FOOTBRIDGES: PEDESTRIAN INDUCED VIBRATIONSBy Stoyan Stoyanoff, Ph.D., P.Eng., Project Director and Mark Hunter, C.E.T., Principal

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INTRODUCTION

Walking, running, and jumping on footbridges producedynamic forces which can activate appreciable vibrations.These vibrations can cause discomfort to pedestrians anddeterioration of the footbridge’s structural integrity.

The lowest natural frequencies of short span footbridges(e.g., less than 30 m) are usually sufficiently high that they arenot susceptible to human-induced vibrations. As spansincrease (spans up to 200 m have been proposed), theirlowest natural frequencies become lower and human-inducedvibrations become a concern. Therefore, it is important thatthis phenomenon is well understood and that reliabletheoretical methods are introduced to determine practicalsolutions.

HUMAN-INDUCED VIBRATIONS

Figure 1 presents an example of the vertical force one personinduces while walking from one end to the other over aflexible structure. This pattern reveals a mean static load plusa periodic activity which creates periodic forces with afrequency typically in the range of 1.5 to 4 Hz (Hz = cycle/sec).Due to the mechanics of body balance, humans also createlateral forces at half that pacing frequency (in the range from0.75 to 2 Hz).

When human-induced frequency (ƒ) synchronizes with one ofthe structural frequencies (ƒο) (e.g., 0.75 to 4 Hz range), thedynamic forces are significantly magnified and a condition ofresonance occurs (illustrated in Figure 2). For small vibrations,the structural damping ratio (ζ) is typically low (in the rangeof 0.5% to 1% of critical). Assuming the typical value of ζ =1% for precast concrete bridges, the amplification of thestatic forces becomes as high as 50.

The potential for these amplified forces to induce appreciablelevels of motion will depend on the number of people on thefootbridge and how well their movements are synchronized.

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ISSUE NO. 15

Artistic impression of the Wichita Bridge,Wichita, Kansas, USA. (Illustration courtesy ofHNTB Corporation)

Pedestrian bridges around the Bellagio Casinoin Las Vegas, Nevada, USA required dampingsystems

Figure 1: Example of force produced by oneperson walking over a footbridge (Rainer et al,1988).

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Research has shown that for fewer than about 20 to 25persons, almost all may synchronize with the footbridgemotions (NBCC, 1995; Fujino, Pacheco, & Nakamura, 1993).For an extremely congested footbridge the number ofwalking people synchronized with the bridge motions dropsto about 20% (Fujino, Pacheco, & Nakamura, 1993).

The amount of vibration people are willing to accept willdepend on their activity (e.g., walking, running, jumping).Figure 3 compares the acceleration comfort criteriasuggested by various sources for walking. Higher limits havebeen suggested for running or jumping. There is also apossibility of so called forced or “vandal” excitations. Thistype of loading occurs when one or a group of individualswould attempt to deliberately excite the bridge. For vandalexcitations, the design criterion is based only on thestructural integrity and not comfort.

IMPROVING DYNAMIC PERFORMANCEIf the lowest natural frequency of a footbridge (or otherflexible structure subjected to human loading) is lower than5 Hz in the vertical and 2.5 Hz in the lateral direction,detailed analysis and comparison with criteria in design codesshould be considered (British Standard, 1978; ENV1992-2,1996; NBCC, ONT83, ISO/DIS 10137, 1995). The motioninduced by pedestrian traffic depends on the amount oftraffic and the type of activity that the users are undertaking.In cases where significant motions are predicted (or exist),the following improvements may be investigated.

STIFFENINGStiffening is best applied to bridges when pedestrianvibrations are judged to border between acceptable andunacceptable. The bridge structure could be stiffened in theappropriate direction or the effective span can be reduced.Significant design modifications may be required.

INCREASING MASSIncreasing the weight of the footbridge will reduce theinfluence of human-induced vibration. A proportionalincrease in stiffness is required to maintain the naturalfrequency. Significant design modifications may be required.

DAMPING SYSTEMSDamping systems increase the amount of energy that isdissipated by the structure. Mass dampers can be tuned tospecific frequencies and visco-elastic dampers can be addedto cover a wider range of frequencies and motions. Dampingsystems can be retrofitted to a footbridge after completion.Allowing for future installation of these devices in the overalldesign of long-span footbridges is worth considering in somecases, especially in view of the difficulty in predicting theinherent damping of these structures.

REFERENCESRainer, J.H., Pernica, G., And Allen, D.E., Dynamic loading andresponse of footbridges, Institute for Research in Construction,Canadian Journal of Civil Engineering, vol. 15, pp. 66-71, 1988.NBCC (1995). Commentary A: Serviceability Criteria for Deflectionsand Vibrations, National Building Code of Canada, Canada, 1995.Fujino, Y., Pacheco, B., & Nakamura, S. Synchronization of humanwalking observed during lateral vibration of a congested pedestrianbridge, Journal of Earthquake Engineering and Structural Dynamics,vol. 22, pp. 741-758, 1993.British Standard (1978). Steel Concrete and Composite Bridges:Specifications for Loads, British Standard BS5400, Part 2, 1978.ENV1992-2 (1996). Design of concrete structures - Part 2: ConcreteBridge, European Committee for Standardization, Brussels, Belgium.ONT83, Ontario Highway Bridge Design Code, Highway EngineeringDivision, Ministry of Transportation and Communications, Toronto,Canada, 1983.ISO/DIS 10137, Bases for Design of Structures - Serviceability ofBuildings against Vibrations, International Standard Organization,Geneva, Switzerland

Figure 2: Dynamic Amplification Function.

Figure 3: Comparison of different comfort criteria for verticalacceleration.