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Responses
Max.relativedisplacementonnorthernbridgebeam/m
Max.relativedisplacementonsouthernbridgebeam/m
Withoutdamper
Withdamper
Earthquake
Sitewave
0.3454
0.1397
0.3413
0.1354
El-Centro
0.3535
0.1901
0.3498
0.1850
Table2RelativevelocityamplitudesofXihoumensuspensionbridgewith/withoutdampers
Max.relativevelocityonnorthernbridgebeam/(m/s)
Max.relativevelocityonsouthernbridgebeam/(m/s)
0.2635
0.1381
0.2739
0.1941
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)
Dampingindexα
0.3
DampingforceF(kN)
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