Wind and extremely long bridges a challenge for computer aided design

Transcription

1 Wind and extemely long bidges a challenge fo compute aided design oian JANJIC anaging iecto TV / entley Systems Gaz, Austia oian Janjic, bon 960, civil engineeing degee fom the Faculty of Civil Engineeing, Saajevo. 5 yeas of expeience in technical eseach, softwae development. Johann STAPER Senio Poject Enginee TV / entley Systems Gaz, Austia Johann Stample, bon 95, civil engineeing degee fom the Technical nivesity of Gaz. Ove 30 yeas of expeience in stuctual analysis in a wide ange of applications. Andeas OAINGO CF Enginee TV GmbH, Gaz, Austia Andeas omaingo, bon 977, Ph degee in technical physics fom the Technical nivesity of Gaz 005. Cuently woking as CF enginee with TV. Summay With eve inceasing span lengths of bidges thooughly investigation of wind elated phenomena has become moe and moe a topic of inteest. any effects wee obseved on aleady existing bidges and suitable theoetical models wee developed. As bidges with such span lengths ae becoming moe and moe a standad situation in bidge design and engineeing, also the need fo accoding design tools inceases. In this aticle the necessay steps to expand existing models and to incopoate them into the design pocess is outlined. Pactical examples fo diffeent aspects ae discussed. eywods: Wind, CF, votex shedding, flutte, buffeting.. Intoduction oden constuction techniques and mateials as well as inceasing expeience and expetise in bidge design allow fo still inceasing span lengths of lage bidges. The needs of well established infastuctue and the tend to make ou ways as shot as possible demand to constuct bidges whee it would not have been possible a few decades ago, fo example acoss wide spans of open wate. In pinciple this impovement pocess is based on the development of new methods and/o mateials, followed by a phase in which this new development is pushed to the limit of applicability. ost of the bidges of such enomous span length ae also subject to stong wind foces due to thei exposed placement. ecause of thei slendeness and elated dynamic behaviou it is no longe sufficient to teat wind gusts and othe fluctuations by equivalent static wind foces. Instead diffeent investigation methods developed fo such exteme situations must be applied to examine the inteaction of oncoming wind and bidge. any of these methods wee inspied and motivated by obsevations made on existing bidges o by compaison to simila effects in the aeonautic industy. An impotant topic in wind analysis is the data management and infomation intechange. ecause of the complexity of the task, many enginees woking on diffeent fields must wok closely togethe. This stats with the measuement and evaluation of meteoological data to descibe the local wind situation and ends with final wind check calculations and accoding decisions. In this sense, not only the analysis methods, but also the data stoage and intechange model plays an impotant ole to accomplish an efficient design pocess. To this end, a softwae implementation which seves as data containe as well as analysis tool was developed. In this pape, the used concepts and methods ae pesented, and diffeent aspects of the calculation ae discussed with pactical examples.. Numeical modelling of inteaction of bidges with wind The fist step to the numeical modelling is a caeful investigation of the aiflow aound the concened bidge coss sections. This is done by applying a CF module based on the iscete

2 Votex ethod (V). y applied post pocessing statistical evaluation, a set of steady state aeodynamic coefficients and flutte deivatives can be obtained. The subsequent wind buffeting analysis sepaates static and dynamic wind foce contibutions. The static pat can be applied as distibuted constant load. The dynamic wind load can be split into aeodynamic damping and stiffness and contibutions due to fluctuating wind. The stuctual esponse is calculated by tansfoming the equations into modal space and fequency domain. y poviding suitable wind pofile data the excitation powe spectum can be calculated and the stuctue peak esponse can be estimated by statistical methods. y solving simplified vesions of the buffeting and flutte equations, wind checks can be obtained fo galloping, tosional divegence, tosional flutte and classical flutte phenomena. Accoding citical wind velocities can be estimated. 3. Application example Calculations wee pefomed fo the Hadange bidge in Noway. Some esults of the wind buffeting analysis ae shown in Fig.. Fig.. Fist two eigenmodes (left) and intenal longitudinal twisting moment due to dynamic wind (ight) of Hadange bidge. 4. Summay and conclusions In this pape the necessay steps fo a complete compute aided wind design of long span bidges wee discussed. The theoy of the analysis pocess can be split into thee pats: fist the ai flow aound the stuctues coss sections ae chaacteized by means of CF methods. The stuctual esponse is then estimated with a wind buffeting analysis based on a quasi-steady theoy. Additionally, wind design checks can be applied to estimate citical wind velocities. Fo the design pocess it is impotant to povide the possibility to pefom the calculations fo diffeent coss section vaiations as well as wind scenaios. This has been taken into account by poviding two stoage containes fo aeodynamic coefficients ( aeo class ) and wind pofiles. This infomation can be abitaily combined to check evey possible situation. The developed compute pogam was applied to pefom diffeent wind calculations fo the planned Hadange suspension bidge. A compaison of the deck twisting moment fo static and dynamic wind evealed the impotance of such wind buffeting calculations. 5. Refeences [] STAPER J., JANJIC., and OAINGO A., Integated Compute Wind esign fo idge Engineeing, IASE Congess, Weima, 007. [] SII E. and SCANAN R.H., Wind Effects on Stuctues: Fundamentals and Application to esign, John Wiley Sons, New Yok, 996. [3] JANJIC. and PIRCHER H., Consistent Numeical odel fo Wind uffeting Analysis of ong-span idges, IASE Congess, Shanghai, 004. [4] STRØEN E. N., Theoy of idge Aeodynamics, Spinge-Velag, elin, 006.

3 Wind and extemely long bidges a challenge fo compute aided design oian JANJIC anaging iecto TV / entley Systems Gaz, Austia oian Janjic, bon 960, civil engineeing degee fom the Faculty of Civil Engineeing, Saajevo. 5 yeas of expeience in technical eseach, softwae development. Johann STAPER Senio Poject Enginee TV / entley Systems Gaz, Austia Johann Stample, bon 95, civil engineeing degee fom the Technical nivesity of Gaz. Ove 30 yeas of expeience in stuctual analysis in a wide ange of applications. Andeas OAINGO CF Enginee TV GmbH, Gaz, Austia Andeas omaingo, bon 977, Ph degee in technical physics fom the Technical nivesity of Gaz 005. Cuently woking as CF enginee with TV. Summay With eve inceasing span lengths of bidges thooughly investigation of wind elated phenomena has become moe and moe a topic of inteest. any effects wee obseved on aleady existing bidges and suitable theoetical models wee developed. As bidges with such span lengths ae becoming moe and moe a standad situation in bidge design and engineeing, also the need fo accoding design tools inceases. In this aticle the necessay steps to expand existing models and to incopoate them into the design pocess is outlined. Pactical examples fo diffeent aspects ae discussed. eywods: Wind, CF, votex shedding, flutte, buffeting.. Intoduction oden constuction techniques and mateials as well as inceasing expeience and expetise in bidge design allow fo still inceasing span lengths of lage bidges. The needs of well established infastuctue and the tend to make ou ways as shot as possible demand to constuct bidges whee it would not have been possible a few decades ago, fo example acoss wide spans of open wate. In pinciple this impovement pocess is based on the development of new methods and/o mateials, followed by a phase in which this new development is pushed to the limit of applicability. An example of such an evolution is shown e.g. in Fig. fo suspension bidges. Span length [km] Yea Fig.. Evolution of span length of suspension bidges []. ost of the bidges of such enomous span length ae also subject to stong wind foces due to thei exposed placement. ecause of thei slendeness and elated dynamic behaviou it is no longe sufficient to teat wind gusts and othe fluctuations by equivalent static wind foces. Instead diffeent investigation methods developed fo such exteme situations must be applied to examine the inteaction of oncoming wind and bidge. any of these methods wee inspied and motivated by obsevations made on existing bidges o by compaison to simila effects in the aeonautic industy. An impotant topic in wind analysis is the data management and infomation intechange. ecause of the complexity of the task, many enginees woking on diffeent fields must wok closely togethe. This stats with the measuement and evaluation of meteoological data to descibe the local wind situation and ends with final wind check calculations and accoding decisions. In this sense, not only the analysis methods, but also the data stoage and intechange model plays an

4 impotant ole to accomplish an efficient design pocess. To this end, a softwae implementation which seves as data containe as well as analysis tool was developed. In this pape, the used concepts and methods ae pesented, and diffeent aspects of the calculation ae discussed with pactical examples.. Numeical modelling of inteaction of bidges with wind The most complete desciption of the inteaction would be a fully consistent calculation by coupling the equations of motion of the bidge with the Navie-Stokes equations which goven the time evolution of the suounding ai flow. The bounday condition which establishes the coupling is the no slip condition at the bidge suface. Additionally, specific inflow conditions which possess the coect statistical popeties accoding to the local weathe conditions by a suitable set of paametes must be pescibed. This vey involved calculation is not possible fo memoy and pefomance easons on standad computes. Instead the poblem is divided into seveal smalle sub-poblems by making simplifying, but well justified, assumptions. The main step is to beak down the analysis into a peliminay calculation of the ai flow aound fixed o moving coss sections and a subsequent stuctual analysis pat. The eduction of 3 to is in geneal applicable, because one dimension the main span, o the height of the pylons of a stuctual pat is dominant with espect to the othe two dimensions, cf. Fig. fo the Stonecuttes bidge. Since the stuctual analysis is based on a modal appoach, the ai flow can be adequately descibed by chaacteizing the wind foces fo fixed coss sections and cetain type of movement. Fig.. odel of Stonecuttes idge.. Aeodynamic chaacteization of coss sections The numeical investigation of the aiflow aound the consideed coss sections is based on a suitable discetization of the Navie-Stokes equations fo viscous fluids. Fo the investigations pesented in this pape a iscete Votex ethod (V) was applied. The advantage of this class of methods is that they wok gid fee, which is vey desiable when calculating moving coss sections. etails on the implementation and application to the Hadange bidge as well as seveal bidges in azil ae given in [] and [3]. Fom an engineeing point of view the most impotant featue of the implemented CF method is that it is embedded within the stuctual analysis pat. This allows fo an easy tansfe of coss sectional data as input and the calculation esults as output. Next to geometic data only a few calculation paametes as well as the ange of wind diections to be consideed must be passed to the CF module. The necessay calculations ae pefomed in an automated batch mode with almost no necessay use inteaction. C [] t [s] Fig. 3. Typical time histoy of lift coefficient. asic output of the CF calculations ae time histoies of dag and lift foce and ovetuning moment. Even fo smooth oncoming flow and fixed coss sections these time histoies show oscillation pattens due to votex shedding in the wake of the consideed coss section as indicated in Fig. 3. Within the following post-pocessing pocedue these time histoies ae educed to a set of chaacteistic coefficients fo the coss section. Fo static wind calculations it is sufficient to povide the mean wind foces and moment acting on the stuctue.

5 They ae given in non-dimensional fom accoding to the steady state coefficients C, C and C C C H C () whee nomally the coss section height H is chosen as nomalization length fo dag and the width fo lift and moment. The ai density is indicated by and is assumed to be constant fo all calculations, and the mean wind velocity is given by. y consideing the powe spectum of the time histoy, cf. Fig. 4, often ponounced peaks at nonzeo fequencies ae obseved. The most dominant peak indicates the votex shedding fequency. It is expessed in a non-dimensional manne by the Stouhal numbe fh St () Fig. 4. Powe spectum of lift coefficient. Fo dynamic calculations the foces must be evaluated also fo moving coss sections. In the case of a modal appoach to the stuctual esponse calculations, it tuns out that it is sufficient to conside hamonic oscillations of the coss section. Following [4], the time dependent foces can be obtained by a linea combination of the coss section displacement and velocity accoding to h A A A h A h H H H h H p P P P p P H (3) whee p, h and indicate hoizontal, vetical and tosional displacement, espectively. The educed cicula fequency of oscillation is given by ω/. The linea coefficients P i, H i and A i in Eq. (3) ae the so-called flutte deivates.. Wind buffeting foces and analysis The tem wind buffeting efes to the foces acting on the stuctue due to tubulent velocity fluctuations. In most of the applications it is justified to assume that the velocity fluctuations and esulting stuctual displacement velocities ae small compaed to the mean wind velocity. In this case the total foces can be deived fom a quasi-steady theoy based on the steady state coefficients. This appoach is pesented fo example in [5] and [6]. The oveall wind foces can be witten as ( ) ( ) ( ) ( ) stiff damp dyn st x x x y z y z y z C C C C C C C w C u C w C C u w C u C C ϑ ϑ ϑ (4) In this equation, the coefficients C i ae evaluated fo the mean angle between wind and coss section, and C i indicates the slope at this angle. The fist tem takes into account the mean wind f [Hz] PS [a.u.]

6 contibutions, the second one the additional foces due to wind fluctuations. The thid tem is connected to the coss section velocity and can thus be consideed togethe with stuctual damping; it is theefoe also called aeodynamic damping. z Analogously, the last tem is called aeodynamic stiffness, because it depends on the coss section ϑ deflection. y w y This situation is indicated in Fig. 5. The oveall effective wind velocity and incident angle esults z H fom a vectoial addition of the single velocity u components. Fo evaluating the foces accoding to Eq. (4), only a lineaization is applied. Fig. 5. Effective wind velocity and angle. To handle the esulting equations of motion of the bidge stuctue numeically, the time-dependent deflections of the bidge ae epesented by a linea combination of suitable basis functions with time-dependent coefficients in the famewok of a modal appoach. To this end, the eigenfequencies and modes of the stuctue with applied pemanent loading ae calculated togethe with the lineaized modal stiffness matix. y consecutive weighting of the equations of motion with the basis functions, a set of diffeential equations fo the linea coefficients is obtained. y pefoming a Fouie tansfomation fom time to fequency domain, one end up with a linea set of equations fo the Fouie tansfoms of the linea coefficients. This pocedue is pesented in detail fo example in [7] and [6]. The tems in Eq. (4) which model damping and stiffness ae easily included into the fequency domain epesentation. y combining the stuctual and aeodynamic contibutions, the so-called mechanical admittance function is obtained. The poblem is that a powe spectum fo the foces due to velocity fluctuations must be established. To this end, a statistical desciption of the possible wind events must be povided. The basic paametes ae the mean wind velocity, tubulence intensity, wind powe spectum and coheence. Fo pactical easons, the available data is commonly fitted to diffeent standad models. y poviding the necessay model paametes, the socalled joint acceptance function [7] can be evaluated which accounts fo the span-wise statistical aveaging of the diffeent wind events. y combining the mechanical admittance and joint acceptance function, the powe spectum of the linea coefficients and hence the standad deviation of deflection of the coesponding can be obtained. If it is assumed that the wind events can be chaacteized by Poisson statistics, the peak esponse is given by the poduct of standad deviation and a suitable peak facto. Finally, a statistical supeposition of the single modes is used to estimate the oveall peak esponse..3 Wind design checks Wind design checks ae usually based on simplified vesions of the full buffeting equations. If aeodynamic damping and stiffness ae expessed by the flutte coefficients, one speaks of the flutte equations, and simplified solutions can yield insight into the dynamic behaviou of the consideed stuctue. Within the developed pogam pesented in this pape, the following checks wee implemented..3. Galloping If only the lowest eigenmode with mainly vetical displacement is consideed, a sustained oscillation of the deck is possible. A necessay condition fo this so-called galloping phenomenon is that the total damping becomes negative. This is only possible if the Glauet-en Hatog citeion holds: C H/ C < 0 [8]..3. Tosional divegence This is a static effect elated to the twist of the deck due to the mean wind ovetuning moment. If the moment inceases with inceasing twisting angle, thee will be a citical point, at which the eactive moment of the deck is not sufficient to countebalance the wind induced moment. This

7 happens at a citical wind velocity fo divegence, which is given by Iω c,div (5) C whee I is the moment of inetia of the consideed coss section and ω the cicula fequency of the lowest tosional eigenmode..3.3 Tosional flutte As fo tosional divegence, a pue tosional deflection of the deck is consideed in this case. Howeve, the analysis is based on a dynamic appoach via the flutte deivatives. y consideing the lowest mainly tosional eigenmode it can be obseved that the aeodynamic damping depends on the flutte coefficient A. y again consideing vanishing total damping as the citical point, a citical value fo this coefficient can be detemined depending on the stuctual damping atio to citical ζ : 4ζ I A, cit (6) 4 y looking up the educed velocity at which this citical value is eached, the citical wind velocity can be deduced. As can be seen, it is a necessay condition fo tosional flutte that A becomes positive. This behaviou is usually not found fo plate-like gides, but can be obseved fo some open-tuss gides, e.g. the Golden Gate idge..3.4 Classical flutte The tem classical flutte efes to a coupled excitation of the lowest vetical and tosional eigenmode. The solution of the flutte equations involves the flutte coefficients H i and A i in this case. The seached citical velocity is again the point of tansition fom decaying to undamped o sustained oscillation..3.5 Votex shedding The votex shedding phenomenon is accompanied by lage oscillating lift foces of the same fequency as the shedding. Related to this poblem is the so called lock-in effect, which happens if the votex shedding fequency lies close to a natual fequency of the stuctue. When the coesponding eigenmode is excited, the votex shedding fequency will be pinned to the diving fequency and massive self inteaction can be obseved. To estimate the effect, votex shedding velocities c,s can be deived fom Eq. () fo the diffeent natual fequencies..4 ata infomation modelling In ode to pefom lage scale engineeing calculations, the developed compute pogam must be capable to deal with stuctues consisting of seveal coss sections and diffeent wind events, because all diffeent possibilities must be checked fo maximum secuity. To this end, two data containes wee intoduced to encapsulate the equied infomation..4. Aeo classes This containe is designed too hold all coss section elated aeodynamic data. This includes the steady state coefficients as well as flutte deivatives and Stouhal numbe. Since the nomalization lengths may not coespond to width and height of the used coss section, additional factos may be enteed. oeove stoage space is eseved fo all stuctual constants which ae needed fo the diffeent design checks..4. Wind pofiles A wind pofile contains the statistical desciption of an abitay stochastic wind event. The basic infomation is stoed to descibe the mean wind velocity pofile, tubulence intensity, wind powe specta fo the thee velocity components and wind coheence data. Fo each type of wind

8 infomation diffeent theoetical models ae available. Futhemoe, the local constuction site wind density can be specified fo de-nomalization of the aeodynamic coefficients. 3. Pactical examples The developed compute pogam is applied fo the Hadange bidge, a suspension bidge with a main span of 30 m and a total length of 380 m which cosses the Hadange fjod in Noway. It will be numbe one in Noway and seven wold wide. The opening is planned fo 0. The main deck will be 8.3 m wide, including two diving lanes and a sepaated cyclist and pedestian path. The Pylons will be moe than 80 m high and the maximum cleaance fo ship vessels will be aound 50 m. The vey lage atio of main span to side spans (cf. Fig. 6) is due to the fact that the shoe of the fjod dops vey deeply, so that the pylons must be placed close to the wate side. The constuction will be done by lifting the individual gide segments and tempoal connection to each othe with hinges. Once all elements ae lifted the final welding will be pefomed. uing this time, the main gide will be even moe susceptible to wind induced vibations. Fig. 6. Stuctual model of Hadange bidge The cable lengths fo main cable and hanges wee calculated by softwae by applying a set of constaints fo sag and cable foces [9] fo the bidge in sevice state. The final geomety of the main gide will not be staight but with a constant adius in elevation. This vetical adius is achieved by a constant bending moment induced between the pylons and the hanges closest to the pylons. asic consideations concening the steady state coefficients of the main gide and wind shadow effects at the pylon legs wee pesented in []. Futhe CF investigations wee pefomed fo the main gide with taffic. The two diving lanes ae loaded with taffic accoding to the sketch pesented in Fig. 7. Thee diffeent cases wee consideed: with both lanes loaded, only with the left lane and only with the ight lane. Fig. 7. Coss section fo taffic calculation. C,C, C [] [ ] Since the application of taffic causes a symmety beak of the coss section layout, the CF calculations must be pefomed fo wind coming fom the left (-0 to 0 ) as well as fom the ight (70 to 90 ). The computed esults fo the case with both taffic lanes ae indicated in Fig. 8. It can be obseved that the slope of the lift coefficient fo wind coming fom the left is negative fo negative angles. y evaluating the Glauet-en Hatog citeion, slightly negative values ae obtained, which indicates a tendency fo galloping. Fig. 8. Steady state coefficients C (x), C (o) and C ( ) fo taffic on both lanes fo wind fom left (solid) and ight (dashed).

9 Fig. 9. Fist two eigenmodes of Hadange bidge deck Accoding to the consideations pesented above, a set of eigenmodes unde pemanent loading was calculated fo the bidge. The fist two modes ae shown in Fig. 9. ased on this set of basis functions, the buffeting analysis was pefomed fo a wind pofile whee the mean wind is given by a logaithmic distibution and the powe spectal density is of aimal type. Some esults of the buffeting analysis fo late wind ae pesented in Fig. 0. y compaing with esults fo static wind only, it is obseved that static and dynamic lateal foces ae of same magnitude. The twisting moment is lage fo the dynamic wind, because due to the fluctuating vetical wind component the effective wind incident angle vaies moe than due to static effects only. Thus the oveall twisting of the deck is amplified and the intenal moment is consequently highe Fig. 0. Intenal shea foce(left) and longitudinal twisting moment (ight) due to lateal wind. 4. Summay and conclusions. In this pape the necessay steps fo a complete compute aided wind design of long span bidges wee discussed. The theoy of the analysis pocess can be split into thee pats: fist the ai flow aound the stuctues coss sections ae chaacteized by means of CF methods. The stuctual esponse is then estimated with a wind buffeting analysis based on a quasi-steady theoy. Additionally, wind design checks can be applied to estimate citical wind velocities. Fo the design pocess it is impotant to povide the possibility to pefom the calculations fo diffeent coss section vaiations as well as wind scenaios. This has been taken into account by poviding two stoage containes fo aeodynamic coefficients ( aeo class ) and wind pofiles. This infomation can be abitaily combined to check evey possible situation. The developed compute pogam was applied to pefom diffeent wind calculations fo the planned Hadange suspension bidge. A compaison of the deck twisting moment fo static and dynamic wind evealed the impotance of such wind buffeting calculations. 5. Refeences [] ist of longest suspension bidge spans, fee encyclopaedia wikipedia. [] STAPER J., JANJIC., and OAINGO A., Integated Compute Wind esign fo idge Engineeing, IASE Congess, Weima, 007.

10 [3] EIER., et al., Wind Tunnel Validation of Votex ethod fo Aeodynamic Coefficients, IASE Congess, Weima, 007. [4] SII E. and SCANAN R.H., Wind Effects on Stuctues: Fundamentals and Application to esign, John Wiley Sons, New Yok, 996. [5] HJORTH-HANSEN E., Wind Engineeing, lectue notes, nivesity of Tondheim, 988. [6] JANJIC. and PIRCHER H., Consistent Numeical odel fo Wind uffeting Analysis of ong-span idges, IASE Congess, Shanghai, 004. [7] STRØEN E. N., Theoy of idge Aeodynamics, Spinge-Velag, elin, 006. [8] EN HARTOG J. P., echanical vibations, cgaw-hill, New Yok, 956. [9] JANJIC., OAN H., and STAPER, J., Compute Aided esign Eection of ong Suspension idges, IASE Congess, Weima, 007.