Practical Solutions for Reducing Rain-Wind-Induced Vibrations of Cables, in Cables-Stayed Bridges.

Transcription

1 Internatinal Balkans Cnference n Challenges f Civil Engineering, BCCCE, May 2011, EPOKA University, Tirana, ALBANIA. Practical Slutins fr Reducing Rain-Wind-Induced Vibratins f Cables, in Cables-Stayed Bridges. Altin SERANAJ 1 Department f Building Cnstructin and Transprtatin Infrastructure, Plytechnic University f Tirana, Albania ABSTRACT Rain vibratin f cables is becming a matter f great cncern recently in Japan and ther cuntry fr design and cnstructin f cables-stayed- bridges. The features f rain vibratin are the strng influence f rain n wind-induced scillatin f cable. The cables in cable-stayed bridges, which are stable with respect t wind acting in dry cnditin, became very unstable with rain, and large amplitude scillatin f cable culd be develped under lw speed wind. The principal parameters that give a great influence in this phenmenn can be classified in tw grups. First the grup f the situatin f cable were included: the rientatin f cable, wind speed, reins intensity. In secnd grup named cables prperties were are included natural perids, damping rati and prperty f the surface f cables. In this article is presented nly a part f the bibligraphic study perfrmed at the Labratire Central des Pnts at Chausse, Paris. This part is fcused n tw aspects, the mechanism f the prblem and the slved slutin by surface mdificatin f cables fr eliminatin f this kind f vibratins n the cables. We pint here the fact that even many investigatin are made this phenmenn is nt well knwn and nt jet is fund a mathematical mdel t simulate exactly the real phenmenn. Here are given nly thse slutins that tend tw stabilise the cable by mdificatin f the surface f the cable. These mdificatins f the surface f cables tend t destry the water rivulets created n the surface f the cables. Ding s, fr every speed and directin f wind and fr any rain intensity the water rivulet have nt chance t be created n the surface f the cable. These findings are taken frm the experiments and investigatin n the cablesstayed bridge f Nrmandy, Paris and cables-stayed bridge f HIGASHI-KOBE, Japan. INTRODUCTION Rain vibratin f cables is becming a matter f great cncern recently in Japan fr design and cnstructin f cables-stayed- bridges. The features f rain vibratin are the strng influence f rain n wind-induced scillatin f cable. The cables in cable-stayed bridges, which are stable with respect t wind acting in dry cnditin, became very unstable with rain, and large amplitude scillatin f cable culd be develped under lw speed wind arund10m/s. fr the first time this phenmena have been seen in the bridge Meik-Nishi (Japan) and after in the thers cable-stayed bridges as: Aratsu, Higashi -Kbe (Japan), Dömitz (Germany), Erasmus (Hlland) est. The name f these phenmena is made frm Hikami [ 1] in 1986 as «Rain- Wind» phenmenn. The same name is als used frm Matsumt in 1988[ 2]. 1

2 Many analytical and experimental investigatins have been made fr knwn the influence f different factrs that prduce this phenmenn in many cuntry. The reasn f this article is t make a representatin t this phenmenn, t represent sme analytical and experimental investigatin made by different authrs and cnclusin yielding frm this investigatin. This article is cmpsed n tw parts. In the first part is expressed the phenmenn, in secnd are given sme slutin that can be used fr eliminatin f vibratins prduced frm this phenmenn. 1. PRINCIPLE OF EXCITING RAIN-WIND MECHANISMS Detailed bservatin f the interactin between the mtin f acrylic tube during the mdel test and the mtin f ne re tw rivulet n the surface f the tube in the circumferential directin led t finding the new mechanism. The respnse f cables subjected t the rain-wind excitatin has been with big amplitudes. Menu experimental investigatin has been made in wind tunnel including als the rain. 1.1 GENERAL DATA FOR THE EXPERIMENT RAIN-WIND Fr the respnse f the mdel are used different deviatin and inclinatin angles (this anglesα, β are given in figure belw). The dimensin f the wind tunnel is 2.7m high and 1.8m wide, the maximum speed is abut 30m/s. Wind tunnel test is presented n the fig. 1.The diameter f mdel is the same as the prttype fr the reasn t eliminate the scale effect f the water rivulet and cable diameter. The cable is inserted inside an acrylic tube with a smth surface. The psitin f shwer that stimulates the rain can be changed depending the mdel psitin. The mment that the respnse f the mdel have big amplitude is when n the mdel is created the water rivulet that mve in circumferential directin. Fr ur study the rain intensity used crrespnds t the intensity with the biggest amplitude in the mdel respnse. 1.2 CROSS SECTION CABLE MODIFICATION Interactin cable rivulet is very difficult t be understd because f the cmplexity. The crss sectin shape is a functin f the water rivulet n the surface f the cable. This psitin is depended n the wind speed rain intensity, dynamic prperty f cable, frictin frce cable-water rivulet. 1.3 ENERGY IMPUT If the resulting wind frce acting n the entire crss sectin is scillating at the same frequency an with the same sign as the scillatin frequency f the cable r with a little time lag psitive wrk is dne and the scillatin system gets an energy input.. Fr a generalized system and a harmnic excitatin frce it can be written as fllws fr x-directin Eq. (1) F t W = F s = x F () x& () t dt = ( t + ) x& sin( ω ) t t Energy input respectively, F x sin ω ϑ t dt ( 1) W x ( t) Frce cmpnent acting parallel t the mmentary vibratin velcity [ ], F velcity N x Amplitude -,,- [ ] [ m/ s], &x Amplitude f -,,- [ m s] N, &x( t ) Mmentary vibratin /, ω Natural angular frequency f the structure [ rad / s],ϑ Angle f phase difference between F x ( t) and xt ( ) In the figure 2 4 this energy is presented with the dark clr. 2

3 1.4 EXCITATION MECHANISM Essentially three types f mechanisms have been bserved. They are characterized by the lcatin f the rivulet n the crss sectin and the vibratin directin f the cable. Fig 2-4 shw the time histry f the fllwing five parameters during tw scillatin perid. 1 Deflectin f the crss sectin. 2 scillatin acceleratin. 3 frce caused by the rivulet (neglecting turbulence and Karman vertices) in wind directin ΔF x, in crss-wind directin fig.3 and F x in fig.4 4 scillatin velcity F y 5 Energy input caused by the rivulets () ( x x t (r) y&( t ) F t & ) Fig.1 Wind tunnel test (inclinatin and deviatin angle) MECHANISM 1(Oscillatin in wind directin) This mechanism is presented in the figure 2. The mvement f rivulets is symmetric. This rivulet is behind the meridian 90. The biggest amplitude fr this mechanism is fr the inclinatin angle α = 30, deviatin angle β =+90 and fr win speedv = 22 m/ s. Fig.2 Input energy fr first mechanism α = 30, β =+90, V = 22 m/ s MECHANIZM 2(crss-wind vibratin tw rivulet) The rivulets are in frnt f the meridian 90 and mvements f rivulet are n symmetrical. This type f rain-wind-induced vibratin can ccur in cables inclined against the wind directin. At a sufficient wind speed the rivulet n the underside f the cable is divided int tw lateral rivulets shrtly in frnt f the lateral 90.Due a stchastic initial lateral mtin f the cable, ne f the rivulet is shifted int the 90 psitin, whereas the ther rivulet mve tward the stagnatin pint. Because these crss sectins shape the pressure distributin becmes asymmetrical and causes a lateral frce Fy. 3

4 MECHANIZM 3(crss-wind vibratin ne rivulet) The rivulet is nw after the meridian (fig.4). This mechanism is presented fr the cable with the angles β =±45 and α = 30.This mechanism is prduced fr lw wind speed. Fr higher speed is prduced the mechanism 1, 2. Fig.3 Input energy fr secnd mechanism α = 30, β = + 90, V = 18m/ s Fig.4 Input energy fr third mechanism α = 30, β = + 0, V = 19m/ s The vibratin are prduced fr wind speed V [ 5 25 ]m/ s and fr the frequencies lw than8. 9Hz. Hwever, at these frequency nly-rain-wind-induced amplitudes f the magnitude f the vrtex excited amplitudes arse. At higher frequencies, increasing vibratin acceleratin makes the water, due t its masse f inertia unable t fllw the mtin f the cable. That culd be the reasn fr lw amplitude fr high frequencies. Fr inclined cable the largest amplitudes ccurred at the angles β ± AERODYNAMIC RESPONSE OF PE STAY CABLES WITH DIFERENT SURFACE ROUGHNES The test are made fr different pattern surface presented n fig 5. The mdel A1 A6 have a unifrm pattern. Fr the mdels B1 B3 and mdels C 2, C 3 is applied a pattern surface as given by the figure belw. The characteristics f this mdel are given in the table. Fr the mdels A B is used the wind tunnel with 2m height and 1m width. Wind speed i, j V = 25m/ sthat crrespnd t the Reynlds number Re = Wile fr the mdels Ck dimensin tunnel are 3m and 2m and the maximum speed is used V = 55 m/ s. 4

5 Tab.1 Mde A, B, C i j k Remarks smth unifrm distributin grid-like pattern all ver surface smth discrete cncave patterns Fig.5 Surface pattern fr mdels The drag cefficient f a bdy with a circular sectin and smth surface in a unifrm V D flw is a functin f the Reynlds number, Re = ϑ V wind speed, D cable length,ϑ kinematics viscsity This means that the flw arund the bdy changes with Reynlds number. Surface rughness causes a shift in the separatin pint alng the bdy were the sectin is circular and this accelerate the transitin in tp the turbulent flw regin.. Since change in drag cefficient is dminated by the lcatin f the separatin pint the surface rughness als has a great effect n the drag cefficient in the range f Reynlds number. Figure 6 thrugh 9 shw measured drag cefficients fr the varius mdels. All f this drag cefficient is nearly 1.2 in the sub critical range. frm figure 6 and 7 it is evident that in the case f cables with a unifrmly distributed surface rughness, the critical Reynlds number drps as the surface rughness increases. With increasing the relative surface rughness k/d, the drag cefficient at the critical Reynlds number exceeds the drag cefficient f the smth rund cable mdels by 0.5. With increasing wind velcity, the drag cefficient increases and has a tendency t rapidly apprach 1.2. Fr mdel A6 which has a unifrm relative surface rughness f abut 1% f its diameter the drag cefficient are abut 0.9 and 1.2 at the critical Reynlds number. Figure 8 shw the drag cefficient fr mdels Bi which have the same degree f rughness as the mdel A4, A5and A6 but in a grid-like pattern. In this case the increase f the drag cefficient increase gradually with increasing f wind velcity. 5

6 Fig.6 Drag cefficient-reynlds Fig.7 Drag cefficient-reynlds number relatin A 1 - A 3 number relatin A 4 - A 6 Figure 9 shws the drag cefficients f mdelsc i. Which have apprximately the same degree f surface rughness as the mdel A6 and B3 but applied discretely. Bth C2 and C3 have the same behaviur The critical number and drag cefficient are R e = and C respectively. With the range f Reynlds number R e = t = 06. that crrespnds t the wind velcityv = 55m/ s the drag cefficient remains cnstant. Fig.8 Drag cefficient-reynlds Fig.9 Drag cefficient-reynlds Number relatin - number relatinc -C B1 B3 1 3 S, equivalent Drag cefficient can be btained with discrete rughness patterns as with smth surfaces within the design wind velcity. 2.1 INFLUENCEOF SURFACE ROUGHNES FOR ELEMEINATION OF THE VIBRATION RAIN-WIND Figure 10 shw the wind tunnel apparatus used. Mdels C1 and C 3 with the length 3m are used fr the test. The mdel was freely fixed n springs in the directin perpendicular the cable axis. Mdel weight was 194N, natural frequency abut 1.8Hz, the lgarithmic structural damping rati ranged frm t and the Scrutn number Table 2 shw the experimental parameters fr each cable with inclinatin angle α = 45 and deviatin angle β = 45. These experiments were dne in an Eiffel type wind tunnel having a 2.5m height and 1.5m width and equipped with a water nzzle. Tableau 2 Mdel dimensins 6

7 Fig.10 Mdel fixatin VIBRATION RESPONSE DURING RAINFALL With simulated rainfall at water vlume f 0.8, 1.4 and 2 l/min.,fr mdel C 1 vibratin ccurred at wind velcities f abut 9 12m/s. This is a characteristic already prved at past experiments Figure 11 shws the damping characteristics f cables at a vibratin amplitude rati A/D f 0.1. Of the three water vlume studied, figure8makes clear that the wind velcity range in which rain vibratin ccurred was the widest and negative damping largest with a water vlume f 8 lit/min. The maximum lgarithmic decrement fr this cable mdel is Unstable vibratin ccurred when the reduced wind velcity V/fD exceeded abut 40. Fr mdels C 2 and C 3 with rughened surfaces n rain vibratin ccurred as shwn in the fig 12. fr these mdels the ther intensity water is used but n vibratin ccurred. Fig.11 Damping characteristics Fig.12 Damping characteristics f mdel C 1 fr the mdel C 2 and C 3 3. ELEMINATION RAIN-WIND VIBRATION SOLUTION USED We have shw the principal vibratin that influence in the respnse f the cables subjected t this excitatin. This are : wind speed, cable rientatin, rain intensity, cable characteristics as natural frequency, damping, cable rughness etc. Based in the result f many analytical and experimental investigatin we are giving here same example that are used in al cables stay bridges. Sam f this bridges have been firstly subjected t this type f excitatin. 3.1 SURFACE MODIFICATION This slutin is used in the Nrmandy bridge (France). As the experiment shws that is very imprtant t destry the water rivulet running n the surface cable. In Fig 13 is presented the surface cable mdificatin that can destry this water rivulet. 7

8 Fig.13 Cable Surface mdificatin used fr Nrmandy Bridge, France Filets with dimensins 1.3mm high and 2mm large are fixed in a helicidally way n the surface f the cable. 3.2 AERODYNAMICS METHOD OF CABLE VIBRATION CONTROL By the resultants f the experiment that shw as the influence f the turbulence, (this investigatin is made during the study fr slving the rain-wind vibratin subjected t the cables-stayed bridge f HIGASHI-KOBE, Japan. One slutin is fund. This is given in fig 14 and cnsist in lngitudinal parallel surface prjectin. These make the turbulence flw that makes the creatin f water rivulet mechanism impssible. After made n place f this slutin and investigatin during 3 years nt vibratin ccurred in the cables. Fig.14 Higachi-Kbe cable stayed bridge aerdynamic slutin CONCLUSIONS Interactin between the rivulet in circumferential directin and the vibratin f the cylinder is fundamental fr the excitatin rain-wind The instability can be fr this cnditin β =±45. The wind speed is arund the interval 5 25m / s. The circumferential scillatin f the upper rivulet is cupled with the vertical scillatin f the cable and is indispensable t the grwth f rain vibratin. The practical slutin by mdificatin f the surface f the cables fr destrying the water rivulet that may be caused in a range f cmbinatin f wind and rain have been prven t be a gd slutin 8

9 REFERENCES [] 1 [ 2] [] 3 [] 4 [] 5 Hikami, Y. (1986). «Rain Vibratins f cables f A Cable Stayed Bridge.» J.Wind Engineering (Japan), N. 27, pp (in Japanese). Langse, H.E. and Larsen, O.D. (1987). «Generating Mechanism fr Cable Oscillatin at the Fare Bridge.» Prc. Int. Cnf.n Cable Stayed Bridges, Bangkk, pp Matsumt, M.,Shiraishi, N,. Kitazawa, M., Knisely, C.W.,Shirat, H., Kim, Y. and Tsujii, M. (1988a). «Aerdynamic Behavir f Inclined Circular Cylindres - Cables Aerdynamics.» Prc. Int. Cllquium n Bluff Bdy Aerdynamics and its Applicatins, Oct.,Kyt,Japan M. Matsumt «Cables vibratin and its Aerdynamic/Mechanical Cntrl», Prc. Of Cable-stayed and Sunspensin Bridges, Deauville, 1994, pp Verwiebe, C. Rain-Wind-Induced Vibratins f Cables and bars. Prceedings Int, Sympsium n Advances in Bridge Aerdynamics, Ship Cllisin Analysis and Operatin and Maintenance, May 1998, Technical Univ. Of denmark, Lyngby, Denmark,1998. Y. Higami - Rain vibratin f cables n cable-stayed bridge - Jur. Of Wind Eng. N. 27,