,” Proc. SPIE, 5933, p. 59330R.
Živanović, S. , and Pavić, A. , 2009, “ Probabilistic Modeling of Walking Excitation for Building Floors,” J. Performance Constr. Facil., 23(3), pp. 132–143. [CrossRef]
Živanović, S. , Pavić, A. , and Reynolds, P. , 2007, “ Probability-Based Prediction of Multi-Mode Vibration Response to Walking Excitation,” Eng. Struct., 29(6), pp. 942–954. [CrossRef]
Antoniou, A. , 2006, Digital Signal Processing, McGraw-Hill, Toronto, Canada.
Smith, S. W. , 1997, The Scientist and Engineer's Guide to Digital Signal Processing, California Technical Pub., San Diego, CA.
Eriksson, P.-E. , 1994, “ Vibration of Low-Frequency Floors-Dynamic Forces and Response Prediction,” Ph.D. thesis, Chalmers University of Technology, Göteborg, Sweden.
Sahnaci, C. , and Kasperski, M. , 2005, “ Random Loads Induced by Walking,” 6th European Conference on Structural Dynamics (EURODYN), Paris, France, Sept. 4–7, pp. 441–446.
Chopra, A. K. , 1995, Dynamics of Structures, Prentice Hall, Englewood Cliffs, NJ.
Živanović, S. , 2015, “ Modelling Human Actions on Lightweight Structures: Experimental and Numerical Developments,” 6th International Conference on Experimental Vibration Analysis for Civil Engineering Structures (EVACES), Dübendorf, Switzerland, Oct. 19–21, p. 1005.
Racic, V. , Brownjohn, J. M. W. , and Pavic, A. , 2012, “ Random Model of Vertical Walking Force Signals,” Topics on the Dynamics of Civil Structures, Vol. 1, Springer, New York, pp. 73–84.
Racic, V. , and Brownjohn, J. M. W. , 2012, “ Mathematical Modelling of Random Narrow Band Lateral Excitation of Footbridges Due to Pedestrians Walking,” Comput. Struct., 90–91, pp. 116–130. [CrossRef]
McCormac, J. C. , and Nelson, J. K. , 2003, Structural Steel Design: LRFD Method, Prentice Hall, Englewood Cliffs, NJ.
Leonard, D. R. , 1966, “ Human Tolerance Levels for Bridge Vibrations,” Road Research Laboratory, Harmondsworth, UK, RRL Report No. 34.
Matsumoto, Y. , Nishioka, T. , Shiojiri, H. , and Matsuzaki, K. , 1978, “ Dynamic Design of Footbridges,” IABSE Proceedings, Bergamo, Italy, May, Vol. 2, pp. 1–15.
Kerr, S. C. , and Bishop, N. W. M. , 2001, “ Human Induced Loading on Flexible Staircases,” Eng. Struct., 23(1), pp. 37–45. [CrossRef]
Matsumoto, Y. , Sato, S. , Nishioka, T. , and Shiojiri, H. , 1972, “ A Study on Design of Pedestrian Over-Bridges,” Trans. JSCE, 4, pp. 50–51.
Kasperski, M. , and Sahnaci, C. , 2007, “ Serviceability of Pedestrian Structures,” 25th International Modal Analysis Conference (IMAC), Orlando, FL, Feb. 19–22, pp. 774–798.
Pachi, A. , and Ji, T. , 2005, “ Frequency and Velocity of People Walking,” Struct. Eng., 84(3), pp. 36–40.
Kramer, H. , and Kebe, H. W. , 1980, “ Man-Induced Structural Vibrations,” Der Bauing., 54(5), pp. 195–199.
Zivanovic, S. , 2006, “ Probability-Based Estimation of Vibration for Pedestrian Structures Due to Walking,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
Wiseman, R. , 2008, Quirkology: The Curious Science of Everyday Lives, Pan Macmillan, Wales, UK.
Schulze, H. , 1980, “ Dynamic Effects of the Live Load on Footbridges,” Signal Schiene, 24(2), pp. 91–93.
Yamasaki, M. , Sasaki, T. , and Torii, M. , 1991, “ Sex Difference in the Pattern of Lower Limb Movement During Treadmill Walking,” Eur. J. Appl. Physiol. Occup. Physiol., 62(2), pp. 99–103. [CrossRef] [PubMed]
Ebrahimpour, A. , Hamam, A. , Sack, R. L. , and Patten, W. N. , 1996, “ Measuring and Modeling Dynamic Loads Imposed by Moving Crowds,” J. Struct. Eng., 122(12), pp. 1468–1474. [CrossRef]
Živanović, S. , Pavic, A. , and Reynolds, P. , 2007, “ Probability Based Estimation of Footbridge Vibration Due to Walking,” 25th International Modal Analysis Conference (IMAC XXV), Orlando, FL, Feb. 19–22, pp. 1772–1782.
Racic, V. , and Brownjohn, J. M. W. , 2011, “ Stochastic Model of Near-Periodic Vertical Loads Due to Humans Walking,” Adv. Eng. Inf., 25(2), pp. 259–275. [CrossRef]
Pavic, A. , Miskovic, Z. , and Živanović, S. , 2008, “ Modal Properties of Beam-and-Block Pre-Cast Floors,” IES J. Part A: Civ. Struct. Eng., 1(3), pp. 171–185. [CrossRef]
Feldmann, M. , 2010, Human-Induced Vibration of Steel Structures (HIVOSS), Office for Official Publications of the European Communities, Luxembourg.
Reynolds, P. , and Pavic, A. , 2015, “ Reliability of Assessment Criteria for Building Floor Vibrations Under Human Excitation,” 50th UK Conference on Human Responses to Vibration, University of Southampton, Human Factors Research Unit, Southampton, UK, Sept. 9, pp. 277–282.

Figures

Grahic Jump Location
Fig. 1

Components of vibration serviceability analysis

Grahic Jump Location
Fig. 2

A single walk cycle. (Reprinted with permission from Racic et al. [19]. The original version was published by Inman et al. [35]. Copyright 1981 by Williams & Wilkins.)

Grahic Jump Location
Fig. 3

Vertical force resulted from a single step. (Reprinted with permission from Racic et al. [19]. Copyright 2009 by Elsevier.)

Grahic Jump Location
Fig. 4

Typical walking and running time histories. (Reprinted with permission from Racic et al. [19]. The original version was published by Galbraith and Barton [34]. Copyright 1970 by Acoustical Society of America.)

Grahic Jump Location
Fig. 5

Vertical force patterns for different modes of movement activity. (Reprinted with permission from Živanović et al. [20]. The original version was published by Wheeler [51]. Copyright 1980 by National Academy of Sciences.)

Grahic Jump Location
Fig. 6

Historical development of force modeling approaches

Grahic Jump Location
Fig. 7

Walking speed and DLF as a function of pacing rate. (Reprinted with permission from Živanović et al. [20]. The original version was published by Yoneda [59]. Copyright 2002 by AFGC.)

Grahic Jump Location
Fig. 8

DLFs gathered from different authors for the first four harmonics of the walking force. (Reprinted with permission from Živanović et al. [20]. The original version was published by Young [60]. Copyright 2005 by Elsevier.)

Grahic Jump Location
Fig. 9

Comparison of the response behavior in (a) low- and (b) high-frequency floor due to successive steps. (Reprinted with permission from Middleton and Brownjohn [30]. Copyright 2010 by Elsevier.)

Grahic Jump Location
Fig. 10

Effective impulse proposed as a function of pacing rate and floor's natural frequency. (Reprinted with permission from Racic et al. [19]. The original version was published by Willford et al. [67]. Copyright 2005 by SPIE.)

Grahic Jump Location
Fig. 11

Autospectral density of the walking force. (Reprinted with permission from Živanović et al. [20]. The original version was published by Eriksson [72]. Copyright 1994 by Chalmers Publication Library.)

Grahic Jump Location
Fig. 12

Measurement of continuous walking force using an instrumented treadmill. (Reprinted with permission from Brownjohn et al. [55]. Copyright 2004 by National Research Council Canada.)

Grahic Jump Location
Fig. 13

Representation of simulated deterministic walking force signal in the frequency domain. (Reprinted with permission from Brownjohn et al. [55]. Copyright 2004 by National Research Council Canada.)

Grahic Jump Location
Fig. 14

Representation of real continuous walking force in the frequency domain. (Reprinted with permission from Brownjohn et al. [55]. Copyright 2004 by National Research Council Canada.)

Grahic Jump Location
Fig. 15

Appearing of the subharmonic amplitudes of the walking force in the frequency domain. (Reprinted with permission from Živanović et al. [69]. Copyright 2007 by Elsevier.)

Grahic Jump Location
Fig. 16

Normal distribution of the step frequency for normal walking, reported after (a) Živanović et al. [69], (b) Matsumoto et al. [82], (c) Kasperski and Sahnaci [83], and (d) Kramer and Kebe [85]. (Reprinted with permission from Pedersen and Frier [54] with modifications. Copyright 2010 by Elsevier.)

Grahic Jump Location
Fig. 17

Normal distribution of walking speed at 1.8 Hz of step frequency. (Reprinted with permission from Racic et al. [19]. The original version was published by Zivanovic [86]. Copyright 2006 by the University of Sheffield.)

Grahic Jump Location
Fig. 18

Nonlinear observed relationship between step length and walking speed. (Reprinted with permission from Racic et al. [19]. The original version was published by Yamasaki et al. [89]. Copyright 1991 by Springer.)

Grahic Jump Location
Fig. 19

DLFs of the first harmonic crowd-walking force as a function of the number of persons and step frequency. (Reprinted with permission from Živanović et al. [20]. The original version was published by Ebrahimpour et al. [90]. Copyright 1996 by ASCE.)

Grahic Jump Location
Fig. 20

(a) Probability of the peak modal acceleration excited by a single pedestrian; (b) cumulative probability that the peak modal acceleration is less than or equal the value specified in the x-axis. (Reprinted with permission from Živanović et al. [91]. Copyright 2007 by Society for Experimental Mechanics.)

Grahic Jump Location
Fig. 21

(a) The 80-step walking force time history measured by an instrumented treadmill for a single pedestrian, (b) DLFs appearing for the main and subharmonics in the frequency domain, (c) phase angle of forces in Fourier spectrum, and (d) period of walking steps. (Reprinted with permission from Živanović et al. [69]. Copyright 2007 by Elsevier.)

Grahic Jump Location
Fig. 22

A portion of actually measured continuous walking force in a 40-s period. (Reprinted with permission from Racic and Brownjohn [92]. Copyright 2011 by Elsevier.)

Grahic Jump Location
Fig. 23

Frequency-based categorization of actually measured walking force signals. (Reprinted with permission from Racic and Brownjohn [92]. Copyright 2011 by Elsevier.)

Grahic Jump Location
Fig. 24

Linear relationship trend between normalized impulse and cycle time. (Reprinted with permission from Racic and Brownjohn [92]. Copyright 2011 by Elsevier.)

Grahic Jump Location
Fig. 25

Algorithm for generating synthesized walking force signals. (Reprinted with permission from Racic and Brownjohn [92]. Copyright 2011 by Elsevier.)

Grahic Jump Location
Fig. 26

Description of the four-parted building floor selected for the comparative study. (Reprinted with permission from Živanović and Pavić [68]. Copyright 2009 by ASCE.)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In