Abstract: Cable-stayed bridges under wind loadingexhibit dynamic behaviours that depend on theaeroelastic forces and coupling among vibration modes.This paper presents a parametric investigation on varioustypes of wind effects on cable stayed bridges. An up-to-date literature review of various types of wind effectsfollowed by control of vibrations in cable stayed bridges.

Key words: Cable-stayed bridges, aerodynamic,buffeting, galloping, vortex-shedding.

INTRODUCTIONCable stayed bridges have only become anestablished solution for long span structures overthe last 60 years. This recent ascendency isprimarily due to the development of reliable highstrength steels for the cables and perhaps moreimportantly, the advent and widespread use ofcomputers to analyse the complex mathematicalmodels.

Nicholas P. Jones and Robert H. Scanlan (2001)developed multimode flutter and buffeting analysisprocedures.They reviewed the current state of theart in long-span bridge wind analysis, focusing theapplication of the theory to the stability (flutter)and serviceability (buffeting) analyses of a newlong-span bridge in North America. This researchwork seeks to exhibit recent developments in thefield to the interested structural/bridge engineer,outline alternative procedures available forassessment of wind effects on cable-supportedbridges, and provide an overview of the basic stepsin the process of a typical aerodynamic analysisand design.

M. Gu, S.R. Chen, C.C. Chang developed anumerical study on four representative cable-stayedbridges in China is performed to investigate thecontribution of the background component to thetotal buffeting response of cable-stayed bridges.The background component usually contributearound or over 15% to the total response of the firstvertical bending mode. Higher natural frequencyand damping and lower wind speed will result inlarger background component.

Ming Gu , Ruoxue Zhang, Haifan Xiang analysedsectional Jiangyin Bridge deck’s models withdifferent dynamic parameters were carried out inthe TJ-1 Boundary Layer.Wind Tunnel toinvestigate the effects of parameters of the testmodel on the flutter derivatives.The flutterderivatives of the plate model and the Jiangyin.Bridge model identified in both smooth andturbulent flow conditions using the present methodindicate that the effects of turbulence on the flutterderivatives are negligible.

J.Y. Fu, J.R. Wu, A. Xu, Q.S. Li, Y.Q. Xiaomeasured wind-induced acceleration and windpressure compared with those obtained from thewind tunnel test to evaluate the accuracy of themodel test results. They concluded that theprobability density function, power spectral densityand mean values of wind-induced response wasconducted in this study. It was found that theprobability density functions of wind-inducedpressures at most pressure transducers are veryclose to the Gaussian distribution. Also the quasi-static hypothesis was testified by analyzing themeasured wind-induced pressure at the windward

Effect of Wind on Cable Stayed Bridges

Osama Maniar1 , Prathamesh Khanwilkar2 , Sucheta Sable3

1Department of Structural Engineering, India, maniarosama@gmail.com

2Department of Structural Engineering, India, prathameshkhanwilkar@yahoo.com

. 3Department of Structural Engineering, India, suchetasable17@gmail.com

side, while the vortex shedding phenomena wasfound for the wind induced pressure at the sidewardside of the building. Slight difference was found forthe mean value of wind-induced pressure obtainedfrom field measurements with those from windtunnel test.

B. N. Sun, Z. G. Wang, J. M. K and Y. Q. Niproposed a nonlinear dynamic model for thesimulation and analysis of a kind of parametricallyexcited vibration of stay cables. Based on thismodel, the oscillation mechanism and dynamicresponse characteristics of this kind of vibrationwere analyzed through numerical computation.They concluded that in cable-stayed bridges, if theratio of natural frequencies of cable to bridge deckfalls into certain range, serious parametricvibrations of the cables with large amplitude mayoccur. The beating frequencies relate to tensionforce of the cable. The larger the static tensionforce is, the lower the beating frequency

Necessity of Wind Analysis for Cable-StayedBridges:

Cable-stayed bridges are subjected to variety ofdynamic loads like traffic, wind, pedestrian andseismic loads.In addition to this the stay cable are very flexibleand have very low inherent damping.Also the geometric and structural properties ofthese bridges are very complex.In addition to these the exact nature of excitationand the mechanism underlying some of thevibration phenomenon still remain to be fullyunderstood.The most important feature of this kind of structureis the non-linearity in geometry and material.

DIFFERENT TYPES OFWIND INDUCEDVIBRATION:

Structural Cables are popular due to their HighFlexibility, Light Weight and Low DampingCharacteristics. They are easily excited andseverely oscillate through Dynamic Effects ofWind.

There are many factors and phenomena cangenerate Cable Vibrations. The cable Vibrations iscoupled with the vibrations of the bridge girder andpylons.

There are different types of wind inducedvibrations such as:- Aerodynamic Stability such asGalloping, Buffeting, Vortex Shedding, WakeEffect. This type of Vibration is caused byinteraction between wind, rivulet and cables. Therivulet motion is coupled with cable vibration in theeffective range of mean wind speed.

Aerodynamic (Galloping):

This is a relatively low-frequency oscillatoryphenomenon of elongated, bluff bodies acted uponby a wind stream. The natural structural frequencyat which the bluff object responds is much lowerthan the frequency of vortex shedding. It is in thissense that galloping may be considered a low-frequency phenomenon

Wake galloping: It is considered of two cylindersone windward, producing a wake, and one leeward,within that wake separated at a few diametersdistance away from each other. In wake gallopingthe downstream cylinder is subjected to gallopingoscillations induced by the turbulent wake of theupstream cylinder. Due to this, the upstreamcylinder tends to rotate clockwise and thedownstream cylinder, anti-clockwise thus inducingtorsional oscillations.

Figure1- Wake galloping

Buffeting:

Buffeting is a high frequency instability, caused byairflow separation or shock wave oscillations fromone object striking another. It is caused by a suddenimpulse of load increasing. This phenomenon isquite different from vortex-induced vibration.

The relation of 2:1 between the aerodynamicdamping coefficients in the along-wind and across-wind direction may contribute to the fact that mostvibration problems in cable stayed bridges occur inthe plane of the cables. The significant increase ofdamping at high wind velocities prevents, most

situations, the occurrence of important cableoscillations under buffeting loads.

For along wind Direction, Aerodynamic dampingCoefficient can be approximated by –

For across wind Direction, Aerodynamic dampingCoefficient can be approximated by –

Vortex Shedding

It is an oscillating flow that takes place when afluid such as air or water flows past a cylindricalbody at certain velocities, depending on the sizeand shape of the body. In this flow, vortices arecreated at the back of the body and detachperiodically from either side of the body. The fluidflow past the object creates alternating low-pressure vortices on the downstream side of theobject. The object will tend to move toward thelow-pressure zone.

Fig 2: vortex shedding

If the cylindrical structure is not mounted rigidlyand the frequency of vortex shedding matches theresonance frequency of the structure, the structurecan begin to resonate, vibrating with harmonicoscillations driven by the energy of the flow.

Wake Effect

Wake effect is the term used for all the vibrationphenomenon of stays that lie in the wake of other

stays or structural elements. The perturbingelement affects the wind flow, creating localturbulent conditions that produce oscillations of thecable.

Wake oscillation cannot be anticipated in thedesign phase. The most common wake effects areas follows: Resonant buffeting and Vortexresonance

Resonant buffeting

The phenomenon was described by davenport andcan occur for bridges with two parallel planes ofcables. Accordingly, the wind gusts strike the up-wind and down-wind planes of cables with a timedelay of B/U, Being the distance between the twoplanes of cables and U the mean wind velocity as inFig. If this delay coincides with half the period Ttassociated with torsional deck mode, then resonanteffects can be attained.

Fig 3: Resonant Buffeting

The critical velocity Ucrfor the resonant buffeting

is then defined by,

Vortex resonance

This phenomenon occurs typically in cable-stayedbridges with two planes of cables. When subjectedto oblique winds. Resonant effects may occur forthe cables behind the pylon that have a naturalfrequency ft close to the shedding frequency. Thecritical wind velocity for the occurrence of vortexresonance of a cable of frequency f in the wake of apylon can therefore be evaluated from

Fig 4: Vortex Resonance

Where H is the projection of the pylon in thedirection transversal to the wind and St is theStrouhal number of the pylon cross section.

Conclusion:

Buffeting has a direct effect on Cables as on otherFlexible Structures although this phenomenonincreases with wind velocity, they do not appear tobe dangerous unless buffeting can produce shock incross-cables.In cable-stayed bridges, if the ratio of naturalfrequencies of cable to bridge deck falls into certainrange, serious parametric vibrations of the cableswith large amplitude may occur.The impact of its intensity, the frequency of axialvortex shedding, the possible interaction betweenvortices along cable axis and in the wake, and therelation between limited-amplitude high-speedvortex excitation and dry inclined cable gallopingneed to be further investigated.The analytical and experimental modal analysisprovides a comprehensive investigation of thedynamic properties of bridges. The analyticalmodal analysis through three dimensional finiteelement modeling gives a detailed description ofthe physical and modal characteristics of the bridge,while the experimental modal analysis through thefield dynamic tests offers a valuable source ofinformation for validating the drawing-basedidealized finite element model.The design predictions of buffeting amplitudes ofvertical and torsional modes were reasonable, butthese were based on overestimates of the windturbulence intensity and overestimates of totaldamping. Further analysis suggests that if thevalues of turbulence and damping found from site

measurements had been used with the designmethod, then the actual vertical

References:

[1] M.S. Troitsky (1988), “Cable-Stayed Bridges –Theory and Design “, pp. 17-83.

[2]Walter Podolny and John B. Scalzi (1986),“Construction and Design of Cable-StayedBridges”, pp. 1-20.

[3] Niels J. Gimsin, “ Cable Supported Bridges –Concept and Design”, pp.23-27.

[4] B. N. Sun, Z. G. Wang, J. M. K and Y. Q. Ni.,“Cable oscillation induced by parametric excitationin Cable-stayed bridges”.

[5] M. S. Pfei and R. C. Batist (1995),“Aerodynamic stability analysis of cable stayedbridges”, Journal of Structural Engineering.

[6] Jin Cheng, Jian-Jing Jiang, Ru-Cheng Xiao,Hai-Fan Xiang (2002), “Advanced aerostaticstability analysis of cable-stayed bridges usingfinite-element method”, Computer and Structure.

[7] Nicholas P. Jones and Robert H. Scanlan (2001),“Theory and full bridge modeling of wind responseof cable supported bridges”, Journal of BridgeEngineering, Vol-6, No.6, Nov/Dec 2001.

[8] Thai Huu-Tai and Kim Seung-Eock (2007),“Triple-girder model for modal analysis of cable-stayed bridges with warping effect”,"Standardization of Construction Specifications andDesign Criteria based on Performance ".

[9] Gregor P. Wollmann (2001), Journal of BridgeEngineering, Vol. 6, No. 4, July/August 2001, pp.227-233

[10] MunenobuKondoh, Motoi Okuda, KoujiKawaguchi, Takefumi Yamazaki(2001),Journal ofBridge Engineering, Vol. 6, No. 3, May/June 2001,pp. 176-182

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