effect of pedestrian traffic

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Acta .Polytechnica Vo 44 No. 2/2004

The Effect of Pedestrian Traffic on theynamic Beh_avior of FootbridgesM Studnickova

Thedy:nltmic response o . l [ o o t b , ~ i d g r ; _ dep,entjf n a 1 f f ] ' X / J J . . - , f ~ l ; . ' l f f " i ' Y f l f r : W B f e n c i e s ofthe structure in vertical, i t y h ? 1 J ~ o , ~ t , I J ~ ~ ~ d . irt t ~ ~ S i o n . lf:o ;any dfthefrequencies in ~ i t i c ~ { is iri i l ~ e range 1 0 HZ to 3. 0 Hz, .tlie d ~ ~ i a m i c r ~ s p o n s e r ~ m _moving , t o J J . . ~ . E ~ ' } f : 5 i . f { r i / J i C . ~ ' E J f tlus case tz n e ~ e s s a r y c ~ l c u l a ~ e mbmtwns takzng z n t o ~ c c o u n t b o t h s ~ r n c e a b t l t t y andulllmate hmzt states. f ~ e s a m ~ problem anses when any ?lthe jrequenczes m honzontal (tmnsversal) or.;tn torstlm are m the rang { Q.] z to 1.5 Hz. \Such frequenczes haveare found namely znfootbridges With laTgeT spans 01 cable-stayed and suspension footbridges. . . . A unique cable-stayed jootbridge with prestnssed conaetl was dynamically analyzed and the dynamic response to simulated pedestrianloading was calculated. The calculated effects were compared with the pedestrian comfort criteria for serviceability limit states. These criteTiaaTe defined in terms of nwximwn acceptable acceleration o he bridge deck.Keywords: vibrations, fiJOtbridge, dynamic actions due to pedestrians, acceptance criteria, response, serviceability.

Fig. 1: Artistic view of the f(>otbridge) Introduction

Modern footbridges are usually slender, light-weightstn1cmres, frequently of unusual strucmral systems, e.g. ofstressed ribbon, suspended or cable-stayed types. If suchfootbridges are designed for static loads only they may be susceptible to vertical as well as to horizontal vibrations. Hence adynamic design is often necessary.

Rhythmical human body motion, e.g., walking, numingor jumping, can cause heavy vibrations of strucmres. rherehave been several accidents in dance halls, grandstands andfootbridges caused by marching, dancing or applauding people. In recent years there have been examples of footbridgesthat have proved to be unacceptably lively to pedestrians. n1elatest case is the Millennium Bridge in London.

A cable-stayed footbridge with, prestressed connete wasdesigned over the main road in Ustf nad Labem in NorthBohemia by SUDO.P .Praha [1]. The strucmre in plan consistof a Y form, and is suspended on two pylons. An artistic viewof the structure is shown in Fig. 1

The pans of the main bridge are 26.1 m 44.7 m17.l m, the mrved pavement ramp is 24.8 m - see Fig 21be height of the I pylon is 14 m, while the height of theH pylon is 17 m. Czech Technical University Publishing House hrtp://ctn.cvnt t:i/a-p/

ij.iII

IiiI JFig. 2: Section of the f()(ltbridge

. \

I

i I

I

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Acta Polytechnica Vol. 44 No. 2/2004

Fig. 3: Computational model of the structure

Model o the structureThe computational model of a footbridge for dynamicanalysis usually consists of truss, beam and 2D elements. " becorrect results of the eigenvalue analysis are strongly depend

ent on the boundary conditions. The implementation of heseinto the calculation must be carefully considered.The computational model of the bridge is shown in Fig. 3.

3 Dynamic analysisI11e dynamic analysis consists of computational eigenvalue analysis and of the analysis of the response to thetime-dependent loads caused by pedestrians.

d a m p i n g / ~ ~ ) h e ~ p f y s ~ q f o o t b r i d g e was. considered'by ~ ( ~ i g l i s 'damping propoitional to mass and stiff- (n e . s s , N ~ t h . y a l J . J , e s of coeflicients corresponding to l o g a r i t h m \ ~a * f l t i l i t f i g ' c ' d l : ~ r e t r t e t i t . I J = ~ : 0 2 . ;

. "Ibe results of the e i g e n v a l t ~ e analysis - five lowest frequencies- are summarised in L


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Fig. 4: Ist mode of the bridgefi = 0.967 Hz

Fig. 6: 3rd mode of the bridgef3 = 1.985 Hz106,0 I - --- ......

tmt ....A II0.2

0,10.5 2 3 6 8 1 2Frequency Hz)

Region A: aceeptableRegion B bearableRegion C unacceptableFig. 8: Criterion for vertical accelerations Czech Technical University Publishing House hrtp: i/ctn .cvt lt .t.:z an/

Acta Polytechnica VoL 44 No. 2/2004

Fig. 5: znd mo4e of.the brldgef2= 1.485 Hz.

Fig. 7: 4th mode oft.he bridgef4 = 2.303 Hz8.003,78i 2,40

~ 1 . 5 0li 0,960J SO0,380,240,150,0860,06

1//

1 \ ~ )> /1.-


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Acta Polytechnica Vol. 44 No. 2/2004

rr 1,0I

1,0 2 3 4 567810Frequency [Hz}

Fig. I0: Proposal of a criterion for horizontal transversevibrationscommended. The available sources provide very little data.N v e t h e r ~ e s s , an approximate criterion can be proposed -seeFig._IO. .

Dynamic forces indu ed bypedestriansMoving people excite the footbridge in vertical, in horizontal (longitudinally or transversally) and in torsion. The

response of a footbridge depends mm1ely on the pacingfrequency ('Jalking, nmning, jumping), the time function ofthe vertical and horizontal dynamic aCtion, the number ofpersons involved, and tl1e dynamic characteristics of thefootbridge.

"Il1e action force Fp(t) due to a single person can be expressed with sufficient accuracy as the sum of the static force(the weight of a person) and the first three harmonic components of the excitation force [3]F t) = G +G1 sin2n fpt +G2 sin(4n pt rtJ'. ) +

+G3sin(6:rt fpt- rp3)(1)

whereG Weight of a person (usually G = 800 N)G1 Load amplitude to the first harmonic componentG2 Load amplitude to the second harmonic componentG3 Load amplitude to the third harmonic component/p Pace frequencyrp2 l'hase shift between the first and second harmoniccomponentsrtJ:l Phase shift between the first and' third harmoniccomponents.

Phase shifts ji can be introduced approximately with values of p2= rp3= n/2.For st;;pdard walkiRg, the frequency of 2 Hz is m o ~ tfreqUent. "lihe results of a number ofmeasurements by anumber of autl10rs are presented in [3], with the conclusion thatthe typical pace frequency of ordinary people is subject to,Gaussian distribution with a mean v ~ t i e of{p = 2 Hz an&the staRdard deviation of at 0,15 Hzf

Du. i ~ g wnni)1g at the d o u b l e ~ tl;le, f i : e q ~ e n c y f l u c t u a t ~ si : - ~ - , f . _ :~ ~ ~ ~ J ? ~ I @ t t s o f 2 , . : ; t ; i j , ~ i 9 . r l 2 - . U H r .. . . . .~ ~ ~ ~ , ~ ~ a _ ~ ~ ~ ~ ' " ' l ; ; ~ : ~ ~ I q : w e v e r , pafe frequenCies than3 a Hz ori:tootondges are rare. i:

Vandals try to tune the structure to one (most frequentlythe lowest) natural frequency withirt the limits .of 0.5 Hz and4.5 Hz. Such cases do not involve merely excitation by footsteps, but also various methods of .periodic force excitationwith the objective of makiljlg the footbridge vibrate with thegreatest possible intensity.

In practical cases the dynamic forces due to moving people can be simplified, and it is considered that only the resonant part of the dynamic action excites the bridge (e.g. [4]).

ln h i ~ case the concentra ted dynamic action for a grouf>ofpeclestrians can be expressed in the formfor vertical vibrations

Fpv(t)=280flv(fv )sin2n fvt [ N ~for horizontal vibrations

where

(2)

fv aJ?(:nding natural frequency of the bridge in vertical'~ f o ~ ~ ~ t to 2'9'Hz,. th ' i ~ ~ ~ ~ ~ n ~ n g ' n ~ t i H , ; : i t J i ' ~ % 1 ~ 1 1 0 ' ofthebridge in hori-'ilzontal o s e ~ t to l.O Hz, 1;1

kvlfv), khifh are magnifYing factors given in Fig. 11.Forces (2) and (3) are applied in the location of ma,'


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v

3

a) 21

0 5

3

b) 2

10 5

1 2 3

1I Ir JI IJ I 1\

~ J H- I I0 7511 25 2 3 4

Fig. 11: Factors a) k v f ~ ) . b) khifl>

{Hz

.--

5

quent pace frequency 2 Hz. The dynamic force of a group ofpedestrians given by 2) was applied in the forced vibrationcakulation. The maximum calculated value of the acceleration response isamax,v ,;0.01 ms-2.

According to Figs. 8 and 9;rhe limit value for accelerationis about 0.7 ms-2. The calculated value of acceleration is verysmall and the pedestrians do threaten the footbtidge. Thefootbridge is very weighty, and walking people are not able tobring it into vibration. Even the continuous stream of pedestri

effect of pedestrian traffic

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