report 8-9-13 - oakland bay bridge seismic retrofit

8/13/2019 Report 8-9-13 - Oakland Bay Bridge Seismic Retrofit

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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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ThisPageIntentionallyLeftBlank


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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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4

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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14

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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InplaneShear,Vuy(MN)

Torsion,Tu(MNm)

Figure19 ForceDiagramsforLoadPathCandLowerBoundPath


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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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report 8-9-13 - oakland bay bridge seismic retrofit

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