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casestudyof参考版

Casestudyofbridgewithviscousdampers

1Protectingfunctionofviscousdampersforexpansionjointsinlongspanbridges

Viscousdampersareusuallyselectedtobeequippedatthebridgeendstorestricttheirdisplacements.Underthiscondition,viscousdampersandexpansionjointsareusuallyparallelinbridgestructure.Whethertheviscousdampershavetheprotectingfunctionornotforexpansionjointundertheimpactforcecausedbyearthquake,windandvehicleetcisfocusedinthiscasestudy.

Xihoumenbridgeisasea-crossingsuspensionbridge（seeFig.1）.Thespanlengthis578m+1650m+485m.Themainbeamsofthenorthsidespanandmidspanaredesignedascontinuousstiffeninggirder.Suspensionstructurewithlateralwind-resistancebearingsisdesignedbetweennorthsidespanandnorthbridgetower,andnolowerbeamisequippedinthenorthbridgetower.Inthesouthbridgetower,lowerbeamisfixedandconnectedwithhugeforce-reactionwall.So,theviscousdampersareinstalledbetweenthestiffeninggirderendandtheforcereactionwall.

Dynamictime-historyanalysisisdoneinEl-Centroearthquakewithprobability3%in100yearreturnperiod.Resultsofprotectingeffectofviscousdampersforexpansionjointsinlongspanbridgesaregivenintable1&2andshowninFig.2&3.ItcanbefoundeasilythatthedisplacementandvelocityresponsesoftheXihoumensupersuspensionbridgeisreducedgreatlywiththeinstallationofviscousdampersbetweenthestiffeninggirderendandtheforcereactionwall.Andalsotheexpansionjointsofthesuspensionbridgecanbeprotectedreliably.

Fig.1ThelayoutofXihoumensuspensionbridge

Table1RelativedisplacementamplitudesofXihoumensuspensionbridgewith/withoutdampers

Responses

Max.relativedisplacementonnorthernbridgebeam/m

Max.relativedisplacementonsouthernbridgebeam/m

Withoutdamper

Withdamper

Withoutdamper

Withdamper

Earthquake

Sitewave

0.3454

0.1397

0.3413

0.1354

El-Centro

0.3535

0.1901

0.3498

0.1850

Table2RelativevelocityamplitudesofXihoumensuspensionbridgewith/withoutdampers

Responses

Max.relativevelocityonnorthernbridgebeam/（m/s）

Max.relativevelocityonsouthernbridgebeam/（m/s）

Withoutdamper

Withdamper

Withoutdamper

Withdamper

Earthquake

Sitewave

0.2635

0.1381

0.2739

0.1941

El-Centro

0.5265

0.4535

0.5752

0.4783

Fig.2Comparisonofrelativedisplacementsofnorthbeamend

Fig.3Comparisonofrelativevelocitiesofnorthbeamend

2Casestudyonlateralresponsereductionoflong-spanrailwaycable-stayedbridgewithviscousdampers

Thelong-spanrailwaycable-stayedbridgeisasemi-floatingsystemwithspanlengthof81m+135m+432m+135m+81m（seeFig.4）.Themainbridgebeamisasteeltrusswithwidthof18mandheightof14m.Thelengthofeachtrusssectionis13.5m.High-strengthsteelwiresareadoptedanddesignedasmaterialsofthe56pairsofstablecables.Thecablespacingdistanceis2.5m-4.0monthemainbridgetowerand13.5monthemainbridgebeam.Thebridgesurfaceisintegralorthotropicsteelplates.

DynamicresponsesareconductedbyMidassoftwareinthreeearthquakeswithprobability2-3%in50yearreturnperiod.Thepeakaccelerationsofthetheeearthquakesareallthesameof0.21g.ThespecificinstallationplacesoftheviscousdamperareshowninFig.5.ComputationalresultsofdynamictransverserelativedisplacementresponsesbetweenbridgepierandbeamareshowninFig.6andthehysteresiscurvesofviscousdampersbetweendampingforceanddisplacementareshowninFig.7.

Itcanbefoundthattheearthquake-reductionsystemisbetterthanothersystemsbysettingupviscousdampersbetweenauxiliarypier,transitionpierandbridgebeam,forlateralseismicresponseofmaintower,auxiliarypierandtransitionpiercanbesignificantlyreduced.Futuremore,seismicperformanceofpilefoundationsforauxiliaryandtransitionpiercanbeimproved.

Fig.4Thelong-spanrailwaycable-stayedbridgemodel（1#istransitionbridgepier,2#isauxiliarybridgepier,3#isbridgemaintower,4#isbridgemaintower,5#istransitionbridgepier,and6#isbridgeabutment）

Fig.5Installationplacesofviscousdampers

Fig.6Transverserelativedisplacementbetween1#pierandbridgebeam

Fig.7Hysteresiscurvesofviscousdamperat2#bridgepier.

3Casestudyonseismicperformanceimprovementforsouthernbranchmainbridgeofasea-crossingbridgewithviscousdampers

Thesouthernbranchmainbridgeofthesea-crossingbridgeinthiscasestudyisasemi-floatingsystemwithspanlengthof130m+290m+130m（seeFig.8）.Thecross-sectionofthemainbeamofthesouthernbranchbridgeissingle-boxconcretesectionwiththreeholes.Theheightofthecrosssectionis3.5mandwidthis32.2m.Theheightofthemainbridgetoweris132.6mabovethebridgepile.

Thisbridgeliesintheearthquake-proneareasandthepeakaccelerationisverybiginthisarea.Inthiscasestudy,thepeakaccelerationis0.311g.Inordertoimprovethedynamicresponsesofthebridgeindesignearthquakeexcitations,viscousdampersareselectedandinstalledunderthemainbridgebeam,namelybetweenthemainlongitudinalbridgebeamandthebridgepier（seeFig.9）.Parameteranalysisofviscousdampers,suchasdampingcoefficientsanddampingindex,isconductedsoastoobtaintheoptimaldamperparameters.TheparametersstudiedinthiscasestudyarelistedinTable3.

Theinfluenceofdamperparameters,dampingcoefficientsanddampingindex,totheenergydissipationratiosofthebridgeareshowninFig.10&11,respectively.AccordingtotheparameteranalysisbasedonthefiguresofFig.10&11,theoptimaldampingparameterscanthenbeeasilyobtainedandgiveninTable4.

Asaresult,twovibrationcontrolplansaredesigned.Thefirstoneisthat4viscousdampersareinstalledbetweenthemainbridgebeamandthebridgepierofthemaintower.Andthesecondisthat4viscousdampersareinstalledbetweenthemainbridgebeamandthebridgepierofthemaintower,and4dampersareinstalledbetweenthemainbridgebeamandthetransitionbridgepier.However,thetotaldampingcoefficientsofthetwoplansarethesameforcomparisonpurpose.ComparisonofenergydissipationratioofthebridgewiththetwocontrolplansareshowninFig.12.ThesymbolmeaningslistedintheFig.12aregiveninTable5.Obviously,theanalysisindicatesthatbothrelativedisplacementofkeypointsandseismicresponseofkeycomponentscouldbeobviouslyreducedwithreasonablychoosingtheparametersandlocationsofdampers.

Fg.8Thesouthernbranchmainbridgemodel

Fg.9Installationoftheviscousdamperunderthemainbridgebeam

Table3Parametersoftheviscousdampers

Items

Parametervalues

Dampingcoefficient（kN/（m/s）α）

1000

2000

3000

4000

6000

8000

10000

Dampingindex

0.2/0.3/0.5/1.0

（a）InfluenceofCtodisplacementofbeamend（b）InfluenceofCtodisplacementoftoptower

（c）InfluenceofCtomomentoftowerbottom（d）InfluenceofCtomomentoftoppile

Fig.10InfluenceofdampingcoefficientsCtotheenergydissipationratioofdifferentparameterresponses

（a）Influenceofαtodisplacementofbeamend（b）Influenceofαtodisplacementoftoptower

（c）Influenceofαtomomentoftowerbottom（d）Influenceofαtomomentoftoppile

Fig.11Influenceofdampingindexαtotheenergydissipationratioofdifferentparameterresponses

Table4Theoptimaldampingparametersoftheviscousdamperusedinthesouthernbranchbridge

Parameters

Values

DampingcoefficientC（kN/（m/s）0.3）

6000

Dampingindexα

0.3

DampingforceF（kN）

6000

Max.StrokeD（mm）

±400

Fig.12Comparisonofenergydissipationratioofthebridgewiththetwocontrolplans

Table5SymbolmeaningslistedintheFig.12.

Symbols

Meanings

Db

Max.relativedisplacementbetweenbeamendandtransitionpier

Dt

Max.relativedisplacementbetweentoptowerandbottomtower

Mt

Max.momentinthebottomtower

Mtp

Max.momentinthetopofthetowerpile

Mp

Max.momentinthebottomofthetransitionpier

Mpp

Max.momentinthetopofthetransition-pierpile

4CasestudyonperformanceimprovementofstaycableofJianshaobridgeusingviscousdampers

Inthiscasestudy,Jianshaocable-stayedbridgewith69,500mlengthand6maintowerisintroduced（seeFig.13）.Thespanlengthis70m+200m+5×428m+200m+70m.Thecablesaremadeupofparallelhigh-strengthsteelwireswithdiametersizeof7mm.Totally,thereare576staycablesand432ofthesestaycablesareinstalledviscoussoastoimprovethevibrationperformance,seeFig.14.TheparametersoftheviscousdampersaregiveninTable6.

SitemeasurementvaluesofthelogarithmicdecrementratiooftheNo.Z5W-B10cablewithandwithoutviscousdampersaregiveninTable7.ThefreedecaycurvesoftheNo.Z5W-B10cableusingalsothesitemeasurementmethodareshowninFig.15.AndthehysteresiscurvesoftheviscousdampersareshowninFig.16.Theresultsshowthatviscousdamperscanbeabletocurbthevibrationofstaycables,whichcanbethepermanentvibrationcontrolmeasureforstaycables.Andtheresultsofthetestingdemonstratethattheviscousdampersshowstableperformance,alltheperformanceindexcanmeetthedesignrequirements.Themeasuredlogarithmicdecrementisabove6%,basicallyincompliancewiththechangingruleofthetheoreticalvalues,provingthattheviscousdampershavesoundvibrationdampingeffect.

Fig.13Jianshaocable-stayedbridge

（a）Beforeinstallationofviscousdampers（b）Afterinstallationofviscousdampers

Fig.14Siteinstallationofviscousdampers

Table6Parameters