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Pedestrian interaction with lively low-frequency structures

Principal investigator: Dr Stana Zivanovic  Proejct overview
Research staff: Mr Hiep Vu Dang
Project duration: 2011-2014
Funding body: EPSRC (£124.2k)


The expectation for high-quality infrastructure and improved quality of life is at its highest point in the contemporary society. At the same time the world is experiencing fast urbanisation, pressure on natural resources and ambitious requirements to provide a sustainable built environment. Structural engineers are responding by utilising high-strength materials and designing more efficient and lighter structures. Coupled with innovations in structural forms and aesthetics, all these factors lead towards lighter and therefore 'livelier' (i.e. more vibration prone) structures. Examples of known (lively) footbridges, building floors and staircases affected by excessive vibrations and unfit for the intended purpose are numerous, despite the tendency to keep the problematic cases far from the public eye due to damaging commercial reputations to those involved.

It is generally accepted now that vibration serviceability requirements are governing the design and determining the cost of these structures, many of which are exposed and suffer from the dynamic excitation induced by human walking. Publicity of the infamous excessive sway of the Millennium Bridge, London, under crowd loading ten years ago, and subsequent expensive retrofitting, demonstrated an urgent need to develop fundamental understanding of pedestrian behaviour on lively low-frequency structures. While research into pedestrian interaction with laterally swaying bridges has since intensified, the interaction with a more frequent class of structures that are prone to excessive vibrations in the vertical direction has been progressed little.

The aim of this project is to characterise the interaction between pedestrians and low-frequency structures that are lively in the vertical direction. The interaction occurs because humans are highly sophisticated and sensitive dynamic systems who react to and adapt to the surrounding (vibrating) environment. Current understanding of this phenomenon is limited and consequently it is ignored in design guidelines. However, it is this understanding that is necessary for achieving high-quality infrastructure fit for intended use. The aims of this project are to:

  • Build a unique experimental facility for studying the interaction,
  • Develop a numerical model of the interaction, and
  • Perform experiments to quantify the interaction and verify the numerical model.

The outputs of this project will enhance understanding of structural vibration performance in operating conditions leading to more efficient and controllable designs. The experimental facility developed will represent an essential platform for future multidisciplinary research collaborations.

Project achievements (updated on 06/10/2016)

Building experimental facility

A unique experimental facility consisting of a low-frequency bridge ("the Warwick Bridge") and equipment for monitoring both human locomotion and structural vibration has been developed. A 16t steel-concrete composite bridge has been built in the Structures Laboratory. Fundamental, vertical, bending vibration mode is easily excitable by human walking. Depending on objectives of experimental work, the Warwick Bridge can be instrumented by motion capture system, electrodynamic exciter and vibration transducers. The human test subjects can also be monitored using a motion capture system. More information about the bridge, its construction, dynamic properties and some experiments is presented on the Warwick Bridge webpages. Please refer to the IMAC 2013 conference paper (Zivanovic et al., 2013) for more information.

Experimental characterisation of human walking on rigid surface

Ten volunteers took part in a testing programme* in the Gait Laboratory aiming to measure key spatial (Figure 1) and temporal walking locomotion parameters. Test subjects were asked to walk on a treadmill at a range of belt speeds (Figure 2). They were instrumented by reflective markers and monitored using the motion capture system Vicon, so that both kinematic and kinetic characteristics of their walking could be recorded. The measured parameters were: the pacing frequency, step length, step width, attack angle, end-of-step angle, trunk rotation and the amplitude of the fundamental harmonic of the ground reaction force. The measured data were used to identify natural randomness in the observed parameters (Figure 3). It was found that, for walking at normal speeds (typically in the 1.15–1.76m/s range), most parameters had a small coefficient of variation (up to about 5%), with an exception of the step width that varied significantly more (up to 39%). This data library represents the benchmark data for human walking on rigid surfaces. More detailed information about this work can be found in our recent paper (Dang and Zivanovic, 2015).

Step length and width

Walking on treadmill

 Pacing rate

Figure 1: Spatial parameters (after Vaughan et al., 1999).

Figure 2: Walking on treadmill.

Figure 3: Variability in pacing rate.

Experimental characterisation of human walking on lively bridge

A series of experiments* has been performed on the Warwick Bridge to quantify properties of human walking gait on this lively surface. The measured properties have been compared against the benchmark data collected in the Gait Laboratory.

Figure 4 shows a typical setup for the experiments performed on the Bridge. A stick model of the test subject is presented in Figure 5 while the trajectories of makers attached to various body parts are given in Figure 6.

Instrumented test subject
Figure 4: Instrumented test subject on the Warwick Bridge.

Stick model
Figure 5: Human Model.

Figure 6: Marker trajectories.

Figure 7 shows the variation in the dynamic loading factor (DLF) for the first forcing harmonic measured in nominally the same tests on rigid and lively surfaces. In this particular case, the oscillations of the bridge caused a reduction in the DLF compared with that measured on the rigid surface. Figure 8a shows the percentage change in the mean pacing frequency when walking on the lively surface compared with walking on the rigid surface. While this change is not significant, it can be seen that the variation of the pacing rate within a trial on the lively bridge tends to be several times larger than the variation when walking on the rigid surface (Figure 8b). In general, vertical vibrations of the deck were found to increase variability in all locomotion parameters, except the step width. The step width is an exception since it is normally utilised for controlling walking stability in the lateral direction (frontal plane) rather than for controlling locomotion in the vertical plane of walking progression (sagittal plane) investigated in this project. In addition, the experiments revealed the existence of the self-excited force (Dang and Zivanovic, 2016), partially verifying the utilsation of an inverted pendulum model for modelling pedestrians on lively structures (Bocian et al., 2013).

Dynamic loading factor
Figure 7: DLF for first forcing harmonic.
HSI - step frequency
Figure 8: Change in walking on a lively bridge compared with a rigid surface.

More detailed information about our quantification of a range of parameters, as well as a database of key experimental data, is available on the publications webpage.

*All tests involving human test subjects have been approved by the Biomedical and Scientific Research Ethics Committee at the University of Warwick.

Collaborations involving use of Warwick Bridge

International seminars


  • Shahabpoor, E., Pavic, A., Racic, V. and Zivanovic, S. (2017) Effect of Group Walking Traffic on Dynamic Properties of Pedestrian Structures (free download). Journal of Sound and Vibration, 387, 207–225.
  • McDonald, M. G. and Zivanovic, S. (2017) Measuring Ground Reaction Force and Quantifying Variability in Jumping and Bobbing Actions (free download). ASCE Journal of Structural Engineering [Data in form of CSV files are available here].
  • Dang, H. V. and Zivanovic, S. (2016) Influence of Low-Frequency Vertical Vibration on Walking Locomotion (free download). ASCE Journal of Structural Engineering, 142 (12). [Data in MATLAB format are available here].
  • Zivanovic, S., McDonald, M. G. and Dang, H. V. (2016) Characterising Randomness in Human Actions on Civil Engineering Structures. IMAC-XXXIV, Orlando, Florida, 25 - 28 January.
  • Zivanovic, S. (2015) Modelling Human Actions on Lightweight Structures: Experimental and Numerical Developments. Keynote lecture. The 6th International Conference on Experimental Vibration Analysis for Civil Engineering Structures, Dübendorf, Switzerland, 19 - 21 October.
  • Dang, H. V. and Zivanovic, S. (2015) Experimental Characterisation of Walking Locomotion on Rigid Level Surfaces using Motion Capture System (free download). Engineering Structures, 91, 141-154.
  • Van Nimmen, K., Maes, K., Zivanovic, S., Lombaert, G., De Roeck, G. and Van den Broeck, P. (2015) Identification and Modelling of Vertical Human-Structure Interaction. IMAC-XXXIII, Orlando, Florida, USA, 2 - 5 February.
  • Dang, H. V. (2014) Experimental and Numerical Modelling of Walking Locomotion on Vertically Vibrating Low-Frequency Structures. PhD Thesis, School of Engineering, University of Warwick, UK.
  • Lasheen, M. R. M, Zivanovic, S., Salem, E. and Dang, H. V. (2014) Static and Dynamic Performance of a Steel-Concrete Composite Bridge. In: Proceedings of the 9th International Conference on Structural Dynamics (EURODYN 2014), Porto, Portugal, 30 Jun - 2 Jul.
  • Zivanovic, S., Feltrin, G., Mottram, J. T. and Brownjohn, J. M. W. (2014) Vibration Performance of Bridges Made of Fibre Reinforced Polymer. IMAC-XXXII, Orlando, Florida, USA, 3 - 6 February.
  • Dang, H. V. and Zivanovic, S. (2013) Modelling Pedestrian Interaction with Perceptibly Vibrating Footbridges. FME Transactions, 41 (4), 271-278.
  • Zivanovic, S. and Dang, H. V. (2013) Modelling Pedestrian Walking Locomotion over Lively Footbridge Decks. In Proceedings of 11th International Conference on Vibration Problems, Lisbon, Portugal, 9 - 12 September.
  • McDonald, M. G. and Zivanovic, S. (2013) Measuring Dynamic Force of a Jumping Person by Monitoring their Body Kinematics. In Proceedings of 11th International Conference RASD 2013, Pisa, Italy, 1 - 3 July.
  • Zivanovic, S., Johnson, R. P., Dang, H. V. and Dobric, J. (2013) Design and Construction of a Very Lively Bridge. IMAC-XXXI, Orange County, California, USA, 11 - 14 February.
  • Istrate, M. V., Zivanovic, S., Lorenzana, A., Iban, N. and Dang, H. V. (2013) Quantifying Differences between Walking Locomotion on Rigid and Flexible Pavements. IMAC-XXXI, Orange County, California, USA, 11 - 14 February.
  • Zivanovic, S. (2012) Benchmark Footbridge for Vibration Serviceability Assessment under Vertical Component of Pedestrian Load. ASCE Journal of Structural Engineering, 138 (10), 1193-1202.
  • Dang, H. V. and Zivanovic, S. (2012) Investigation of Human-Structure Dynamic Interaction using Biomechanical Model. Expert Scientific Meeting, Department of Health Science and Technology, Aalborg University, Denmark, 1 - 4 August.