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SanFranciscoOaklandBayBridgeSeismicRetrofit
Project
IndependentReview
of
Analysis
and
Strategy
to
Shim
Bearings
atPierE2toAchieveSeismicDesignRequirements
ModjeskiandMasters,Inc.
August9,2013
IndependentReviewofAnalysisandStrategytoShimBearingsatPier
E2oftheSFOBBtoAchieveSeismicDesignRequirements
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TableofContents
1. Authorization........................................................................................................................................... 3
2. Scope........................................................................................................................................................ 3
3. Background.............................................................................................................................................. 4
3.1 SeismicForcesandAssumedBehaviorofBearingsandShearKeys.................................................. 4
3.2 MaterialProperties(ProvidedbyEOR,anchorboltcapacityconfirmedbyMM)............................. 8
3.3 PreviouslyStatedShearCapacitiesofBearingsandShearKeys........................................................ 8
4. Approach.................................................................................................................................................. 9
4.1 General............................................................................................................................................... 9
4.2 AnalysisofLoadTransferinBearingsandShearKeys..................................................................... 10
4.2.1 FreeBodyDiagrams.................................................................................................................. 10
4.2.2 CoefficientsofFrictionatInterfaces......................................................................................... 16
4.2.3CapacityofBearingsandShearKeys (individualandcombined)at100%SEEApproximate
MechanicsAnalysis............................................................................................................................. 16
4.2.4 CapacityofBearingsandShearKeys(individualandcombined)at100%SEERefinedFinite
Element Analysis................................................................................................................................ 18
4.3 CapacityofOBGsandthePierE2CrossGirdertoDeliverLoadtotheShimmedBearingsandShear
Keys,Respectively................................................................................................................................... 24
4.3.1 Introduction.............................................................................................................................. 24
4.3.2 Bearings..................................................................................................................................... 24
4.3.3 ShearKeys3and4.................................................................................................................... 25
4.4CapacityofStrut................................................................................................................................ 26
4.4.1Introduction............................................................................................................................... 26
4.4.2StructuralAnalysis...................................................................................................................... 26
4.4.3SectionalChecks......................................................................................................................... 27
4.4.4Results........................................................................................................................................ 27
4.5 TransferofHorizontalLoadFromBearingBasePlatetoStruttoColumn...................................... 33
4.6 PotentialtoDamagethePermanentBearingsorOtherComponentsifShimsareInstalled.........35
5. ConclusionsandRecommendations...................................................................................................... 35
Appendices15
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1
ExecutiveSummaryandConclusions
ModjeskiandMasters,Inc.(MM)wasretainedtoconductapeerreviewofthesuitabilityofthe"Shim
Concept" to provide sufficient seismic capacity at Pier E2 of the San FranciscoOakland Bay Bridge
(SFOBB)towithstandtheSafetyEarthquakeEvent(SEE)forcesuntiltheshearkeysarerepaired. Thezone
oftheSFOBBconsidered isthe loadtransfermechanismatPierE2fromthesuperstructurebearingand
shearkeysupportstothetopsofthecolumns.
Inthecurrentcontext,apeerreviewinvolvesdeterminingiftheworkbeingreviewedmeetstheoverall
projectsafetyrequirements. Itisnotnecessarytoagreecompletelyinaquantitativesensesolongas
theconclusionofthereviewisadequatelysupported.
Based on the engineering studies described herein, MM concludes that the concept of temporarily
shimmingthebearingsatPierE2oftheSanFranciscoOaklandBayBridgeasdescribed intheJuly15th
informationpackage entitled "Seismic Evaluationof SASat E2BentPrior toCompletionof Shear Keys
S1land S2", and the proposed details, will provide more than sufficient capacity between the
superstructureandthestrutatPierE2 toresistthedesignSafetyEvaluationEarthquake. Theservice
andseismicdesign forces inPierE2arenotchangedsignificantlyby the redirectionofseismic forces
resulting from the shimming. Therefore the response of the concrete strut and columns are not
expectedtobedifferent.Otherthanthepossibilityofscratchingthepaintsystemeitherwhentheshims
areinsertedorasthebridgerotatesinservice,theredoesnotappeartobeanyreasonablepossibilityof
damaging thebridgeasa resultof installingand removing the shims. Assuming that the restof the
structurehasbeenproperlydesigned,weconcludethatthesafetyofthetravelingpublicisimprovedby
movingtrafficontothenewbridge.
Theexactdistributionofforcesinthebearingsandshearkeysishighlydependentontheplannedand
accidentaltolerances(gaps)betweenvariouscomponents. Aprecisequantificationoftheforcesis,for
practicalpurposes,unknowable. Itis,however,possibletomakeestimatesofthereasonablerangeof
possibilities rather than relying on a single solution; MMs assessment is based on that approach.
Various assumptions have been used to place reliance on the set of shear keys and on the set of
shimmedbearings,separatelyand incombination. Analysisofthe resultingdistributionof forceswas
thebasis forconcluding that the temporaryshimmedconditionprovidessufficientresistance tomeet
thedemandsfromtheSEE.
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3
IndependentReviewofAnalysisandStrategytoShimBearingsatPier
E2oftheSFOBBtoAchieveSeismicDesignRequirements
1. Authorization
EngineeringservicesrequiredtodevelopthisreportwereauthorizedbytheBayAreaTollAuthorityby
AgreementofJuly16th,2013.
2. Scope
ThefollowingtechnicalScopeisexcerptedfromtheAgreementofJuly16th:
The services to be performed by Consultant shall consist of services requested by the Project
Manageroradesignatedrepresentativeincluding,butnotlimitedto,thefollowing:
Task1:
Consultant shall provide an independent review of the engineering analysis and strategy as
related to theproposal to shim the existing bearings at Pier E2 to achieve the seismic design
requirementsoftheneweastspanoftheSanFranciscoOaklandBayBridge.
Consultant shall conduct a peer review of the suitability of the "Shim Concept" to provide
sufficient seismic capacity at Pier E2 of the San FranciscoOakland Bay Bridge to withstand the
Safety Earthquake Event (SEE)forces until the shear keys are repaired. Inperforming the work,
Consultantshalluse:
1.
Load
demands
at
Pier
E2
from
the
analysis
of
the
SEE
pushover
by
the
engineer
of
record
(EOR)assummarizedin"SeismicEvaluationofSASatE2BentPriortoCompletionofShear
KeysSlandS2"datedJuly15,2013(July15thinformationpackage)
2. Detailsofthebearings,shearkeysandcapbeamatPierE2andthesupportsofshearkeysandbearingsintheorthotropicboxgirdersprovidedbyEOR;and
3. Other calculations,plan sheets, shop drawings and engineering summariesprepared orsuppliedbyrequesttotheEORasmaybeneeded.
ThezoneoftheSFOBBtobeconsideredistheloadatPierE2fromtheboxgirderbearingandshear
keysupports
to
the
tops
of
the
columns.
Thefollowingisexpresslynotincluded:
1. Reviewofthefailuresofthe2008anchorbolts;2. Independent seismic analysis or evaluation other thanforce transfer in the zone identified
above;
3. Any capacity of the box girders or the substructure other than the force transfer zone
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identifiedabove;
4. Anyevaluationoftherepairoftheshearkeys(SlandS2)ortheresultingsuitability;5. AnyevaluationoftheoriginaldesignofthecapbeamatPierE2otherthanasmaybeneeded
toevaluatethechangestotheloadpathcausedbythetemporaryshimming;and
6. Anyotherfunctionoftheshearkeysandbearingsotherthantransferringseismicdemandsinthe
temporary
shimmed
condition.
Deliverable:
IndependentReviewReport
3. Background
Figure1 through Figure9, from the July 15th informationpackage,wereprovidedby the EOR, TYLin
International.
3.1 SeismicForcesandAssumedBehaviorofBearingsandShearKeys
The original load path with clearances preventing the bearings from participating in resisting
horizontalandtransverseshearisillustratedinFigure1. Thefourbearingswereintendedtocarry
onlyvertical loads,the fourshearkeyswere intendedtocarrytransverseshear,andshearkeys1
and2wereintendedtocarrylongitudinalshear.
Shimming isproposed to close the gapsandprovidea contact loadpath through thebearing to
transmitlongitudinalandtransverseshear. ThelocationoftheshimsisshowninFigure2. Dueto
failure of many of the anchor bolts at shear keys S1 and S2, it has been decided that all shear
capacityattheseshearkeysshouldbeignoreduntiltheyarerepaired. Withtheshimsinplace,the
proposed loadpath isshown inFigure3. Thebearingscarryvertical loadsas in theoriginal load
path,butarenow intended tocarry theentire longitudinalshearandaportionof the transverse
shear. Shear keys 3 and 4 are still intended to carry some of the transverse shear, but the
distributionofshearbetweenthebearingsandshearkeysrequiresconsideration. Withshearkeys
S1andS2consideredineffectiveduetoanchorboltfractures,thelongitudinalshimmingisrequired
inanyeventtoprovideaneffectiveloadpathinthatdirectionuntilthepermanentrepairofshear
keysS1andS2incompleted.
TheSafetyEvaluationEarthquake (SEE)demandsandthenominalshearcapacitiesofthebearings
andshearkeysforthreescenarios(loadpaths)areshowninFigure4;loadpathAisasdesigned,
loadpathCisbasedontheshimmingofthebearingsandtheparticipationofshearkeys3and4,
i.e.thestartingpointforthisinvestigation.
ThemagnitudesanddirectionsofseismicforcesgivenintheJuly15thinformationpackage,excerpts
ofwhicharerepeatedbelow,areacceptedwithoutreviewperscope:
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Bearing forces were extracted from a seismic (time history) analysis of the selfanchored
suspensionbridgeincludingthebearingsandshearkeys.Thetotallongitudinal,transverse,and
vertical loads transferred from the westbound and eastbound box girders to Pier E2 were
extractedfromtheanalysisanddistributedto thebearingsandshearkeys inaccordancewith
theplans.ThebearingloadsareshowninTable1.
Normalfunctioningofthebearingcorrespondstothecase"ShearKeyEngaged".Thebearingis
onlyrequiredtocarryverticalloads.Theseareeitherdownwards caseC orupwards caseU.
Upwardsloadsareofgreatestconcernandareaddressedinthisreport.A"safetyfactor"of1.4
isappliedtothecalculatedloadsfromtheseismicanalysis.
The bearing is also intended tofunction as a secondary mechanism to resist longitudinal and
transverse loads should the shear keys fail. The three cases of greatest interest are those
correspondingtothepeakupliftonthebearing(caseU),thepeaktransverseload(caseT),and
thepeak longitudinal load(caseL). Ineachcasetheorthogonal loadsoccurringsimultaneously
with thepeak loads arealso tabulated (and analyzed). These loads areapplied witha "safety
factor"of1.0,sincetheyarebasedontheconservativeassumptionthattheshearkeyhasfailed.
BearingForces(SF=1.4)
Case Case Trans. Long. Vert.
ShearKeyEngaged
(LoadPathA)
C 0 310 81104
U 0 108 13355
BearingForces(SF=1.0)
Case Case Trans. Long. Vert.
ShearKeyFailed(Load Path B&C See
Note)
C 10799 4770 57932
U 25287 1628
9539
T 30496 8186 16441
L 1340 13232 19255
Note:ThesameseismicdemandsareconservativelyassumedforLoadPathC.
Table1,BearingLoads
Asmentionedpreviously, the loadingon themodel isassignedat theCGof thebearingshaft,
whichtransfersthefocusfromthebearingupperhousingtothebearinglowerhousing.
Theloadismodeledaspressureloadingappliedatrelevantsurfaces,withsomesimplifications.
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Figure1 Originalloadpaththroughshearkeysandbearings
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Figure2 Shimmedbearing
Figure3 Revisedloadpaththroughshearkeysandbearings
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Thedifferencebetweentheindividualforcesprovidedinthelongitudinalandtransversedirections
andavectorsumofthoseforceswasfoundtobesmall,ontheorderofafewpercent;theindividual
forceswilloftenbeusedhereinforsimplicity.
4.2 AnalysisofLoadTransferinBearingsandShearKeys
4.2.1 FreeBodyDiagrams
Figure5throughFigure9illustratethebasicflowofforcesthroughtheshearkeysandthebearings.
For both types of assemblies, the shear from the seismic event is transferred from the upper
housing toa lowerhousingatdiscretepoints,shownastheshearkeybushingortheshaft in the
caseofthebearing. TherestoftheloadpathsinFigure5throughFigure9areglobalstaticsandwill
beusedasastartingpointfortheinvestigationsreportedherein. Thedistributionofstresswithin
theassembliesandtheparticipationofindividualanchorboltscanbemorecomplex.
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Figure5 Loadpaththroughshearkey
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Figure6 Loadpaththroughbearing longitudinalshear
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Figure7 Loadpaththroughbearing transverseshear
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Figure8 Loadpaththroughbearing compression
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Figure9 Loadpaththroughbearing uplift
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arelimitedto86%oftheirnominaltotalshearcapacity(42MNand30MN,respectively)toprotect
thebearings. Thetransverseresistancewouldbeabout175MN,greaterthanthe120MNneeded
for themaximum transverse forcecase. Alternatively, if theshearkeys reached theirnominal42
MNcapacityandthebearingswerelimitedtotheirshearcapacitybasedonthereducedclamping
force(25.7MN),thetotalresistancewouldbe187MN.
Inthemaximumupliftcase,theshearcapacityofthebearingsisfurtherreducedto21.7MNor72%
of theircapacitybasedon theunreducedclamping force fora totalcapacityof the4bearingsof
about87MNwhichislessthanthetransverseshearassociatedwiththemaximumuplift,estimated
by proportion to be about 100 MN . Again, some participation from the shear keys is needed.
Followingthelogicusedabove,ifthetotalshearresistancewasbasedonallbearingsandshearkeys
being limited to 70%of theirnominal capacity toprotect the bearings, the resistance would be
about143MN. Thisisgreaterthanthe120MNmaximumtransverseshearandevengreaterthan
theproportioned100MNtransverseshearfortheupliftcase. Iftheshearkeysreachedtheir full
resistanceandthebearingsreachedtheirreducedcapacity(21.7MN),theshearresistancewould
be171MN.
AsshownintheSection4.2.4,inwhichthedisplacementcompatiblesystembehavioroftheshear
keysandbearingsisdiscussed,MMsanalysisshowsthat,forarangeofassumedgaps,moreofthe
transverse load is carriedby the shear keysand lessby thebearings than considerationof their
nominalcapacitieswouldindicate. Theneteffectisthatthedisplacementcompatibledemandson
thebearingsaresmallerthantheclampingreducedcapacitiespresentedinthissection.
Furtherboundingtheanalyses,iffullreliancewereplacedequallyonthetwoshearkeyseachwould
have tocarry60MN. This isgreater than thenominal42MNcapacitybut less than theirsliding
capacityofabout81MN. Thisimpliesthateithersomeyieldingoftheshearkeystuborhousing,or
participationof thebearings,wouldbenecessary tocarry the full load. This is investigatedusing
morerefinedanalysisinthenextsection.
Longitudinalshearinbearingsisnotaffectedbythereducedclampingforce issuediscussedabove
because the reducedclampingwouldbeon thesideof thesplitbaseplatewhich isneglected in
calculatingtheshearcapacity. Thusthe15MNresistanceperbearingor60MNtotalfor4bearings
giveninFigure4 isdeemedappropriateandmorethanthe50MNreportedtoberequiredbythe
SEE.
The shear keys are not affected by the reduced clamping force issue because tension and
compression,fromoverturning,arebothcarriedbythesameelementssothereisnonetchangein
theclampingforce.
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4.2.4 CapacityofBearingsandShearKeys(individualandcombined)at100%SEERefinedFinite
Element Analysis
Apotential issue thatwas identifiedearly in the review is thesharingof loadbetween theshear
keysandthebearings. Both theshearkeysandthebearings,when fullyengaged,provideavery
stiffloadpathfortheseismicforcesbetweentheOBGandPierE2. Asnotedearlier,thebearingsweredesignedwithsufficientclearancestopreventthemfromtransferringhorizontalload. Some,
butnot all of these clearances will be addressed by the proposed shimming operations. In the
transverse direction, there is a horizontal gap with an asdesigned valueof 2 mm, between the
lower housing and the hold down assembly, which will remain after shimming. See Figure 10.
Additionally, there isanasdesigned3mm vertical gap thatallows the lowerhousing to rotatea
smallamount. Thesegapsallowacertainamountof freemovementof thebearingsbefore they
becomeengagedintransferringlateralforceswhichwillaffectthedistributionofloadsbetweenthe
shearkeysandthebearings.
Figure10 Detailsfromthedesigndrawingsshowing2mmand3mmgaps
Twoanalyseswereperformedtoevaluatethedistributionofloadbetweentheshearkeysandthe
bearings. A3D FEA including theholddownassemblyand the lowerhousingwasperformed to
determine the forcedisplacementbehavior intheasdesignedcondition. Themodel includedthe
2mmand3mmgaps,aswellascompressiononlycontactsurfaces. Figure11showsageneralview
of themodelandFigure12showsthedeformedshapewithstresscontours. AseparateFEAwas
performed on the top housing and its stiffness was included to find the total bearing force
displacementrelationship. Additionally,theforcedisplacementrelationshipwascalculatedbyhand
usingtypicalengineeringapproximations.
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Figure11 Finiteelementmodelofthelowerhousingandholddownassembly
Figure12 Endonviewofthedeformedshapedunderlateralandupliftloading
Loadcase: 1:Increment 1
Results file: Bearing Lower Housing Restraint Refined 2.mysEntity: Stress - Solids
Component: SE
0.535536
0.476032
0.416528
0.357024
0.29752
0.238016
0.178512
0.119008
0.059504
Maximum 0.5365 at node 2513
Minimum 0.964063E-3 at node 3431
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Figure13 Loadvs.displacementforbearingswithvaryingverticalload
Figure13showsthelateralloadvs.displacementrelationshipfortwoconditions;withverticalload
(uplift in the case shown) and with no vertical loads. There is a coupling between lateral
displacementandverticalloadthroughtherotationofthelowerhousing. Becausethepresenceof
vertical load during the times of large lateral loading cannot be guaranteed, the curve without
verticalloadwasusedinfurtherevaluations. Theplateausinthegraphsaretheapproximateload
levelsatwhichfrictionisovercome,andthebearingsbegintoslideonthesteeltosteelinterface.
Finiteelementmodelswerealsodevelopedfortheshearkey;boththestubandthehousingwere
modeledinseparateanalyses. Becauseofthepotentialforexceedingthestatedcapacityof42MN
fortheshearkeys,nonlinearmaterialbehaviorwasincludedinthemodels. Thelateralstiffnessoftheshearkeyswasdeterminedfromtheseanalyses,aswellasfromindependenthandcalculations.
Figure14showstheloadvs.displacementrelationshipfortheshearkey. Thecurveisquitelinearto
loadswell inexcessof thenominalcapacity,withsofteningbecomingapparentonlyatvery large
loadlevels(>70MN). A0.5mmgapwasassumedbetweenthestubandthesphericalring. Itwas
indicatedthattheactualfreeplayintheshearkeysmaybelargerandthisisexploredbelow.
0
5000
10000
15000
20000
25000
30000
0 1 2 3 4 5 6 7 8 9
BearingLateralLo
ad
(kN)
Displacement(mm)
BearingLoadvs.Displacement
WithVerticalLoadAppliedWithoutVerticalLoad
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Figure14
Shear
key
load
vs.
displacement
A total force vs. displacement curve can now be assembled from the individual curves for the
interfacebetweentheOBGandPierE2with4bearingsand2shearkeys. ThisisshowninFigure15.
Table2liststheforcesintheshearkeysandbearingsforseveraldisplacementsbasedonthecurves
above. Because thebearingsdonotcarry loaduntilthevariousgapshaveclosed, theshearkeys
carryamajorityoftheseismicload.
Figure15 Combinedloadvs.displacementforbearingsandshearkeys
0
20000
40000
60000
80000
100000
120000
0 2 4 6 8 10 12 14 16 18 20
Load(kN)
Displacement(mm)
ShearKeyLoadvs.Displacement
020000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 1 2 3 4 5 6 7
TotalShear(kN)
RelativeDisplacement(mm)
Loadvs.DisplacementatE2
SingleBearing
SingleShearKey
Total
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Table2 Loadsinbearingsandshearkeysatvariousdisplacements
Displ.(mm)
Load (kN)
Ea.Bearing
Ea. ShearKey
Total
3.69 0 30883 61767
4.8057 9206 41589 120001
4.8487 9566 42000 122264
5.6799 17059 49882 168001
6.527 22100 57803 204006
Duetotheverylargestiffnessoftheforcetransfermechanismsatplay,verysmallvariationsinthe
sizeofgapscanhaveasignificanteffectonthedistributionofloadbetweenthecomponents. The
previousanalysescanberepeatedwithvariousassumedgapsinboththeshearkeysandbearings.
Twocaseswereexamined: thegapsintheshearkeysandtheshimmedbearingsareapproximately
equal and a relatively greater gap in the bearings such that they do not become engaged until
approximately6mmrelativedisplacement.TheseareshowninFigure16. Table3andTable4list
theforcesinthecomponentsatvariousdisplacementlevelsforthesetwocases.
Figure16 Loadvs.displacementforvariablerelativegaps
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 5 10
Load(kN)
Displacement(mm)
EqualGaps
Ea.Bearing
Ea.ShearKey
Total
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 5 10
Load(kN)
Displacement(mm)
LargeBearingGaps
Ea.Bearing
Ea.ShearKey
Total
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Table3 Loadsincomponentswithequalgapsinbearingsandshearkeys
Displ.(mm)
Load (kN)
Ea.
Bearing
Ea. Shear
Key Total3.69 0 0 0
4 1998 0 7990
6.4194 18279 23443 120001
6.939 22100 28464 145326
8.1182 22100 39800 168000
Table4 Loadsincomponentswith6mmrelativegapbetweenshearkeyandbearings
Displ.(mm)
Load (MN)
Ea.Bearing
Ea. ShearKey
Total
4.3481 0 42000 84000
5.9301 1547 56906 120000
7.0206 8579 66835 168000
Based on the above investigations, the best approach to evaluating the distribution of loads
betweentheshearkeysandthebearingsistoboundthesolution. Inadditiontotheuncertaintyin
themagnitudeof the freeplaybetweenbearings and shear keys, it is likely that variationsexist
betweenthetwoshearkeysandamong the fourbearings. Thiswould increase the loadanyone
component may experience beyond that found assuming equal distribution among the same
components. Another factor is theeffectofdynamic impact. Duringaseismicevent,thegaps in
these components will close at some nonzero velocity, and this will result in localized impact
loading. Simple2DOFstudiesweremade todetermine theorderofmagnitudeof these impact
forces;theywerefoundtobeverysensitivetoassumeddampinglevels. Regardless,impactvalues
of10%ormoredonotseem impractically large. Therefore, the rangeof loading toevaluate the
shearkeysshouldbefrom23.4MNto56.9MN,andfortheshimmedbearingsfrom1.5MNto18.3
MN. Basedontheevaluationof thecapacitiesofthebearings,thereremainsapproximately18%
reservecapacitybeforesliding. Fortheshearkeys,althoughyieldingwasfoundtooccurataloadin
the vicinity of 50 MN, significant capacity exists above that load. Based on the nonlinear finite
elementanalysisdiscussedinAppendix2,amaximumcapacityof65MNappearstobereasonable.
This load level limits the amount of inelastic behavior while still taking advantage of the large
reserve capacity of the shear keys. Based on this, the reserve capacity of the shear keys is
approximately 15% over the SEE demand. Thus, both the bearings and the shear keys have
adequate reserve to coveruncertainties in themagnitudesof the loads, including someunequal
loadsharingwithinsetoflikeunits.
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Aquestionmightbe asked as towhy shim thebearings if shear keys S3 and S4appear tohave
adequate capacity to carry the full SEE demand by themselves. As discussed above, there are
multiple sources of uncertainty regarding the magnitude of the loads and the behavior and
robustnessofthesystemisimprovedbytheadditionofthetransverseshimming.
4.3 CapacityofOBGsandthePierE2CrossGirdertoDeliverLoadtotheShimmedBearingsand
ShearKeys,Respectively
4.3.1 Introduction
Thesteelorthotropicboxgirder(OBG)andsteelcrossgirder (CG)wereevaluatedatPierE2forthe
seismicforcesappliedthroughthebearingsandtheS3andS4shearkeyspriortothecompletionof
theS1andS2shearkeys. Thebearingandshearkey locationswereexamined independently to
determinecapacities. Insomecases, inconsistentconservativeassumptionsweremaderegarding
loads or load paths. For example, the tension in anchor bolts might be maximized to analyze
bearingplatesand stiffeners,and thenminimized todetermine friction from clamping. Another
examplewouldbe that alternative loadpathswouldbe ignoredwhendeterminingdemand in a
givencomponent. Thedemandstodeterminedemandtocapacityratios(D/C)wereassumedtobe
as listed in Table 5. Note that in keepingwith the approach toboundpossibilities, it hasbeen
assumedthateithertheshearkeysorthebearingscarryallofthetransverseforcefromthedesign
SEE. For thepurposeofevaluating theOBGsand theCGatPierE2, these loadsare local to the
individualelementandarenotadditive, i.e. in the temporaryshimmed condition theOBGsneed
onlybeevaluatedforthe loadsfromthebearingsandthecrossgirderneedonlybeevaluatedfor
theloadsfromtheshearkeys.
Table5 Seismicdemands(MN)
B1 S1 B2 S3 S4 B3 S2 B4
Longitudinal 15 0 15 0 0 15 0 15
Transverse 30 0 30 60 60 30 0 30
4.3.2 Bearings
Thereare4bearingsatPierE2,twoundereachboxgirder,as illustrated inFigure4. TheOBG is
attachedtothe
bearings
using
56
2diameter
A354
Grade
BD
rods
anchored
into
stiffened
anchor
seatswithintheOBG. Theseanchorrodsarepretensionedtoclampthebearingontothethickened
bottomflange(keyplate)oftheOBG. Theresultingfrictioncarriesthelongitudinalandhorizontal
forcesbetweentheOBGandthebearings. Thevariouselementsincludinglongitudinalshearplates,
transversewebs,andvariousstiffenersanddiaphragmsoftheOBGatthebearingattachmentare
illustratedinthedesigndrawingsinAppendix3C.
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Thestiffenedanchorseatswereanalyzedfortheinitialtensioningforce,aswellastheentirelocal
OBGassemblagebeinganalyzed for the transferof the seismic forcesbetween theOBGand the
bearing. Theplatesareallstiffenedcompactelementsthatareassumedtobeabletoreachtheir
yield point of 345 MPa (50 ksi). Table 6 lists the demand to capacity ratios (D/C) for various
elements. The calculations for these values are contained in Appendix 3A. Similar calculations
performedbytheEORwithcomparableresultsarecontainedinAppendix3B.
Table6 Demand/CapacityratiosOBG
Component Force Demand/CapacityD/C(%)
1. Keyplate Longitudinal 15%
Transverse 26%
2. Longitudinalshearplate Longitudinal 72%
3. Floorbeamwebs Transverse 49%
4. Anchorboltbearingplate Bending 66%
5. Centerbrgstiffenerplate Axial 84%
Shear 48%6. Sidebrgstiffenerplate Axial 35%
Shear 21%
7. Floorbeamweb Anchorassemblytearout 53%
8. 50mmx700mmplates Shear 95%
9. Bearingsurface Friction 95%
10. LocalverticalOBGelements Normalstresses 72%
ItshouldbenotedthatthebearingsurfaceslidingfrictionD/Cratioisnotforthemaximumseismic
forcesoccurringsimultaneouslyinallthreeorthogonaldirections,but isforthemaximumupliftof
9.5MNalongwith the concurrent transverseandhorizontal forces (see calculations inAppendix3A).
The D/C ratios in Table 6 indicate that OBGs have more than sufficient capacity to resist the
demands of the design SEE at pier E2. This conclusion is further supported by the analyses in
Sections4.2.3and4.2.4whichindicatethatthebearingswillnotbesubjectedtothenominal30MN
underthedesignSEE.
4.3.3 ShearKeys3and4
Shearkeys3and4arelocated2900mmeithersideofmidspanofthesteelcrossgirderatPierE2
(seeFigure4andDesignDrawingsinAppendix3C). TheCGisattachedtotheshearkeysusing483diameterA354GradeBDrodsanchoredintostiffenedanchorseatsand323diameteranchor
rodsboltingthetopplateoftheshearkeydirectlytothebottomflangeoftheCG. Theseanchor
rodsarepretensionedtoclamptheshearkeyontothethickenedbottomflange(keyplate)ofthe
CG. TheresultingfrictioncarriesthetransverseseismicforcesfromtheCGintotheshearkey. The
variouselementsoftheCGattheshearkeyattachmentincludingfloorbeamwebs,diaphragms,and
stiffenersareillustratedintheDesignDrawingsinAppendix3C.
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Thestiffenedanchorseatswereanalyzedfortheinitialtensioningforce,aswellastheentirelocal
CGassemblagebeinganalyzedforthetransferoftheseismicforcesbetweentheCGandtheshear
key. Theplatesareallstiffenedcompactelementsthatareassumedtobeabletoreachtheiryield
pointof345MPa (50ksi). Table7 liststhedemandtocapacityratios (D/C) forvariouselements.
ThecalculationsforthesevaluesarecontainedinAppendix3A.
Table7 Demand/Capacityratiossteelcrossgirder
Component Force Demand/CapacityD/C(%)
1. Keyplate Transverse 38%
2. Floorbeamwebs Transverse 74%
3. Anchorboltbearingplates Interfaceshear 80%
Bending 65%
4. Centerbrgstiffenerplate Axial 81%
Shear 92%
5. Sidebrgstiffenerplate Axial 42%
Shear
37%
6. Diaphragms Anchorassemblytearout 76%
7. Floorbeamweb Anchorassemblytearout 94%
8. Bearingsurface Friction 60%
9. LocalverticalCGelements Normalstresses 41%
10. Bending+axialglobalest. Normalstresses 50%
TheD/CratiosinTable7indicatethattheCGatPierE2hasmorethansufficientcapacitytoresist
thedemandsof thedesignSEE. This conclusion is further supportedby theanalyses inSections
4.2.3and4.2.4which indicate that thebearingswillnotbe subjected to the60MNused in this
evaluationunderthedesignSEE.
4.4CapacityofStrut
4.4.1Introduction
TheeffectsoftheforcescorrespondingtoloadpathConthestrutatPierE2wereinitiallyanalyzed
using the conventional method of strength of materials. A simple static frame analysis was
performed todetermine the internal forcesof thestrut. Critical strut sectionswith forces larger
than those reported for loadpathBwerecheckedaccording to theAASHTO LRFDSpecifications.
Thisassumes(perthescopeforthisreview)thatthecomponentswereadequatelydesignedbythe
EOR for this load path. In addition, a lower bound load path wherein all the seismic force isassumedtobetransferredthroughshearkeysS3andS4wasalsoevaluated.
4.4.2StructuralAnalysis
TheLusasframemodelshowninFigure17wassubjectedtotheloadingeffectsindicatedbyTable8
forloadpathC. Theeccentricitybetweenthecenterofrotationofthebearingsandshearkeysand
thestrutcenterlinewasconsideredinthedefinitionofthemodelinputloads. Table9presentsthe
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envelopeofthesectionalforcesatthecriticalbearingandshearkeylocationsincludingthegravity
andaxialposttensioningeffectsofthestrut. TheredvaluesindicatedinTable9correspondtothe
demand forces thatweremorecritical than theircounterpartsof loadpathB. Figure18 through
Figure20showthedifferentforceeffectdiagramsofthestrutforloadpathCandthelowerbound
path.
4.4.3SectionalChecks
ThecriticalforcesfromTable8andtheirconcurrenteffectswerecomparedtothesectioncapacities
determinedaccordingtotheAASHTOLRFDSpecifications.
Asummaryof theprincipalcheck findings ispresented inTable9. The rednumbers indicate the
critical force effect taken from the envelope and the blue shaded numbers mean that the
correspondingD/Cchecksaresatisfactory.ThecompletecalculationscanbefoundinAppendix4.
4.4.4Results
The results showed that themaximumbiaxial flexure interaction equation valueswere 0.91and
0.94 atbearingB2and shear key S2, respectively,while thedemandtocapacity ratios for shear
were0.82atbearingB3,and0.58atshearkeyS2(seeFigure17for locationofbearingandshear
key sections) indicatingmore thanadequate capacity to resist theSEE forces. The forceson the
cantileverportionsof thestrut resulted in insignificantdemandswhencompared to theavailable
capacityofthosecomponents. Infact,thestressesinthecantileveredsectionofthestrutbasedon
thissectionalanalysiswere found tobebelow themodulusof rupturewhen theposttensioning
effectswereincluded,meaningtheconcretewouldlikelynotevencrackduringanearthquake.
Forthelowerboundloadpath,althoughtheminimumaxialforceinthestrutwascontrolledbythis
loading case, thebiaxial flexure interaction checks showed that thiswasnot a critical condition.
Betweenthecolumns,thedemandsaredrivenbytheglobalframeactionmomentsandshearssuch
thatthechange inforcescausedbytransferringtheseismicloadsthroughthebearingshadavery
minoreffectonallbuttheaxialloads,ascanbeseeninthecomparisonoftheforceeffectdiagrams
betweenloadpathCandthelowerboundpathinFigure18throughFigure20.
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a.
b.Figure17 OverviewofPierE2Framemodel;a.3Dview.b.IdentificationofStrutCrossSections
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LoadPathC LowerBoundPath
AxialLoad,Pu(MN)
InplaneMoment,Mux(MNm)
Figure18ForceDiagramsforLoadPathCandLowerBoundPath(Note:axialposttensioningeffects
arenotincludedinthediagrams)
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LoadPathC LowerBoundPath
InplaneShear,Vuy(MN)
Torsion,Tu(MNm)
Figure19 ForceDiagramsforLoadPathCandLowerBoundPath
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LoadPathC LowerBoundPath
OutofplaneMoment,Muy(MNm)
OutofplaneShear,Vux(MN)
Figure20 ForceDiagramsforLoadPathCandLowerBoundPath
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Table8 SuperstructureloadsonStrutatPierE2
Bearings
B1,B2,B3,B4
ShearKeys
S3,S4
Transverse Long. Vertical Transverse
KN KN KN KN
Load
pathB
Transverse 30496 8186 16441 0Long. 1340 13232 19255 0
Vertical 10799 4770 57932 0
Uplift 25287 1628 9539 0
Load
pathC
Transverse 20331 8186 16441 20331
Long. 893 13232 19255 893
Vertical 7199 4770 57932 7199
Uplift 16858 1628 9539 16858
Lower
bound
pathTransverse 0 8186 16441 60992
Long. 0 13232 19255 2680
Vertical 0 4770 57932 21598
Uplift 0 1628 9539 50574
Table9 Envelopeofsectionalforcesatbearingsandshearkeys
Pu Vuy Vux Tu Muy Mux
AxialInplane
Shear
Outof
planeshearTorsion
Outofplane
moment
Inplane
moment
MN MN MN MNm MNm MNm
Load
pathB
Bearings
B1,B2,B3,B4
max 114 86 13 57 3 855
min 180 61 13 53 2 797
ShearKeys
S1,S2
max 118 89 13 57 6 844
min 180 52 13 49 58 1136
Load
pathC
Bearings
B1,B2,B3,B4
max 104 89 13 53 3 941
min 185 61 13 53 2 912
ShearKeys
S1,S2
max 104 92 13 53 5 1232
min 185 64 13 53 58 968
Lower
bound
path
Bearings
B1,B2,B3,B4
max 84 89 13 53 3 799
min 206 61 13 53 2 770
ShearKeys
S1,S2
max 84 92 13 53 5 1177
min 206 64 13 53 58 913
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Table10 CriticalSectionalForcesandCapacityChecks
Units: Force: MN Moments: MNm Stress: MPa
Element: Bearings ShearKeys
Controllingforce: Muxmax Muxmin Vuymax Pumin Muxmax Vuymax Pumin
Section: B3 B2 B3 B3 S2 S2 S2
1. Sectionalloadingeffects:Axial(if0 Topfiberintension) Mux= 941 912 304 799 1232 688 1177
Outofplanebendingmoment Muy= 3 3 2 3 32 18 32
Torsion Tu= 0 0 19 0 33 19 33
Inplaneshear Vuy= 70 50 89 71 89 92 90
Outofplaneshear Vux= 0 0 5 0 8 5 8
2. Normalstressesassumingelasticbehavior:
(if>0compressivestress) fc1= 42 29 17 38 44 26 43
%f'c= 75% 53% 32% 68% 80% 47% 78%
fc2= 29 39 6 22 33 17 30
%f'c= 53% 70% 10% 40% 59% 30% 55%
3. Axialandflexuralforceeffects:
Pnx= 172 174 209 248 195 177 227
Mnx= 1239 1274 1291 1341 1528 1497 1577
eyratio= 1.00 1.00 1.00 1.00 1.00 1.00 1.00Pny= 1063 1209 1065 1082 997 845 1112
Mny= 31 27 26 11 712 873 535
exratio= 1.00 1.00 1.00 1.00 1.00 1.00 1.00
IE= 0.86 0.91 0.27 0.72 0.94 0.53 0.89
4. Shearandtorsionalforceeffects:
Torsionaleffects: Tn= 82 82 94 88 46 52 47
Tu/Tn= 0.00 0.00 0.20 0.00 0.71 0.37 0.69
Inplaneshear: Vn= 88 87 109 97 135 158 139
Vu/Vn= 0.79 0.58 0.82 0.73 0.66 0.58 0.65
Outofplaneshear: Vc= 51 51 51 51 63 63 63
Vu/Vc= 0.00 0.00 0.08 0.00 0.12 0.07 0.12
4.5Transfer
of
Horizontal
Load
From
Bearing
Base
Plate
to
Strut
to
Column
Due to thesizeand localized loadingconditionsof the concretepierstrut,strutandtiemodelswere
developed for the two regions shown in Figure 21 as an additional check beyond the sectional
interaction values of Section 4.4. Since the controlling loading case corresponds to the transverse
forces,onlytwodimensionalmodelssubjectedtotheseforceswereconsideredinthisstudy.
Todetermineanappropriatestrutandtiemodelthataccuratelyrepresentstheflowofforcesinthese
disturbed regions,anelasticanalysisofaplane stressmodelof the strutwasperformed in Lusas to
obtaintheprincipalstressesintheuncrackedregions. Strutandtieconfigurationswerethendeveloped
basedon the flowof forces in thesemodels (see Figure 22). Inorder tobound thepotential loads
appliedat thebearingsandshearkeys, thebearingswereevaluated for the forces from loadpathB,
whileshearkeys3and4wereloadedwiththelowerboundforces,assumingalltransverseseismicforce
istransmittedthroughthesetwoshearkeys. Resultsoftheframeanalysiswereusedtodeterminethe
boundary loads applied to the strut and tie models. Results of the analysis indicate that there is
sufficientcapacitytoaccommodatethechanges in loadpathcausedbytheshimmingofthebearings.
Oneanomalousresultwasencounteredregardingthetiecapacityinthetensionsideofthepiercolumn.
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Since this isoutsideof thescopeof this review, itwasnotpursuedbutwas reported to theEOR for
furtherreview.
ThecompletecalculationscorrespondingtothestrutandtiemodelsarepresentedinAppendix5.
Figure21 Strutregionsanalyzedwithstrutandtiemodels
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Figure22 Principalstresstrajectoriesandstrutandtiemodels(blue:compression,red:tension)
4.6 PotentialtoDamagethePermanentBearingsorOtherComponentsifShimsareInstalled
TheanalysisofPierE2inSection4.4showsthattheserviceandseismicdesignforcesinthepierarenot
changedsignificantlyby the redirectionofseismic forces resulting from theshimming. Therefore the
responseoftheconcretestrutandcolumnsarenotexpectedtobedifferentwithorwithouttheshims.
Basedonthissubjectiveassessmentoftheglobaleffects,combinedwiththequantitativeassessmentof
the local elements in the load transfer zone, it is concluded that there does not appear to be any
reasonable possibility of damaging the bridge as a result of installing the shims, other than the
possibilityofdamagingthepaintsystemeitherwhentheshimsareinsertedorasthebridgerotatesin
service
5. ConclusionsandRecommendations
Theexactdistributionofforcesinthebearingsandshearkeys,andhencethedemandsonotherpartsof
the load transferzoneatPierE2which is thescopeof this investigation, ishighlydependenton the
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