Bridge Design Manual M 23-50 Chapter 4 Seismic Design · PDF fileWSDOT Bridge Design Manual M...

WSDOT Bridge Design Manual M 23-50.17 Page 4-i June 2017

4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-1

4.2 WSDOTAdditionsandModificationstoAASHTOGuide Specifications for LRFD Seismic Bridge Design (SEISMIC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24.2.2 EarthquakeResistingSystems(ERS)RequirementsforSeismicDesignCatagories

(SDCs)CandD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24.2.3 SeismicGroundShakingHazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-74.2.4 SelectionofSeismicDesignCategory(SDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-94.2.5 TemporaryandStagedConstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-94.2.6 LoadandResistanceFactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-94.2.7 BalancedStiffnessRequirementsandBalancedFrameGeometryRecommendation . 4-104.2.8 SelectionofAnalysisProceduretoDetermineSeismicDemand . . . . . . . . . . . . . . . . . .4-104.2.9 MemberDuctilityRequirementforSDCsCandD . . . . . . . . . . . . . . . . . . . . . . . . . . .4-104.2.10 LongitudinalRestrainers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-104.2.11 Abutments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-104.2.12 Foundation–General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-154.2.13 Foundation–SpreadFooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-154.2.14 Procedure3:NonlinearTimeHistoryMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-154.2.15 IeffforBoxGirderSuperstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-154.2.16 FoundationRocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-154.2.17 DrilledShafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-164.2.18 LongitudinalDirectionRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-164.2.19 LiquefactionDesignRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-164.2.20 ReinforcingSteel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-164.2.21 ConcreteModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-174.2.22 ExpectedNominalMomentCapacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-174.2.23 InterlockingBarSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-174.2.24 SplicingofLongitudinalReinforcementinColumnsSubjecttoDuctilityDemands

forSDCsCandD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-174.2.25 DevelopmentLengthforColumnBarsExtendedintoOversizedPileShaftsf

orSDCsCandD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-174.2.26 LateralConfinementforOversizedPileShaftforSDCsCandD . . . . . . . . . . . . . . . . .4-184.2.27 LateralConfinementforNon-OversizedStrengthenedPileShaftforSDCsCandD . . . .4-184.2.28 RequirementsforCapacityProtectedMembers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-184.2.29 SuperstructureCapacityDesignforTransverseDirection(IntegralBentCap)for

SDCsCandD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-184.2.30 SuperstructureDesignforNonIntegralBentCapsforSDCsB,C,andD . . . . . . . . . . .4-194.2.31 JointProportioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-194.2.32 Cast-in-PlaceandPrecastConcretePiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-19

4.3 SeismicDesignRequirementsforBridgeModificationsandWideningProjects . . . .4-204.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-204.3.2 BridgeWideningProjectClassification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-204.3.3 SeismicDesignGuidance: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-214.3.4 ScopingforBridgeWideningandLiquefactionMitigation . . . . . . . . . . . . . . . . . . . . . .4-244.3.5 DesignandDetailingConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24

Chapter 4 Seismic Design and Retrofit Contents

Contents

Page 4-ii WSDOT Bridge Design Manual M 23-50.17 June 2017

4.4 SeismicRetrofittingofExistingBridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-264.4.1 SeismicAnalysisRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-264.4.2 SeismicRetrofitDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-264.4.3 ComputerAnalysisVerification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-274.4.4 EarthquakeRestrainers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-274.4.5 IsolationBearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-27

4.5 SeismicDesignRequirementsforRetainingWalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-284.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-28

4.6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-29Appendix4-B1 DesignExamplesofSeismicRetrofits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30Appendix4-B2 SAP2000SeismicAnalysisExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35

4.99 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-118

WSDOT Bridge Design Manual M 23-50.17 Page 4-1 June 2017

Chapter 4 Seismic Design and Retrofit

4.1 GeneralSeismicdesignofnewbridgesandbridgewideningsshallconformtoAASHTO Guide Specifications for LRFD Seismic Bridge Design (SEISMIC)asmodifiedbySections4.2and4.3.AnalysisanddesignofseismicretrofitsforexistingbridgesshallbecompletedinaccordancewithSection4.4.SeismicdesignofretainingwallsshallbeinaccordancewithSection4.5.Fornonconventionalbridges,bridgesthataredeemedcriticaloressential,orbridgesthatfalloutsidethescopeoftheGuideSpecificationsforanyotherreasons,projectspecificdesignrequirementsshallbedevelopedandsubmittedtotheWSDOTBridgeDesignEngineerforapproval.

TheimportanceclassificationsforallhighwaybridgesinWashingtonStateareclassifiedas“Normal”exceptforspecialmajorbridges.Specialmajorbridgesfittingtheclassificationsofeither“Critical”or“Essential”willbesodesignatedbyeithertheWSDOTBridgeandStructuresEngineerortheWSDOTBridgeDesignEngineer.

Theperformanceobjectivefor“normal”bridgesislifesafety.BridgesdesignedinaccordancewithAASHTOGuideSpecificationsareintendedtoachievethelifesafetyperformancegoals.

Seismic Design and Retrofit Chapter 4

-2 WSDOT Bridge Design Manual M 23-50.17 June 2017

4.2 WSDOTAdditionsandModificationstoAASHTOGuide Specifications for LRFD Seismic Bridge Design (SEISMIC)

WSDOTamendmentstotheAASHTOSEISMICareasfollows:

4.2.1 DefinitionsGuide Specifications Article 2.1 – Addthefollowingdefinitions:• Oversized Pile Shaft – Adrilledshaftfoundationthatislargerindiameterthanthesupportedcolumnandhasareinforcingcagelargerthanandindependentofthecolumns.ThesizeoftheshaftshallbeinaccordancewithSection7.8.2.

• Owner – Personoragencyhavingjurisdictionoverthebridge.ForWSDOTprojects,regardlessofdeliverymethod,theterm“Owner”intheseGuideSpecificationsshallbetheWSDOTBridgeDesignEngineeror/andtheWSDOTGeotechnicalEngineer.

4.2.2 Earthquake Resisting Systems (ERS) Requirements for Seismic Design Catagories (SDCs) C and D

Guide Specifications Article 3.3 – WSDOTGlobalSeismicDesignStrategies:• Type 1 – DuctileSubstructurewithEssentiallyElasticSuperstructure.Thiscategoryispermissible.

• Type 2 – EssentiallyElasticSubstructurewithaDuctileSuperstructure.Thiscategoryisnotpermissible.

• Type 3 – ElasticSuperstructureandSubstructurewithaFusingMechanismBetweentheTwo.ThiscategoryispermissiblewithWSDOTBridgeDesignEngineer’sapproval.

WiththeapprovaloftheBridgeDesignEngineer,forType1ERSforSDCCorD,ifcolumnsorpierwallsareconsideredanintegralpartoftheenergydissipatingsystembutremainelasticatthedemanddisplacement,theforcestouseforcapacitydesignofothercomponentsaretobeaminimumof1.2timestheelasticforcesresulting

fromthedemanddisplacementinlieuoftheforcesobtainedfromoverstrengthplastichinginganalysis.Becausemaximumlimitinginertialforcesprovidedbyyieldingelementsactingataplasticmechanismlevelisnoteffectiveinthecaseofelasticdesign,thefollowingconstraintsareimposed.ThesemayberelaxedonacasebycasebasiswiththeapprovaloftheBridgeDesignEngineer.

1. Unlessananalysisthatconsidersredistributionofinternalstructureforcesduetoinelasticactionisperformed,allsubstructureunitsoftheframeunderconsiderationandofanyadjacentframesthatmaytransferinertialforcestotheframeinquestionmustremainelasticatthedesigngroundmotiondemand.

2. Effectivemembersectionpropertiesmustbeconsistentwiththeforcelevelsexpectedwithinthebridgesystem.Reinforcedconcretecolumnsandpierwallsshouldbeanalyzedusingcrackedsectionproperties.Forthispurpose,inabsenceofbetterinformationorestimatedbyFigure5.6.2-1,amomentofinertiaequaltoonehalfthatoftheun-crackedsectionshallbeused.



3. Foundationmodelingmustbeestablishedsuchthatuncertaintiesinmodelingwillnotcausetheinternalforcesofanyelementsunderconsiderationtoincreasebymorethan10percent.

4. Whensitespecificgroundresponseanalysisisperformed,theresponsespectrumordinatesmustbeselectedsuchthatuncertaintieswillnotcausetheinternalforcesofanyelementsunderconsiderationtoincreasebymorethan10percent.

5. Thermal,shrinkage,prestressorotherforcesthatmaybepresentinthestructureatthetimeofanearthquakemustbeconsideredtoactinasensethatisleastfavorabletotheseismicloadcombinationunderinvestigation.

6. P-Deltaeffectsmustbeassessedusingtheresistanceoftheframeinquestionatthedeflectioncausedbythedesigngroundmotion.

7. Jointsheareffectsmustbeassessedwithaminimumofthecalculatedelasticinternalforcesappliedtothejoint.

8. DetailingasnormallyrequiredineitherSDCCorD,asappropriate,mustbeprovided.

Itispermittedtouseexpectedmaterialstrengthsforthedeterminationofmemberstrengthsforelasticresponseofmembers.

TheuseofelasticdesigninlieuofoverstrengthplastichingingforcesforcapacityprotectiondescribedaboveshallonlybeconsideredifdesignerdemonstratesthatcapacitydesignofArticle4.11oftheAASHTOGuide Specifications for LRFD Bridge Seismic Designisnotfeasibleduetogeotechnicalorstructuralreasons.

Type3ERSmaybeconsideredonlyifType1strategyisnotsuitableandType3strategyhasbeendeemednecessaryforaccommodatingseismicloads.UseofisolationbearingsneedstheapprovalofWSDOTBridgeDesignEngineer.IsolationbearingsshallbedesignedpertherequirementspecifiedinSection9.3

Ifthecolumnsorpierwallsaredesignedforelasticforces,allotherelementsshallbedesignedforthelesseroftheforcesresultingfromtheoverstrengthplastichingingmomentcapacityofcolumnsorpierwallsandtheunreducedelasticseismicforceinallSDCs.Theminimumdetailingaccordingtothebridgeseismicdesigncategoryshallbeprovided.Sheardesignshallbebasedon1.2timeselasticshearforceandnominalmaterialstrengthsshallbeusedforcapacities.LimitationsontheuseofERSandEREareshowninFigures3.3-1a,3.3-1b,3.3-2,and3.3-3.• Figure3.3-1bType6,connectionwithmomentreducingdetailshouldonlybeusedatcolumnbaseifprovednecessaryforfoundationdesign.FixedconnectionatbaseofcolumnremainsthepreferredoptionforWSDOTbridges.

• Thedesigncriteriaforcolumnbasewithmomentreducingdetailshallconsiderallapplicableloadsatservice,strength,andextremeeventlimitstates.

• Figure3.3-2Types6and8arenotpermissiblefornon-liquefiedconfigurationandpermissiblewithWSDOTBridgeDesignEngineer’sapprovalforliquefiedconfiguration

ForERSsandEREsrequiringapproval,theWSDOTBridgeDesignEngineer’sapprovalisrequiredregardlessofcontractingmethod(i.e.,approvalauthorityisnottransferredtootherentities).


Page 4-4 WSDOT Bridge Design Manual M 23-50.17 June 2017

Figure 3.3-1a Permissible Earthquake-Resisting Systems (ERSs).

Longitudinal ResponseUponApproval

PermissibleUponApproval

1

LongitudinalResponse

Permissible

Plastichingesininspectablelocationsorelasticdesignofcolumns.

AbutmentresistancenotrequiredaspartofERS

Knock-offbackwallspermissible

Transverse Response

2

LongitudinalResponse

Isolationbearingsaccommodatefulldisplacement

AbutmentnotrequiredaspartofERS

3Permissible

Plastichingesininspectablelocations.

AbutmentnotrequiredinERS,breakawayshearkeyspermissiblewithWSDOTBridgeDesignEngineer’sApproval

4

TransverseorLongitudinalResponse

Plastichingesininspectablelocations

Isolationbearingswithorwithoutenergydissipaterstolimitoveralldisplacements


5

Transverse or LongitudinalResponse

Permissible

Abutmentrequiredtoresistthedesignearthquakeelastically

Longitudinalpassivesoilpressureshallbelessthan0.70ofthevalueobtainedusingtheproceduregiveninBDMArticle4.2.11

6LongitudinalResponse

Multiplesimply-supportedspanswithadequatesupportlengths

Plastichingesininspectablelocationsorelasticdesignofcolumns

NotPermissible

Figure3.3-1aPermissibleEarthquake-ResistingSystems(ERSs)BDM Figure 4.2.2-1



Figure 3.3-1 b Permissible Earthquake-Resisting Elements (EREs)

Columnswitharchitecturalflares–withorwithoutanisolationgap

SeeArticle8.14

Seatabutmentswhosebackwallisdesignedtoresisttheexpectedimpactforceinanessentiallyelasticmanner

3

Pierwallswithorwithoutpiles.

SpreadfootingsthatsatisfytheoverturningcriteriaofArticle6.3.4

Capacity-protectedpilecaps,includingcapswithbatteredpiles,whichbehaveelastically

Pileswith‘pinned-head’conditions

Seismicisolationbearingsorbearingsdesignedtoaccommodateexpectedseismicdisplacementswithnodamage

Plastichingesbelowcapbeamsincludingpilebents

Aboveground/neargroundplastichinges

Tensileyieldingandinelasticcompressionbucklingofductileconcentricallybracedframes

Plastichingesatbaseofwallpiersinweakdirection

Seatabutmentswhosebackwallisdesignedtofuse

PassiveabutmentresistancerequiredaspartofERSUse70%ofpassivesoilstrengthdesignatedinBDMArticle4.2.11

isolationgapoptional

1

2

4

56

7 8

9

10

11

12

13

Permissible


Permissible

NotPermissible


Permissible

Permissible


Permissibleexceptbatteredpilesarenotallowed

Permissible

Permissible

Permissible–isolationgapisrequired

14

Permissible

Columnswithmomentreducingorpinnedhingedetails

Permissible

Figure3.3-1bPermissibleEarthquake-ResistingElements(EREs)BDM Figure 4.2.2-2



Figure 3.3-2 Permissible Earthquake-Resisting Elements that Require Owner’s Approval

1 Passive abutment resistance required as part of ERS Passive StrengthUse 100% of strength designated in Article 5 .2 .3

2

3Ductile End-diaphragms in superstructure (Article 7 .4 .6) 4

Sliding of spread footing abutment allowed to limit force transferred

Limit movement to adjacent bent displacement capacity

Foundations permitted to rock

Use rocking criteria according to Appendix A

5

More than the outer line of piles in group systems allowed to plunge or uplift under seismic loadings

6Wall piers on pile foundations that are not strong enough to force plastic hinging into the wall, and are not designed for the Design Earthquake elastic forces

Ensure Limited Ductility Response in Piles according to Article 4 .7 .1

7Plumb piles that are not capacity-protected (e .g ., integral abutment piles or pile-supported seat abutments that are not fused transversely)


8In-ground hinging in shafts or piles .


9

Batter pile systems in which the geotechnical capacities and/or in-ground hinging define the plastic mechanisms .


NotPermissible

NotPermissible

NotPermissible

NotPermissible

NotPermissible

NotPermissible

NotPermissible

PermissibleUponApprovalforLiquefiedConfiguration

PermissibleUponApprovalforLiquefiedConfiguration

Figure3.3-2PermissibleEarthquake-ResistingElementsThatRequireOwner’sApprovalBDM Figure 4.2.2-3



Figure 3.3-3 Earthquake-Resisting Elements that Are Not Recommended for New Bridges

NotPermissible

Bearing systems that do not provide for the expected displacements and/or forces (e .g ., rocker bearings)

Battered-pile systems that are not designed to fuse geotechnically or structurally by elements with adequate ductility capacity

Cap beam plastic hinging (particularly hinging that leads to vertical girder movement) also includes eccentric braced frames with girders supported by cap beams

Plastic hinges in superstructure

12

3 4

NotPermissible

NotPermissible

NotPermissible

Figure3.3-3Earthquake-ResistingElementsthatAreNotRecommendedforNewBridgesBDM Figure 4.2.2-4

4.2.3 Seismic Ground Shaking HazardGuide Specifications Article 3.4–ForbridgesthatareconsideredcriticaloressentialornormalbridgeswithasiteClassF,theseismicgroundshakinghazardshallbedeterminedbasedontheWSDOTGeotechnicalEngineerrecommendations.

IncaseswherethesitecoefficientsusedtoadjustmappedvaluesofdesigngroundmotionforlocalconditionsareinappropriatetodeterminethedesignspectrainaccordancewithgeneralprocedureofArticle3.4.1(suchastheperiodattheendofconstantdesignspectralaccelerationplateau(Ts)isgreaterthan1.0secondortheperiodatthebeginningofconstantdesignspectralaccelerationplateau(To)islessthan0.2second),asite-specificgroundmotionresponseanalysisshallbeperformed.

Inthegeneralprocedure,thespectralresponseparametersshallbedeterminedusingtheUSGS2014SeismicHazardMapswithSevenPercentProbabilityofExceedancein75yr(1000-yrReturnPeriod).



GuideSpecificationsArticle3.4.2.3-SiteCoefficientsThesitecoefficientsforpeakgroundacceleration,Fpga,short-periodrangeFa,andforlong-periodrangeFvshallbetakenasspecifiedinthefollowingTables:

Site ClassMappedPeakGroundAccelerationCoefficient(PGA)

PGA≤0.10 PGA=0.2 PGA=0.3 PGA=0.4 PGA=0.5 PGA≥0.6A 0 .8 0 .8 0 .8 0 .8 0 .8 0 .8B 0 .9 0 .9 0 .9 0 .9 0 .9 0 .9C 1 .3 1 .2 1 .2 1 .2 1 .2 1 .2D 1 .6 1 .4 1 .3 1 .2 1 .1 1 .1E 2 .4 1 .9 1 .6 1 .4 1 .2 1 .1F * * * * * *

ValuesofSiteCoefficient,Fpga,forPeakGroundAccelerationTable 3.4.2.3-1A

Site ClassMappedSpectralAccelerationCoefficientatPeriod0.2sec(Ss)

Ss≤0.25 Ss=0.50 Ss=0.75 Ss=1.00 Ss=1.25 Ss≥1.50A 0 .8 0 .8 0 .8 0 .8 0 .8 0 .8B 0 .9 0 .9 0 .9 0 .9 0 .9 0 .9C 1 .3 1 .3 1 .2 1 .2 1 .2 1 .2D 1 .6 1 .4 1 .2 1 .1 1 .0 1 .0E 2 .4 1 .7 1 .3 * * *F * * * * * *

ValuesofSiteCoefficient,Fa,for0.2-secPeriodSpectralAccelerationTable 3.4.2.3-1B

Site ClassMappedSpectralAccelerationCoefficientatPeriod1.0sec(S1)

S1≤0.1 S1=0.2 S1=0.3 S1=0.4 S1=0.5 S1≥0.6A 0 .8 0 .8 0 .8 0 .8 0 .8 0 .8B 0 .8 0 .8 0 .8 0 .8 0 .8 0 .8C 1 .5 1 .5 1 .5 1 .5 1 .5 1 .4D 2 .4 2 .2 2 .0 1 .9 1 .8 1 .7E 4 .2 3 .3 2 .8 2 .4 2 .2 2 .0F * * * * * *

*Site-specific response geotechnical investigation and dynamic site response analysis should be considered .Note: Use straight line interpolation for intermediate values of PGA, Ss, and S1 .

ValuesofSiteCoefficient,Fv,for1.0-secPeriodSpectralAccelerationTable 3.4.2.3.2



GroundMotionToolThegroundmotionsoftwaretoolcalledSpectradevelopedbytheBridgeandStructuresOfficeallowstheusertogeneratethedesignresponsespectrumusingtheUSGS2014SeismichazardmapsandtheupdatedSiteCoefficients.SpectraisatoolintheBridgeLinkBEToolboxapplication.DownloadBridgeLinkfromtheWSDOTwebsiteatwww.wsdot.wa.gov/eesc/bridge/software.

Afterdownloadingandinstalling,startBridgeLink,selectFile>NewandselecttheSpectratooltobeginanewresponsespectrumproject.

WSDOT Bridge Design Manual M 23-50.16June 2016

Page 4-9


4.2.4 Selection of Seismic Design Category (SDC)

Guide Specifications Article 3.5 – PushoveranalysisshallbeusedtodeterminedisplacementcapacityforbothSDCsCandD.

4.2.5 Temporary and Staged Construction

Guide Specifications Article 3.6 – Forbridgesthataredesignedforareducedseismicdemand,thecontractplansshalleitherincludeastatementthatclearlyindicatesthatthebridgewasdesignedastemporaryusingareducedseismicdemandorshowtheAccelerationResponseSpectrum(ARS)usedfordesign.

4.2.4 Selection of Seismic Design Category (SDC)Guide Specifications Article 3.5–PushoveranalysisshallbeusedtodeterminedisplacementcapacityforbothSDCsCandD.

4.2.5 Temporary and Staged ConstructionGuide Specifications Article 3.6–Forbridgesthataredesignedforareducedseismicdemand,thecontractplansshalleitherincludeastatementthatclearlyindicatesthatthebridgewasdesignedastemporaryusingareducedseismicdemandorshowtheAccelerationResponseSpectrum(ARS)usedfordesign.Noliquefactionassessmentrequiredfortemporarybridges.

4.2.6 Load and Resistance FactorsGuide Specifications Article 3.7–Reviseasfollows:

Useloadfactorsof1.0forallpermanentloads.Theloadfactorforliveloadshallbe0.0whenpushoveranalysisisusedtodeterminethedisplacementcapacity.Useliveloadfactorof0.5forallotherextremeeventcases.Unlessotherwisenoted,allϕfactorsshallbetakenas1.0.

http://www.wsdot.wa.gov/eesc/bridge/software



4.2.7 Balanced Stiffness Requirements and Balanced Frame Geometry Recommendation

Guide Specifications Articles 4.1.2 and 4.1.3–BalancedstiffnessbetweenbentswithinaframeandbetweencolumnswithinabentandbalancedframegeometryforadjacentframesarerequiredforbridgesinbothSDCsCandD.DeviationsfrombalancedstiffnessandbalancedframegeometryrequirementsrequireapprovalfromtheWSDOTBridgeDesignEngineer.

4.2.8 Selection of Analysis Procedure to Determine Seismic DemandGuide Specifications Article 4.2–AnalysisProcedures:• Procedure1(EquivalentStaticAnalysis)shallnotbeused.• Procedure2(ElasticDynamicAnalysis)shallbeusedforall“regular”bridgeswithtwothroughsixspansand“notregular”bridgeswithtwoormorespansinSDCsB,C,orD.

• Procedure3(NonlinearTimeHistory)shallonlybeusedwithWSDOTBridgeDesignEngineer’sapproval.

4.2.9 Member Ductility Requirement for SDCs C and DGuide Specifications Article 4.9–In-groundhingingfordrilledshaftandpilefoundationsmaybeconsideredfortheliquefiedconfigurationwithWSDOTBridgeDesignEngineerapproval.

4.2.10 Longitudinal RestrainersGuide Specifications Article 4.13.1 – Longitudinalrestrainersshallbeprovidedattheexpansionjointsbetweensuperstructuresegments.RestrainersshallbedesignedinaccordancewiththeFHWASeismicRetrofittingManualforHighwayStructure(FHWA-HRT-06-032)Article8.4TheIterativeMethod.SeetheearthquakerestrainerdesignexampleintheAppendixofthischapter.RestrainersshallbedetailedinaccordancewiththerequirementsofGuideSpecificationsArticle4.13.3andSection4.4.5.RestrainersmaybeomittedforSDCsCandDwheretheavailableseatwidthexceedsthecalculatedsupportlengthspecifiedinEquationC4.13.1-1.

OmittingrestrainersforliquefiablesitesshallbeapprovedbytheWSDOTBridgeDesignEngineer.

Longitudinalrestrainersshallnotbeusedattheendpiers(abutments).

4.2.11 AbutmentsGuide Specifications Article 5.2–DiaphragmAbutmenttypeshowninFigure5.2.3.2-1shallnotbeusedforWSDOTbridges.

Guide Specifications Article 5.2–Abutmentstoberevisedasfollows:

5.2.1 - General

Theparticipationofabutmentwallsinprovidingresistancetoseismicallyinducedinertialloadsmaybeconsideredintheseismicdesignofbridgeseithertoreducecolumnsizesorreducetheductilitydemandonthecolumns.Damagetobackwallsandwingwallsduringearthquakesmaybeconsideredacceptablewhenconsideringno



collapsecriteria,providedthatunseatingorotherdamagetothesuperstructuredoesnotoccur.Abutmentparticipationintheoveralldynamicresponseofthebridgesystemshallreflectthestructuralconfiguration,theloadtransfermechanismfromthebridgetotheabutmentsystem,theeffectivestiffnessandforcecapacityofthewall-soilsystem,andthelevelofacceptableabutmentdamage.Thecapacityoftheabutmentstoresistthebridgeinertialloadsshallbecompatiblewiththesoilresistancethatcanbereliablymobilized,thestructuraldesignoftheabutmentwall,andwhetherthewallispermittedtobedamagedbythedesignearthquake.Thelateralloadcapacityofwallsshallbeevaluatedonthebasisofarationalpassiveearth-pressuretheory.

TheparticipationofthebridgeapproachslabintheoveralldynamicresponseofbridgesystemstoearthquakeloadingandinprovidingresistancetoseismicallyinducedinertialloadsmaybeconsideredpermissibleuponapprovalfromboththeWSDOTBridgeDesignEngineerandtheWSDOTGeotechnicalEngineer.

TheparticipationoftheabutmentintheERSshouldbecarefullyevaluatedwiththeGeotechnicalEngineerandtheOwnerwhenthepresenceoftheabutmentbackfillmaybeuncertain,asinthecaseofslumpingorsettlementduetoliquefactionbeloworneartheabutment.

5.2.2 - Longitudinal Direction

Underearthquakeloading,theearthpressureactiononabutmentwallschangesfromastaticconditiontooneoftwopossibleconditions:• Thedynamicactivepressureconditionasthewallmovesawayfromthebackfill,or• Thepassivepressureconditionastheinertialloadofthebridgepushesthewallintothebackfill.

Thegoverningearthpressureconditiondependsonthemagnitudeofseismicallyinducedmovementoftheabutmentwalls,thebridgesuperstructure,andthebridge/abutmentconfiguration.

Forsemi-integral(Figure5.2.2-a),L-shapeabutmentwithbackwallfuse

(Figure5.2.2-b),orwithoutbackwallfuse(Figure5.2.2-c),forwhichtheexpansionjointissufficientlylargetoaccommodateboththecyclicmovementbetweentheabutmentwallandthebridgesuperstructure(i.e.,superstructuredoesnotpushagainstabutmentwall),theseismicallyinducedearthpressureontheabutmentwallshallbeconsideredtobethedynamicactivepressurecondition.However,whenthegapattheexpansionjointisnotsufficienttoaccommodatethecyclicwall/bridgeseismicmovements,atransferofforceswilloccurfromthesuperstructuretotheabutmentwall.Asaresult,theactiveearthpressureconditionwillnotbevalidandtheearthpressureapproachesamuchlargerpassivepressureloadconditionbehindthebackwall.Thislargerloadconditionisthemaincauseforabutmentdamage,asdemonstratedinpastearthquakes.Forsemi-integralorL-shapeabutments,theabutmentstiffnessandcapacityunderpassivepressureloadingareprimarydesignconcerns.




4.2.11 Abutments

(a)Semi-integralAbutment (b)L-shapeAbutmentBackwallFuses

(c)L-shapeAbutmentBackwallDoesNotFuse

Figure5.2.2- AbutmentStiffnessandPassivePressure EstimateBDM Figure 4.2.11-1

Wherethepassivepressureresistanceofsoilsbehindsemi-integralorL-shapeabut-mentswillbemobilizedthroughlargelongitudinalsuperstructuredisplacements,thebridgemaybedesignedwiththeabutmentsaskeyelementsofthelongitudinalERS.Abutmentsshallbedesignedtosustainthedesignearthquakedisplacements.Whenabutmentstiffnessandcapacityareincludedinthedesign,itshouldberecognizedthatthepassivepressurezonemobilizedbyabutmentdisplacementextendsbeyondtheactivepressurezonenormallyusedforstaticserviceloaddesign.Thisisillustrat-edschematicallyinFigures1aand1b. Dynamicactiveearthpressureactingontheabutmentneednotbeconsideredinthedynamicanalysisofthebridge. Thepassiveabutmentresistanceshallbelimitedto70%ofthevalueobtainedusingtheproceduregiveninArticle5.2.2.1.

5.2.2.1 - Abutment Stiffness and Passive Pressure Estimate

Abutmentstiffness,Keff inkip/ft,andpassivecapacity,Pp inkips,shouldbecharac-terizedbyabilinearorotherhigherordernonlinearrelationshipasshowninFigure5.2.2.1.Whenthemotionofthebackwallisprimarilytranslation,passivepressuresmaybeassumeduniformlydistributedovertheheight(Hw)ofthebackwallorenddiaphragm.Thetotalpassiveforcemaybedeterminedas:

Pp = pp Hw Ww (5.2.2.1-1)

where:


4.2.11 Abutments







Pp = pp Hw Ww (5.2.2.1-1)

where:


4.2.11 Abutments







Pp = pp Hw Ww (5.2.2.1-1)

where:

(a) Semi-integral Abutment (b) L-shape Abutment Backwall Fuses

(c) L-shape Abutment Backwall Does Not Fuse

Figure5.2.2-AbutmentStiffnessandPassivePressureEstimateFigure 4.2.11-1

Wherethepassivepressureresistanceofsoilsbehindsemi-integralorL-shapeabutmentswillbemobilizedthroughlargelongitudinalsuperstructuredisplacements,thebridgemaybedesignedwiththeabutmentsaskeyelementsofthelongitudinalERS.Abutmentsshallbedesignedtosustainthedesignearthquakedisplacements.Whenabutmentstiffnessandcapacityareincludedinthedesign,itshouldberecognizedthatthepassivepressurezonemobilizedbyabutmentdisplacementextendsbeyondtheactivepressurezonenormallyusedforstaticserviceloaddesign.ThisisillustratedschematicallyinFigures4.2.11-1aand4.2.11-1b.Dynamicactiveearthpressureactingontheabutmentneednotbeconsideredinthedynamicanalysisofthebridge.Thepassiveabutmentresistanceshallbelimitedto70percentofthevalueobtainedusingtheproceduregiveninArticle5.2.2.1.


Abutmentstiffness,Keffinkip/ft,andpassivecapacity,Ppinkips,shouldbecharacterizedbyabilinearorotherhigherordernonlinearrelationshipasshowninFigure5.2.2.1.Whenthemotionofthebackwallisprimarilytranslation,passivepressuresmaybeassumeduniformlydistributedovertheheight(Hw)ofthebackwallorenddiaphragm.Thetotalpassiveforcemaybedeterminedas:

Pp = pp Hw Ww (5 .2 .2 .1-1)

Where: pp = passive lateral earth pressure behind backwall or diaphragm (ksf) Hw = height of back wall or end diaphragm exposed to passive earth pressure (feet) Ww = width of back wall or diaphragm (feet)

Pp = pp Hw Ww (5.2.2.1-1)

where:

pp =passivelateralearthpressurebehindbackwallordiaphragm(ksf)

Hw =heightofbackwallorenddiaphragmexposedtopassiveearthpressure(ft)

Ww =widthofbackwallordiaphragm(ft)

(a) Semi-integralAbutment (b): L-shapeAbutment

Figure5.2.2.1- CharacterizationofAbutmentCapacityandStiffnessBDM Figure 4.2.11-2

5.2.2.2- Calculation of Best Estimate Passive Pressure Pp

Ifthestrengthcharacteristicsofcompactedornaturalsoilsinthe"passivepressurezone"areknown,thenthepassiveforceforagivenheight,Hw, maybecalculatedus-ingacceptedanalysisprocedures.Theseproceduresshouldaccountfortheinterfacefrictionbetweenthewallandthesoil.Thepropertiesusedshallbethoseindicativeoftheentire"passivepressurezone"asindicatedinFigure1. Therefore,thepropertiesofbackfillpresentimmediatelyadjacenttothewallintheactivepressurezone maynotbeappropriateasaweakerfailuresurfacecandevelopelsewhereintheembank-ment.

ForL-shapeabutmentswherethebackwallisnotdesignedtofuse,Hw

shallconservativelybetakenasthedepthofthesuperstructure,unlessamorerationalsoil-structureinteractionanalysisisperformed.

Ifpresumptivepassivepressuresaretobeusedfordesign,thenthefollowingcriteriashallapply:

Pp = pp Hw Ww (5.2.2.1-1)

where:

pp =passivelateralearthpressurebehindbackwallordiaphragm(ksf)

Hw =heightofbackwallorenddiaphragmexposedtopassiveearthpressure(ft)

Ww =widthofbackwallordiaphragm(ft)

(a) Semi-integralAbutment (b): L-shapeAbutment

Figure5.2.2.1- CharacterizationofAbutmentCapacityandStiffnessBDM Figure 4.2.11-2

5.2.2.2- Calculation of Best Estimate Passive Pressure Pp

Ifthestrengthcharacteristicsofcompactedornaturalsoilsinthe"passivepressurezone"areknown,thenthepassiveforceforagivenheight,Hw, maybecalculatedus-ingacceptedanalysisprocedures.Theseproceduresshouldaccountfortheinterfacefrictionbetweenthewallandthesoil.Thepropertiesusedshallbethoseindicativeoftheentire"passivepressurezone"asindicatedinFigure1. Therefore,thepropertiesofbackfillpresentimmediatelyadjacenttothewallintheactivepressurezone maynotbeappropriateasaweakerfailuresurfacecandevelopelsewhereintheembank-ment.

ForL-shapeabutmentswherethebackwallisnotdesignedtofuse,Hw

shallconservativelybetakenasthedepthofthesuperstructure,unlessamorerationalsoil-structureinteractionanalysisisperformed.

Ifpresumptivepassivepressuresaretobeusedfordesign,thenthefollowingcriteriashallapply:

(a) Semi-integral Abutment (b) L-shape AbutmentFigure5.2.2.1-CharacterizationofAbutmentCapacityandStiffness

Figure 4.2.11-2



5.2.2.2 - Calculation of Best Estimate Passive Pressure Pp

Ifthestrengthcharacteristicsofcompactedornaturalsoilsinthe"passivepressurezone"areknown,thenthepassiveforceforagivenheight,Hw,maybecalculatedusingacceptedanalysisprocedures.Theseproceduresshouldaccountfortheinterfacefrictionbetweenthewallandthesoil.Thepropertiesusedshallbethoseindicativeoftheentire"passivepressurezone"asindicatedinFigure1.Therefore,thepropertiesofbackfillpresentimmediatelyadjacenttothewallintheactivepressurezonemaynotbeappropriateasaweakerfailuresurfacecandevelopelsewhereintheembankment.

ForL-shapeabutmentswherethebackwallisnotdesignedtofuse,Hwshallconservativelybetakenasthedepthofthesuperstructure,unlessamorerationalsoil-structureinteractionanalysisisperformed.

Ifpresumptivepassivepressuresaretobeusedfordesign,thenthefollowingcriteriashallapply:• Soilinthe"passivepressurezone"shallbecompactedinaccordancewithStandard

SpecificationsSection2-03.3(14)I,whichrequirescompactionto95percentmaximumdensityforall“BridgeApproachEmbankments”.

• Forcohesionless,nonplasticbackfill(finescontentlessthan30percent),thepassivepressureppmaybeassumedequalto2Hw/3ksfperfootofwalllength.

Forothercases,includingabutmentsconstructedincuts,thepassivepressuresshallbedevelopedbyageotechnicalengineer.

5.2.2.3 - Calculation of Passive Soil Stiffness

Equivalentlinearsecantstiffness,Keffinkip/ft,isrequiredforanalyses.Forsemi-integralorL-shapeabutmentsinitialsecantstiffnessmaybedeterminedasfollows:

5.2.2.3- Calculation of Passive Soil Stiffness

Equivalentlinearsecantstiffness,Keff inkip/ft,isrequiredforanalyses.Forsemi-integralorL-shapeabutmentsinitialsecantstiffnessmaybedeterminedasfol-lows:

( )ww

peff HF

PK =1 (5.2.2.3-1)

where:

Pp =passivelateralearthpressurecapacity(kip)

Hw =heightofbackwall(ft)

Fw = thevalueofFw touseforaparticularbridgemaybefoundinTableC3.11.1-1oftheAASHTO LRFD Bridge Design Specifications.

ForL-shapeabutments,theexpansiongapshouldbeincludedintheinitialestimateofthesecantstiffnessasspecifiedin:

( )gww

peff DHF

PK

+=1 (5.2.2.3-2)

where:

Dg =widthofgapbetweenbackwallandsuperstructure(ft)

ForSDCsCandD,wherepushoveranalysesareconducted,valuesofPp andtheini-tialestimateofKeff1 shouldbeusedtodefineabilinearload-displacementbehavioroftheabutmentforthecapacityassessment.

5.2.2.4-Modeling Passive Pressure Stiffness in the Longitudinal Direction

Inthelongitudinaldirection,whenthebridgeismovingtowardthesoil, thefullpas-siveresistanceofthesoilmaybemobilized,butwhenthebridgemovesawayfromthesoilnosoilresistanceismobilized. Sincepassivepressureactsatonlyoneabutmentatatime,linearelasticdynamicmodelsandframepushovermodelsshouldonlyincludeapassivepressurespringatoneabutmentinanygivenmodel.Secantstiffnessvaluesforpassivepressureshallbedevelopedindependentlyforeachabut-ment.

(5 .2 .2 .3-1)

Where: Pp = passive lateral earth pressure capacity (kip) Hw = height of back wall (feet) Fw = the value of Fw to use for a particular bridge may be found in Table C3 .11 .1-1 of the AASHTO LRFD .


5.2.2.3- Calculation of Passive Soil Stiffness

Equivalentlinearsecantstiffness,Keff inkip/ft,isrequiredforanalyses.Forsemi-integralorL-shapeabutmentsinitialsecantstiffnessmaybedeterminedasfol-lows:

( )ww

peff HF

PK =1 (5.2.2.3-1)

where:

Pp =passivelateralearthpressurecapacity(kip)

Hw =heightofbackwall(ft)

Fw = thevalueofFw touseforaparticularbridgemaybefoundinTableC3.11.1-1oftheAASHTO LRFD Bridge Design Specifications.


( )gww

peff DHF

PK

+=1 (5.2.2.3-2)

where:

Dg =widthofgapbetweenbackwallandsuperstructure(ft)

ForSDCsCandD,wherepushoveranalysesareconducted,valuesofPp andtheini-tialestimateofKeff1 shouldbeusedtodefineabilinearload-displacementbehavioroftheabutmentforthecapacityassessment.

5.2.2.4-Modeling Passive Pressure Stiffness in the Longitudinal Direction

Inthelongitudinaldirection,whenthebridgeismovingtowardthesoil, thefullpas-siveresistanceofthesoilmaybemobilized,butwhenthebridgemovesawayfromthesoilnosoilresistanceismobilized. Sincepassivepressureactsatonlyoneabutmentatatime,linearelasticdynamicmodelsandframepushovermodelsshouldonlyincludeapassivepressurespringatoneabutmentinanygivenmodel.Secantstiffnessvaluesforpassivepressureshallbedevelopedindependentlyforeachabut-ment.

(5 .2 .2 .3-2)

Where: Dg = width of gap between backwall and superstructure (feet)

ForSDCsCandD,wherepushoveranalysesareconducted,valuesofPpandtheinitialestimateofKeff1shouldbeusedtodefineabilinearload-displacementbehavioroftheabutmentforthecapacityassessment.

http://www.wsdot.wa.gov/Publications/Manuals/M41-10.htm




5.2.2.4 - Modeling Passive Pressure Stiffness in the Longitudinal Direction

Inthelongitudinaldirection,whenthebridgeismovingtowardthesoil,thefullpassiveresistanceofthesoilmaybemobilized,butwhenthebridgemovesawayfromthesoilnosoilresistanceismobilized.Sincepassivepressureactsatonlyoneabutmentatatime,linearelasticdynamicmodelsandframepushovermodelsshouldonlyincludeapassivepressurespringatoneabutmentinanygivenmodel.Secantstiffnessvaluesforpassivepressureshallbedevelopedindependentlyforeachabutment.

Asanalternative,forstraightorwithhorizontalcurvesupto30degreessingleframebridges,andcompressionmodelsinstraightmulti-framebridgeswherethe

passivepressurestiffnessissimilarbetweenabutments,aspringmaybeusedateachabutmentconcurrently.Inthiscase,theassignedspringvaluesateachendneedto

bereducedbyhalfbecausetheyactinsimultaneously,whereastheactualbackfillpassiveresistanceactsonlyinonedirectionandatonetime.Correspondingly,theactualpeakpassiveresistanceforceateitherabutmentwillbeequaltothesumofthepeakforcesdevelopedintwosprings.Inthiscase,secantstiffnessvaluesforpassivepressureshallbedevelopedbasedonthesumofpeakforcesdevelopedineachspring.Ifcomputedabutmentforcesexceedthesoilcapacity,thestiffnessshouldbesoftenediterativelyuntilabutmentdisplacementsareconsistent(within30percent)withtheassumedstiffness.

5.2.3 - Transverse Direction

TransversestiffnessofabutmentsmaybeconsideredintheoveralldynamicresponseofbridgesystemsonacasebycasebasisuponBridgeDesignEngineerapproval.

Uponapproval,thetransverseabutmentstiffnessusedintheelasticdemandmodelsmaybetakenas50percentoftheelastictransversestiffnessoftheadjacentbent.

Girderstopsaretypicallydesignedtotransmitthelateralshearforcesgeneratedbysmalltomoderateearthquakesandserviceloadsandareexpectedtofuseatthedesigneventearthquakelevelofaccelerationtolimitthedemandandcontrolthedamageintheabutmentsandsupportingpiles/shafts.Linearelasticanalysiscannotcapturetheinelasticresponseofthegirderstops,wingwallsorpiles/shafts.Therefore,theforcesgeneratedwithelasticdemandassessmentmodelsshouldnotbeusedtosizetheabutmentgirderstops.Girderstopsforabutmentssupportedonaspreadfootingshallbedesignedtosustainthelesseroftheaccelerationcoefficient,As,timesthesuperstructuredeadloadreactionattheabutmentplustheweightofabutmentanditsfootingorslidingfrictionforcesofspreadfootings.Girderstopsforpile/shaftsupportedfoundationsshallbedesignedtosustainthesumof75percenttotallateralcapacityofthepiles/shaftsandshearcapacityofonewingwall.

Theelasticresistancemaybetakentoincludetheuseofbearingsdesignedtoaccommodatethedesigndisplacements,soilfrictionalresistanceactingagainstthebaseofaspreadfootingsupportedabutment,orpileresistanceprovidedbypilesactingintheirelasticrange.

Thestiffnessoffusingorbreakawayabutmentelementssuchaswingwalls(yieldingornon-yielding),elastomericbearings,andslidingfootingsshallnotbereliedupontoreducedisplacementdemandsatintermediatepiers.



Unlessfixedbearingsareused,girderstopsshallbeprovidedbetweenallgirdersregardlessoftheelasticseismicdemand.Thedesignofgirderstopsshouldconsiderthatunequalforcesthatmaydevelopineachstop.

Whenfusinggirderstops,transverseshearkeys,orotherelementsthatpotentiallyreleasetherestraintofthesuperstructureareused,thenadequatesupportlengthmeetingtherequirementsofArticle4.12oftheAASHTOSEISMICmustbeprovided.Additionally,theexpectedredistributionofinternalforcesinthesuperstructureandotherbridgesystemelementmustbeconsidered.Boundinganalysesconsideringincrementalreleaseoftransverserestraintateachendofthebridgeshouldalsobeconsidered.

5.2.4 - Curved and Skewed Bridges

PassiveearthpressureatabutmentsmaybeconsideredasakeyelementoftheERSofstraightandcurvedbridgeswithabutmentskewsupto20degrees.Forlargerskews,duetoacombinationoflongitudinalandtransverseresponse,thespanhasatendencytorotateinthedirectionofdecreasingskew.Suchmotionwilltendtocausebindingintheobtusecornerandgenerateunevenpassiveearthpressureforcesontheabutment,exceedingthepassivepressurenearoneendofthebackwall,andprovidinglittleornoresistanceatotherend.Thisrequiresamorerefinedanalysistodeterminetheamountofexpectedmovement.Thepassivepressureresistanceinsoilsbehindsemi-integralorL-shapeabutmentsshallbebasedontheprojectedwidthoftheabutmentwallnormaltothecenterlineofthebridge.Abutmentspringsshallbeincludedinthelocalcoordinatesystemoftheabutmentwall.

4.2.12 Foundation – GeneralGuide Specifications Article 5.3.1–Therequiredfoundationmodelingmethod(FMM)andtherequirementsforestimationoffoundationspringsforspreadfootings,pilefoundations,anddrilledshaftsshallbebasedontheWSDOTGeotechnicalEngineer’srecommendations.

4.2.13 Foundation – Spread FootingGuide Specifications Article C5.3.2 –FoundationspringsforspreadfootingsshallbedeterminedinaccordancewithSection7.2.7,Geotechnical Design Manual Section6.5.1.1andtheWSDOTGeotechnicalEngineer’srecommendations.

4.2.14 Procedure 3: Nonlinear Time History MethodGuide Specifications Article 5.4.4–ThetimehistoriesofinputaccelerationusedtodescribetheearthquakeloadsshallbeselectedinconsultationwiththeWSDOTGeotechnicalEngineerandtheWSDOTBridgeDesignEngineer.

4.2.15 Ieff for Box Girder SuperstructureGuide Specifications Article 5.6.3–Grossmomentofinertiashallbeusedforboxgirdersuperstructuremodeling.

4.2.16 Foundation RockingGuide Specifications Article 6.3.9–FoundationrockingshallnotbeusedforthedesignofWSDOTbridges.




4.2.17 Drilled ShaftsGuide Specifications Article C6.5–ForWSDOTbridges,thescalefactorforp-ycurvesorsubgrademodulusforlargediametershaftsshallnotbeusedunlessapprovedbytheWSDOTGeotechnicalEngineerandWSDOTBridgeDesignEngineer.

4.2.18 Longitudinal Direction RequirementsGuide Specifications Article 6.7.1 – Case2:EarthquakeResistingSystem(ERS)withabutmentcontributionmaybeusedprovidedthatthemobilizedlongitudinalpassivepressureisnotgreaterthan70percentofthevalueobtainedusingproceduregiveninArticle5.2.2.1.

4.2.19 Liquefaction Design RequirementsGuide Specifications Article 6.8–SoilliquefactionassessmentshallbebasedontheWSDOTGeotechnicalEngineer’srecommendationandGeotechnical Design Manual Section6.4.2.8.

4.2.20 Reinforcing SteelGuide Specifications Article 8.4.1–Reinforcingbars,deformedwire,cold-drawwire,weldedplainwirefabricandweldeddeformedwirefabricshallconformtothematerialstandardsasspecifiedinAASHTOLRFD.

ASTMA615reinforcementshallnotbeusedinWSDOTBridges.OnlyASTMA706Grade60reinforcingsteelshallbeusedinmemberswhereplastichingingisexpectedforSDCsB,C,andD.ASTMA706Grade80reinforcingsteelsmaybeusedforcapacity-protectedmembersasspecifiedinArticle8.9.ASTMA706Grade80reinforcingsteelshallnotbeusedforoversizedshaftswhereingroundplastichingingisconsideredasapartofERS.

DeformedweldedwirefabricmaybeusedwiththeWSDOTBridgeDesignEngineer’sapproval.

Wireropeorstrandsforspiralsandhighstrengthbarswithyieldstrengthinexcessof75ksishallnotbeused.

Guide Specifications Article C8.4.1–AddthefollowingparagraphtoArticleC8.4.1.

TherequirementforplastichingingandcapacityprotectedmembersdonotapplytothestructuresinSDCA,thereforeuseofASTMA706Grade80reinforcingsteelispermittedinSDCA.

ForSDCsB,C,andD,themoment-curvatureanalysesbasedonstraincompatibilityandnonlinearstressstrainrelationsareusedtodeterminetheplasticmomentcapacitiesofallductileconcretemembers.Furtherresearchisrequiredtoestablishtheshapeandmodelofthestress-straincurve,expectedreinforcingstrengths,strainlimits,andthestress-strainrelationshipsforconcreteconfinedbylateralreinforcementmadewithASTMA706Grade80reinforcingsteel.




4.2.21 Concrete ModelingGuide Specifications Article 8.4.4- Revise the last paragraph as follows:

Wherein-groundplastichingingapprovedbytheWSDOTBridgeDesignEngineerispartoftheERS,theconfinedconcretecoreshallbelimitedtoamaximumcompressivestrainof0.008.Theclearspacingbetweenthelongitudinalreinforcementsandbetweenspiralsandhoopsindrilledshaftsshallnotbelessthan6inchesormorethan8incheswhentremieplacementofconcreteisanticipated.

4.2.22 Expected Nominal Moment CapacityGuide Specifications Article 8.5–Addthefollowingparagraphsafterthirdparagraph.

TheexpectednominalcapacityofcapacityprotectedmemberusingASTMA706Grade80reinforcementshallbedeterminedbystrengthdesignbasedontheexpectedconcretestrengthandyieldstrengthof80ksiwhentheconcretereaches0.003orthereinforcingsteelstrainreaches0.090for#10barsandsmaller,0.060for#11barsandlarger.

Replacethedefinitionof

4.2.18 Longitudinal Direction Requirements

4.2.19 Liquefaction Design Requirements

Guide Specifications Article 6.8 – SoilliquefactionassessmentshallbebasedontheWSDOTGeotechnicalEngineer’srecommendationandWSDOTGeotechnical Design Manual Section6.4.2.8.

4.2.20 Reinforcing Steel

4.2.21 Concrete Modeling

4.2.22 Expected Nominal Moment Capacity

Guide Specifications Article 8.5 – Addthefollowingparagraphsafterthethirdparagraph.

Theexpectednominalcapacityofcapacityprotectedmembers usingASTMA706Grade80reinforcementshallbedeterminedby strengthdesignformulasspecifiedintheAASHTO LRFD Bridge design Specifications basedontheexpectedconcretestrengthandreinforcingsteelyieldstrengthswhentheconcretereaches 0.003orthereinforcingsteelstrainreaches0.090for#10barsandsmaller,0.060for#11barsandlarger.

Replacethedefinitionof moλ withthefollowing:

moλ =overstrengthfactor

=1.2forASTMA706Grade60reinforcement=1.4forASTMA615Grade60reinforcement

4.2.23 Interlocking Bar Size

Guide Specifications Article 8.6.7 – Thelongitudinalreinforcingbarinsidetheinterlockingportionofa column(interlockingbars)shallbethesamesizeofbarsusedoutsidetheinterlockingportion.

4.2.24 Splicing of Longitudinal Reinforcement in Columns Subject to Ductility Demands for SDCs C and D

Guide Specifications Article 8.8.3 – Thesplicingoflongitudinalcolumnreinforcementoutsidetheplastichingingregionshallbeaccomplishedusingmechanicalcouplersthatarecapableofdevelopingthetensilestrengthof thesplicedbar.Splicesshallbestaggeredatleast2ft.Lapsplicesshallnotbeused.Thedesignengineershallclearlyidentifythelocationswheresplicesinlongitudinalcolumnreinforcementarepermittedontheplans.Ingeneralwherethelengthoftherebarcageislessthan60ft(72ftforNo.14andNo.18bars),nospliceinthelongitudinalreinforcementshallbeallowed.

4.2.25 Development Length for Column Bars Extended into Oversized Pile

withthefollowing:

4.2.18 Longitudinal Direction Requirements

4.2.19 Liquefaction Design Requirements

Guide Specifications Article 6.8 – SoilliquefactionassessmentshallbebasedontheWSDOTGeotechnicalEngineer’srecommendationandWSDOTGeotechnical Design Manual Section6.4.2.8.

4.2.20 Reinforcing Steel

4.2.21 Concrete Modeling

4.2.22 Expected Nominal Moment Capacity

Guide Specifications Article 8.5 – Addthefollowingparagraphsafterthethirdparagraph.

Theexpectednominalcapacityofcapacityprotectedmembers usingASTMA706Grade80reinforcementshallbedeterminedby strengthdesignformulasspecifiedintheAASHTO LRFD Bridge design Specifications basedontheexpectedconcretestrengthandreinforcingsteelyieldstrengthswhentheconcretereaches 0.003orthereinforcingsteelstrainreaches0.090for#10barsandsmaller,0.060for#11barsandlarger.

Replacethedefinitionof moλ withthefollowing:

moλ =overstrengthfactor

=1.2forASTMA706Grade60reinforcement=1.4forASTMA615Grade60reinforcement

4.2.23 Interlocking Bar Size

Guide Specifications Article 8.6.7 – Thelongitudinalreinforcingbarinsidetheinterlockingportionofa column(interlockingbars)shallbethesamesizeofbarsusedoutsidetheinterlockingportion.


Guide Specifications Article 8.8.3 – Thesplicingoflongitudinalcolumnreinforcementoutsidetheplastichingingregionshallbeaccomplishedusingmechanicalcouplersthatarecapableofdevelopingthetensilestrengthof thesplicedbar.Splicesshallbestaggeredatleast2ft.Lapsplicesshallnotbeused.Thedesignengineershallclearlyidentifythelocationswheresplicesinlongitudinalcolumnreinforcementarepermittedontheplans.Ingeneralwherethelengthoftherebarcageislessthan60ft(72ftforNo.14andNo.18bars),nospliceinthelongitudinalreinforcementshallbeallowed.

4.2.25 Development Length for Column Bars Extended into Oversized Pile

= overstrengthfactor = 1.2forASTMA706Grade60reinforcement = 1.4forASTMA615Grade60reinforcement

4.2.23 Interlocking Bar SizeGuide Specifications Article 8.6.7–Thelongitudinalreinforcingbarinsidetheinterlockingportionofcolumn(interlockingbars)shallbethesamesizeofbarsusedoutsidetheinterlockingportion.


Guide Specifications Article 8.8.3–Thesplicingoflongitudinalcolumnreinforcementoutsidetheplastichingingregionshallbeaccomplishedusingmechanicalcouplersthatarecapableofdevelopingthetensilestrengthofthesplicedbar.Splicesshallbestaggeredatleast2feet.Lapsplicesshallnotbeused.Thedesignengineershallclearlyidentifythelocationswheresplicesinlongitudinalcolumnreinforcementarepermittedontheplans.Ingeneralwherethelengthoftherebarcageislessthan60ft(72ftforNo.14andNo.18bars),nospliceinthelongitudinalreinforcementshallbeallowed.

4.2.25 Development Length for Column Bars Extended into Oversized Pile Shafts f or SDCs C and D

Guide Specifications Article 8.8.10–ExtendingcolumnbarsintooversizedshaftshallbeperSection7.4.4.C,basedonTRACReportWA-RD417.1“Non-ContactLapSpliceinBridgeColumn-ShaftConnections.”

http://www.wsdot.wa.gov/Research/Reports/400/417.1.htm




4.2.26 Lateral Confinement for Oversized Pile Shaft for SDCs C and D Guide Specifications Article 8.8.12–Therequirementofthisarticleforshaftlateralreinforcementinthecolumn-shaftsplicezonemaybereplacedwithSection7.8.2K.

4.2.27 Lateral Confinement for Non-Oversized Strengthened Pile Shaft for SDCs C and D

Guide Specifications Article 8.8.13–Nonoversizedcolumnshaft(thecrosssectionoftheconfinedcoreisthesameforboththecolumnandthepileshaft)isnotpermissibleunlessapprovedbytheWSDOTBridgeDesignEngineer.

4.2.28 Requirements for Capacity Protected MembersGuide Specifications Article 8.9–Addthefollowingparagraphs:

ForSDCsCandDwhereliquefactionisidentified,withtheWSDOTBridgeDesignEngineer’sapproval,pileanddrilledshaftin-groundhingingmaybeconsideredasanERE.Wherein-groundhingingispartofERS,theconfinedconcretecoreshouldbelimitedtoamaximumcompressivestrainof0.008andthememberductilitydemandshallbelimitedto4.

Bridgesshallbeanalyzedanddesignedforthenon-liquefiedconditionandtheliquefiedconditioninaccordancewithArticle6.8.ThecapacityprotectedmembersshallbedesignedinaccordancewiththerequirementsofArticle4.11.Toensuretheformationofplastichingesincolumns,oversizedpileshaftsshallbedesignedforanexpectednominalmomentcapacity,Mne,atanylocationalongtheshaft,thatis,equalto1.25timesmomentdemandgeneratedbytheoverstrengthcolumnplastichingemomentandassociatedshearforceatthebaseofthecolumn.Thesafetyfactorof1.25maybereducedto1.0dependingonthesoilpropertiesandupontheWSDOTBridgeDesignEngineer’sapproval.

Thedesignmomentsbelowgroundforextendedpileshaftmaybedeterminedusingthenonlinearstaticprocedure(pushoveranalysis)bypushingthemlaterallytothedisplacementdemandobtainedfromanelasticresponsespectrumanalysis.Thepointofmaximummomentshallbeidentifiedbasedonthemomentdiagram.Theexpectedplastichingezoneshallextend3Daboveandbelowthepointofmaximummoment.Theplastichingezoneshallbedesignatedasthe“nosplice”zoneandthetransversesteelforshearandconfinementshallbeprovidedaccordingly.

4.2.29 Superstructure Capacity Design for Transverse Direction (Integral Bent Cap) for SDCs C and D

Guide Specifications Article 8.11–Revisethelastparagraphasfollows:

ForSDCsCandD,thelongitudinalflexuralbentcapbeamreinforcementshallbecontinuous.Splicingofcapbeamlongitudinalflexuralreinforcementshallbeaccomplishedusingmechanicalcouplersthatarecapableofdevelopingaminimumtensilestrengthof85ksi.Splicesshallbestaggeredatleast2feet.Lapsplicesshallnotbeused.



4.2.30 Superstructure Design for Non Integral Bent Caps for SDCs B, C, and DGuide Specifications Article 8.12–NonintegralbentcapsshallnotbeusedforcontinuousconcretebridgesinSDCB,C,andDexceptattheexpansionjointsbetweensuperstructuresegments.

4.2.31 Joint ProportioningGuide Specifications Article 8.13.4.1.1 –Revisethelastbulletasfollows:

Exteriorcolumnjointsforboxgirdersuperstructureandothersuperstructuresifthecapbeamextendsthejointfarenoughtodevelopthelongitudinalcapreinforcement.

4.2.32 Cast-in-Place and Precast Concrete PilesGuide Specifications Article 8.16.2–Minimumlongitudinalreinforcementof0.75percentofAgshallbeprovidedforCIPpilesinSDCsB,C,andD.LongitudinalreinforcementshallbeprovidedforthefulllengthofpileunlessapprovedbytheWSDOTBridgeDesignEngineer.



4.3 SeismicDesignRequirementsforBridgeModificationsandWideningProjects

4.3.1 GeneralAbridgewideningisdefinedaswheresubstructurebentsaremodifiedandnewcolumnsorpiersareadded,oranincreaseofbridgedeckwidthorwideningstothesidewalkorbarrierrailsofanexistingbridgeresultinginsignificantmassincreaseorstructuralchanges.

BridgewideningsinWashingtonStateshallbedesignedinaccordancewiththerequirementsofthecurrenteditionoftheAASHTOLRFD.TheseismicdesignshallbeinaccordancewiththerequirementsoftheAASHTOSEISMIC,andWSDOTBDM. ThespectralresponseparametersshallbedeterminedusingUSGS2014SeismicHazardMapsandSiteCoefficientsdefinedinSection4.2.3. Thewideningportion(newstructure)shallbedesignedtomeetcurrentWSDOTstandardsfornewbridges.Seismicanalysisisnotrequiredforsingle-spanbridgesandbridgesinSDCA.However,existingelementsofsinglespanbridgesshallmeettherequirementsofAASHTOSeismicasapplicable.

4.3.2 Bridge Widening Project ClassificationBridgewideningprojectsareclassifiedaccordingtothescopeofworkaseitherminorormajorwideningprojects.

A. Minor Modification and Widening Projects

Abridgewideningprojectisclassifiedasaminorwideningprojectifallofthefollowingconditionsaremet:• Substructurebentsarenotmodifiedandnonewcolumnsorpiersareadded,whileabutmentsmaybewidenedtoaccommodatetheincreaseofbridgedeckwidth.

• Thenetsuperstructuremassincreaseisequalorlessthan10percentoftheoriginalsuperstructuremass.

• Fixityconditionsofthefoundationsareunchanged.• Therearenomajorchangesoftheseismicityofthebridgesitethatcanincreaseseismichazardlevelsorreduceseismicperformanceofthestructuresincetheinitialscreeningormostrecentseismicretrofit.

• Nochangeinliveloaduseofthebridge

B. Major Modifications and Widening Projects

Abridgewideningprojectisclassifiedasamajorwideningprojectifanyofthefollowingconditionsaremet:• Substructurebentsaremodifiedandnewcolumnsorpiersareadded,exceptingabutments,whichmaybewidenedtoaccommodatetheincreaseofbridgedeckwidth.

• Thenetsuperstructuremassincreaseismorethan20percentoftheoriginalsuperstructuremass.



• Fixityconditionsofthefoundationsarechanged.• Therearemajorchangesoftheseismicityofthebridgesitethatcanincreaseseismichazardlevelsorreduceseismicperformanceofthestructuresincetheinitialscreeningormostrecentseismicretrofit.

• Changeinliveloaduseofthebridge

Majorchangesinseismicityinclude,butarenotlimitedto,thefollowing:nearfaulteffect,significantliquefactionpotential,orlateralspreading.IfthereareconcernsaboutchangestotheSeismicDesignResponseSpectrumatthebridgesite,aboutapreviousretrofittotheexistingbridge,oranunusualimbalanceofmassdistributionresultingfromthestructurewidening,thedesignershouldconsulttheWSDOTBridgeandStructuresOffice.

4.3.3 Seismic Design Guidance:TheSeismicDesignguidanceforBridgeModificationsandWideningareasfollows:

1. BridgewideningprojectsclassifiedasMinorWideningprojectsdonotrequireeitheraseismicevaluationoraretrofitofthestructure.IftheconditionsforMinorWideningprojectaremet,itisanticipatedthatthewidened/modifiedstructurewillnotdrawenoughadditionalseismicdemandtosignificantlyaffecttheexistingsub-structureelements.

2. Ifthenetsuperstructuremassincreaseisbetween10percentto20percentoftheoriginalsuperstructuremass,andifalltheotherbulletedcriterialistedforMinorWideningprojectsaremet,thenthe“DoNoHarm”policyandprofessionaljudgmentcouldbeuseduponapprovaloftheBridgeDesignEngineer.The"DoNoHarm"policyrequiresthedesignertocomparetheC/Dratiosoftheexistingbridgeelementsinthebeforewideningconditiontothoseoftheafterwideningcondition.IftheC/Dratiosarenotdecreased,thewideningcanbedesignedandconstructedwithoutretrofittingexistingdeficientbridgeelements.ElementsoftheexistingstructurewithC/Dratiosmadeworsebythewidening/modificationworkshallberetrofittedtorestoretheirC/Dratiostobefore-wideningvalues,ataminimum.Foundationelementswithseismicdeficiencies(C/Dratiosmadeworsebythewidening/modificationwork)shallbedeferredtotheSeismicRetrofitProgramforrehabilitation.

3. SeismicanalysisisrequiredforallMajorModificationsandWideningprojectsatprojectscopinglevel.AcompleteseismicanalysisisrequiredforbridgesinSeismicDesignCategory(SDC)B,C,andDformajormodificationsandwideningprojectsasdescribedbelow.Aprojectgeotechnicalreport(includinganyunstablesoilorliquefactionissues)shallbeavailabletothestructuralengineerforseismicanalysis.Seismicanalysisshallbeperformedforbothexistingandwidenedstructures.Capacity/Demand(C/D)ratiosarerequiredforexistingbridgeelementsincludingfoundation.

4. ThewideningportionofthestructureshallbedesignedforliquefiablesoilsconditioninaccordancetotheAASHTOSeismic,andWSDOTBDM,unlesssoilsimprovementisprovidedtoeliminateliquefaction.



5. SeismicimprovementofexistingcolumnsandcrossbeamstoC/D>1.0isrequired.Thecostofseismicimprovementshallbepaidforwithwideningprojectfunding(notfromtheRetrofitProgram).TheseismicretrofitoftheexistingstructureshallconformtotheBDM,whilethenewlywidenedportionsofthebridgeshallcomplywiththeAASHTOSeismic,exceptforbalancedstiffnesscriteria,whichmaybedifficulttomeetduetotheexistingbridgeconfiguration.However,thedesignershouldstriveforthebestbalancedframestiffnessfortheentirewidenedstructurethatisattainableinacosteffectivemanner.MajorWideningProjectsrequirethedesignertodeterminetheseismicC/Dratiosoftheexistingbridgeelementsinthefinalwidenedcondition.IftheC/Dratiosofcolumnsandcrossbeamofexistingstructurearelessthan1.0,theimprovementofseismicallydeficientelementsismandatoryandthewideningprojectshallincludetheimprovementofexistingseismicallydeficientbridgeelementstoC/Dratioofabove1.0aspartofthewideningprojectfunding.TheC/Dratioof1.0isrequiredtopreventthecollapseofthebridgeduringtheseismiceventasrequiredforlifesafety.Seismicimprovementoftheexistingfoundationelements(footings,pilecaps,piles,andshaftstoC/Dratios>1.0)couldbedeferredtotheBridgeSeismicRetrofitProgram.



ModificationsorWidening Alterations SeismicDesignGuidance IllustrationMinorModifications• Deck Rehabilitations• Traffic Barrier

Replacements• sidewalk addition/

rehabilitation • No change in LL use

• Superstructure mass increase is less than 10%

• Fixity conditions are not changed

• Do not Require seismic evaluation

• Do not require retrofit of the structure

MajorModificationsMinor Modifications PLUS• Replacing/adding girder

and slab • Change in LL use

• Superstructure mass increase between 10% to 20% and/or

• Fixity conditions are changed

• Seismic evaluation of the structure is required .

• Do-No-Harm is required for substructure .

• Do-No-Harm is required for foundation .

MajorWidening–Case1Minor Modifications PLUS• Superstructure or Bent

Widening

• Superstructure mass increase is more than > 20% and/or

• Substructure/bents modified and/or

• Fixity conditions are changed


• C/D ratio of equal or greater than 1 .0 is required for substructure .

• Do-No-Harm could be used for Foundation .

MajorWidening–Case2• widening on one side

• Substructure or bents are modified. Columns are added on one side .




MajorWidening–Case3• widening on both sides

• Substructure or bents are modified. Columns are added on both sides .




SeismicDesignCriteriaforBridgeModificationsandWideningFigure 4.3-1



4.3.4 Scoping for Bridge Widening and Liquefaction MitigationTheRegionprojectmanagershouldcontacttheBridgeOfficeforbridgewideningandretainingwallscopingassistancebeforeprojectfundingcommitmentsaremadetothelegislatureandthepublic.TheBridgeOfficewillworkwiththeGeotechnicalOfficetoassessthepotentialforliquefactionorotherseismichazardsthatcouldaffectthecostoftheproposedstructures.TheinitialevaluationdesigntimeandassociatedcostsfortheGeotechnicalandBridgeOfficesshallbeconsideredatthescopingphase.

4.3.5 Design and Detailing ConsiderationsSupport Length–Thesupportlengthatexistingabutments,piers,in-spanhinges,andpavementseatsshallbechecked.Ifthereisaneedforlongitudinalrestrainers,transverserestrainers,oradditionalsupportlengthontheexistingstructure,theyshallbeincludedinthewideningdesign.

Connections Between Existing and New Elements–Connectionsbetweenthenewelementsandexistingelementsshouldbedesignedformaximumover-strengthforces.Whereyieldingisexpectedinthecrossbeamconnectionattheextremeeventlimitstate,thenewstructureshallbedesignedtocarryliveloadsindependentlyattheStrengthIlimitstate.Incaseswherelargedifferentialsettlementand/oraliquefaction-inducedlossofbearingstrengthareexpected,theconnectionsmaybedesignedtodeflectorhingeinordertoisolatethetwopartsofthestructure.Elementssubjecttoinelasticbehaviorshallbedesignedanddetailedtosustaintheexpecteddeformations.

Longitudinaljointsbetweentheexistingandnewstructurearenotpermitted.

Differential Settlement–Thegeotechnicaldesignershouldevaluatethepotentialfordifferentialsettlementbetweentheexistingstructureandwideningstructure.Additionalgeotechnicalmeasuresmayberequiredtolimitdifferentialsettlementstotolerablelevelsforbothstaticandseismicconditions.Thebridgedesignershallevaluate,design,anddetailallelementsofnewandexistingportionsofthewidenedstructureforthedifferentialsettlementwarrantedbytheWSDOTGeotechnicalEngineer.Angulardistortionsbetweenadjacentfoundationsgreaterthan0.008(RAD)insimplespansand0.004(RAD)incontinuousspansshouldnotbepermittedinsettlementcriteria.

Thehorizontaldisplacementofpileandshaftfoundationsshallbeestimatedusingproceduresthatconsidersoil-structureinteraction(seeGeotechnical Design Manual Section8.12.2.3).Horizontalmovementcriteriashouldbeestablishedatthetopofthefoundationbasedonthetoleranceofthestructuretolateralmovementwithconsiderationofthecolumnlengthandstiffness.Toleranceofthesuperstructuretolateralmovementwilldependonbridgeseatwidths,bearingtype(s),structuretype,andloaddistributioneffects.

Foundation Types–Thefoundationtypeofthenewstructureshouldmatchthatoftheexistingstructure.However,adifferenttypeoffoundationmaybeusedforthenewstructureduetogeotechnicalrecommendationsorthelimitedspaceavailablebetweenexistingandnewstructures.Forexample,ashaftfoundationmaybeusedinlieuofspreadfooting.




Existing Strutted Columns–Thehorizontalstrutbetweenexistingcolumnsmayberemoved.Theexistingcolumnsshallthenbeanalyzedwiththenewunbracedlengthandretrofittedifnecessary.

Non Structural Element Stiffness–Medianbarrierandotherpotentiallystiffeningelementsshallbeisolatedfromthecolumnstoavoidanyadditionalstiffnesstothesystem.

DeformationcapacitiesofexistingbridgemembersthatdonotmeetcurrentdetailingstandardsshallbedeterminedusingtheprovisionsofSection7.8oftheRetrofitting Manual for Highway Structures: Part 1 – Bridges,FHWA-HRT-06-032.DeformationcapacitiesofexistingbridgemembersthatmeetcurrentdetailingstandardsshallbedeterminedusingthelatesteditionoftheAASHTOSEISMIC.

JointshearcapacitiesofexistingstructuresshallbecheckedusingCaltrans Bridge Design Aid,14-4JointShearModelingGuidelinesforExistingStructures.

Inlieuofspecificdata,thereinforcementpropertiesprovidedinTable4.3.2-1shouldbeused.

Property Notation BarSizeASTM A706

ASTM A615 Grade 60

ASTM A615 Grade 40*

Specified minimum yield stress (ksi) ƒy No . 3 - No . 18 60 60 40Expected yield stress (ksi) ƒye No . 3 - No . 18 68 68 48Expected tensile strength (ksi) ƒue No . 3 - No . 18 95 95 81Expected yield strain εye No . 3 - No . 18 0 .0023 0 .0023 0 .00166

Onset of strain hardening εsh

No . 3 - No . 8 0 .0150 0 .0150

0 .0193No . 9 0 .0125 0 .0125

No . 10 & No . 11 0 .0115 0 .0115No . 14 0 .0075 0 .0075No . 18 0 .0050 0 .0050

Reduced ultimate tensile strain


Page 4.3-4 WSDOT Bridge Design Manual M 23-50.06 July 2011

• Deformation capacities of existing bridge members that do not meet current detailing standards shall be determined using the provisions of Section 7.8 of the Retrofitting Manual for Highway Structures: Part 1 – Bridges, FHWA-HRT-06-032. Deformation capacities of existing bridge members that meet current detailing standards shall be determined using the latest edition of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.

• Joint shear capacities of existing structures shall be checked using Caltrans Bridge Design Aid, 14-4 Joint Shear Modeling Guidelines for Existing Structures.

• In lieu of specific data, the reinforcement properties provided in Table 4.3.2-1 should be used.

Property Notation Bar Size ASTM A706

ASTM A615 Grade 60

ASTM A615 Grade 40

Specified minimum yield stress (ksi) ƒy #3 - #18 60 60 40

Expected yield stress (ksi) ƒye #3 - #18 68 68 48

Expected tensile strength (ksi) ƒue #3 - #18 95 95 81

Expected yield strain εye #3 - #18 0 .0023 0 .0023 0 .00166

Onset of strain hardening εsh

#3 - #8 0 .0150 0 .0150

0 .0193#9 0 .0125 0 .0125

#10 & #11 0 .0115 0 .0115#14 0 .0075 0 .0075#18 0 .0050 0 .0050

Reduced ultimate tensile strain

BDM Chapter 4 Seismic Design and Retrofit

Bridge Design Manual M23-50-02 Page 31

Property Notation Bar Size ASTMA706

ASTM A615 Grade 60

ASTM A615 Grade 40

Specifiedminimum yield stress (ksi)

yf #3 - #18 60 60 40

Expected yield stress (ksi) yef #3 - #18 68 68 48

Expectedtensile strength (ksi)

uef #3 - #18 95 95 81

Expected yield strain ye #3 - #18 0.0023 0.0023 0.00166

Onset of strain hardening sh

#3 - #8 0.0150 0.0150

0.0193

#9 0.0125 0.0125

#10 & #11 0.0115 0.0115

#14 0.0075 0.0075

#18 0.0050 0.0050 Reducedultimate tensile strain

Rsu

#4 - #10 0.090 0.060 0.090

#11 - #18 0.060 0.040 0.060

Ultimate tensile strain su

#4 - #10 0.120 0.090 0.120

#11 - #18 0.090 0.060 0.090

Table 4.3.2-1 Stress Properties of Reinforcing Steel Bars.

#4 - #10 0 .090 0 .060 0 .090#11 - #18 0 .060 0 .040 0 .060

Ultimate tensile strain εsu

#4 - #10 0 .120 0 .090 0 .120#11 - #18 0 .090 0 .060 0 .090

Stress Properties of Reinforcing Steel BarsTable 4.3.2-1

No . 4 - No . 10 0 .090 0 .060 0 .090No . 11 - No . 18 0 .060 0 .040 0 .060

Ultimate tensile strain εsuNo . 4 - No . 10 0 .120 0 .090 0 .120No . 11 - No . 18 0 .090 0 .060 0 .090

* ASTM A615 Grade 40 is for existing bridges in widening projects .

StressPropertiesofReinforcingSteelBarsTable 4.3.2-1

Isolation Bearings–Isolationbearingsmaybeusedforbridgewideningprojectstoreducetheseismicdemandthroughmodificationofthedynamicpropertiesofthebridge.Thesebearingsareaviablealternativetostrengtheningweakelementsornon-ductilebridgesubstructuremembersoftheexistingbridge.UseofisolationbearingsneedstheapprovalofWSDOTBridgeDesignEngineer.IsolationbearingsshallbedesignedpertherequirementsspecifiedinSection9.3.

https://www.fhwa.dot.gov/publications/research/infrastructure/bridge/06032/06032.pdf


http://www.dot.ca.gov/hq/esc/techpubs/manual/bridgemanuals/bridge-design-aids/page/bda-sec14-4.pdf

http://www.dot.ca.gov/hq/esc/techpubs/manual/bridgemanuals/bridge-design-aids/page/bda-sec14-4.pdf



4.4 SeismicRetrofittingofExistingBridgesSeismicretrofittingofexistingbridgesshallbeperformedinaccordancewiththeFHWApublicationFHWA-HRT-06-032,Seismic Retrofitting Manual for Highway Structures: Part 1 – BridgesandWSDOTamendmentsasfollows:• Article1.5.3ThespectralresponseparametersshallbedeterminedusingUSGS2014SeismicHazardMapsandSiteCoefficientsdefinedinSection4.2.3.

• Article7.4.2SeismicLoadinginTwoorThreeOrthogonalDirections

Revisethefirstparagraphasfollows:

Whencombiningtheresponseoftwoorthreeorthogonaldirectionsthedesignvalueofanyquantityofinterest(displacement,bendingmoment,shearoraxialforce)shallbeobtainedbythe100-30percentcombinationruleasdescribedinAASHTOGuide SpecificationsArticle4.4.• DeleteEq.7.44andreplacewiththefollowing:

Lp=themaximumof[(8800εydb)or(0.08L+4400εydb)] (7-44)

• DeleteEq.7.49andreplacewiththefollowing:

4.4 SeismicRetrofittingof ExistingBridgesSeismicretrofittingofexistingbridgesshallbeperformedinaccordancewiththeFHWApublicationFHWA-HRT-06-032, Seismic Retrofitting Manual for Highway Structures: Part 1 – Bridges andWSDOTamendmentsasfollows:

• Article7.4.2SeismicLoadinginTwoorThreeOrthogonalDirectionsRevisethefirstparagraphasfollows:Whencombiningtheresponseoftwoorthreeorthogonaldirectionsthedesignvalueofanyquantityofinterest(displacement,bendingmoment,shearoraxialforce)shallbeobtainedbythe100-30percentcombinationruleasdescribedinAASHTO Guide Specifications Article4.4.


(7.49)


(7.51)

4.4.1 Seismic Analysis RequirementsThefirststepinretrofittingabridgeistoanalyzetheexistingstructuretoidentifyseismicallydeficientelements.Theinitialanalysisconsistsofgeneratingcapacity/demandratiosforallrelevantbridgecomponents.Seismicdisplacementandforcedemandsshallbedeterminedusingthemulti-modespectralanalysisofSeismic Retrofitting Manual Section5.4.2.2(asaminimum).Prescriptiverequirements,suchassupportlength,shallbeconsideredmandatoryandshallbeincludedintheanalysis.Seismic capacitiesshallbedeterminedinaccordancewiththerequirementsoftheSeismic Retrofitting Manual.DisplacementcapacitiesshallbedeterminedbytheMethodD2– StructureCapacity/Demand(Pushover)MethodofSeismic Retrofitting Manual Section5.6.Theseismicanalysisneedonlybeperformedfortheupperlevel(1,000yearreturnperiod)groundmotionswithalifesafetyseismicperformancelevel.

4.4.2 Seismic Retrofit Design

Onceseismicallydeficientbridgeelementshavebeenidentified,appropriateretrofitmeasuresshallbeselectedanddesigned.Table 1-11,Chapters8,9,10,11,andAppendicesDthruFoftheSeismic Retrofitting Manual shallbeused inselectinganddesigningtheseismicretrofitmeasures.TheWSDOTBridgeandStructureOfficeSeismicSpecialistwill beconsulted intheselectionanddesignoftheretrofit measures.

yfi

mip VV

VV φφ

+

−−

= 25

yjfji

jhjip VV

VVφφ

+

−

−= 24

(7 .49)


4.4 SeismicRetrofittingof ExistingBridgesSeismicretrofittingofexistingbridgesshallbeperformedinaccordancewiththeFHWApublicationFHWA-HRT-06-032, Seismic Retrofitting Manual for Highway Structures: Part 1 – Bridges andWSDOTamendmentsasfollows:

• Article7.4.2SeismicLoadinginTwoorThreeOrthogonalDirectionsRevisethefirstparagraphasfollows:Whencombiningtheresponseoftwoorthreeorthogonaldirectionsthedesignvalueofanyquantityofinterest(displacement,bendingmoment,shearoraxialforce)shallbeobtainedbythe100-30percentcombinationruleasdescribedinAASHTO Guide Specifications Article4.4.


(7.49)


(7.51)

4.4.1 Seismic Analysis RequirementsThefirststepinretrofittingabridgeistoanalyzetheexistingstructuretoidentifyseismicallydeficientelements.Theinitialanalysisconsistsofgeneratingcapacity/demandratiosforallrelevantbridgecomponents.Seismicdisplacementandforcedemandsshallbedeterminedusingthemulti-modespectralanalysisofSeismic Retrofitting Manual Section5.4.2.2(asaminimum).Prescriptiverequirements,suchassupportlength,shallbeconsideredmandatoryandshallbeincludedintheanalysis.Seismic capacitiesshallbedeterminedinaccordancewiththerequirementsoftheSeismic Retrofitting Manual.DisplacementcapacitiesshallbedeterminedbytheMethodD2– StructureCapacity/Demand(Pushover)MethodofSeismic Retrofitting Manual Section5.6.Theseismicanalysisneedonlybeperformedfortheupperlevel(1,000yearreturnperiod)groundmotionswithalifesafetyseismicperformancelevel.

4.4.2 Seismic Retrofit Design

Onceseismicallydeficientbridgeelementshavebeenidentified,appropriateretrofitmeasuresshallbeselectedanddesigned.Table 1-11,Chapters8,9,10,11,andAppendicesDthruFoftheSeismic Retrofitting Manual shallbeused inselectinganddesigningtheseismicretrofitmeasures.TheWSDOTBridgeandStructureOfficeSeismicSpecialistwill beconsulted intheselectionanddesignoftheretrofit measures.

yfi

mip VV

VV φφ

+

−−

= 25

yjfji

jhjip VV

VVφφ

+

−

−= 24 (7 .51)

4.4.1 Seismic Analysis RequirementsThefirststepinretrofittingabridgeistoanalyzetheexistingstructuretoidentifyseismicallydeficientelements.Theinitialanalysisconsistsofgeneratingcapacity/demandratiosforallrelevantbridgecomponents.Seismicdisplacementandforcedemandsshallbedeterminedusingthemulti-modespectralanalysisofSection5.4.2.2(ataminimum).Prescriptiverequirements,suchassupportlength,shallbeconsideredademandandshallbeincludedintheanalysis.SeismiccapacitiesshallbedeterminedinaccordancewiththerequirementsoftheSeismic Retrofitting Manual.DisplacementcapacitiesshallbedeterminedbytheMethodD2–StructureCapacity/Demand(Pushover)MethodofSection5.6.FormostWSDOTbridges,theseismicanalysisneedonlybeperformedfortheupperlevel(1,000yearreturnperiod)groundmotionswithalifesafetyseismicperformancelevel.

4.4.2 Seismic Retrofit DesignOnceseismicallydeficientbridgeelementshavebeenidentified,appropriateretrofitmeasuresshallbeselectedanddesigned.Table1-11,Chapters8,9,10,11,andAppendicesDthruFoftheSeismic Retrofitting Manualshallbeusedinselectinganddesigningtheseismicretrofitmeasures.TheWSDOTBridgeandStructureOfficeSeismicSpecialistwillbeconsultedintheselectionanddesignoftheretrofitmeasures.

http://www.fhwa.dot.gov/publications/research/infrastructure/bridge/06032/






4.4.3 Computer Analysis VerificationThecomputerresultswillbeverifiedtoensureaccuracyandcorrectness.Thedesignershouldusethefollowingproceduresformodelverification:• Usinggraphicstochecktheorientationofallnodes,members,supports,joint,andmemberreleases.Makesurethatallthestructuralcomponentsandconnectionscorrectlymodeltheactualstructure.

• Checkdeadloadreactionswithhandcalculations.Thedifferenceshouldbelessthan5percent.

• Calculatefundamentalandsubsequentmodesbyhandandcompareresultswithcomputerresults.

• Checkthemodeshapesandverifythatstructuremovementsarereasonable.• Increasethenumberofmodestoobtain90percentormoremassparticipationineachdirection.GTSTRUDL/SAP2000directlycalculatesthepercentageofmassparticipation.

• Checkthedistributionoflateralforces.Aretheyconsistentwithcolumnstiffness?Dosmallchangesinstiffnessofcertaincolumnsgivepredictableresults?

4.4.4 Earthquake RestrainersLongitudinalrestrainersshallbehighstrengthsteelrodsconformtoASTMF1554Grade105,includingSupplementRequirementsS2,S3andS5.Nuts,andcouplersifrequired,shallconformtoASTMA563GradeDH.WashersshallconformtoAASHTOM293.Highstrengthsteelrodsandassociatedcouplers,nutsandwashersshallbegalvanizedafterfabricationinaccordancewithAASHTOM232.Thelengthoflongitudinalrestrainersshallbelessthan24feet.

4.4.5 Isolation BearingsIsolationbearingsmaybeusedforseismicretrofitprojectstoreducethedemandsthroughmodificationofthedynamicpropertiesofthebridgeasaviablealternativetostrengtheningweakelementsofnon-ductilebridgesubstructuremembersofexistingbridge.UseofisolationbearingsneedstheapprovalofWSDOTBridgeDesignEngineer.IsolationbearingsshallbedesignedpertherequirementsspecifiedinSection9.3.

http://www.portlandbolt.com/technical/specifications/astm-f1554/

http://www.portlandbolt.com/technical/specifications/astm-f1554/

http://www.portlandbolt.com/technical/specifications/astm-a563/



4.5 SeismicDesignRequirementsforRetainingWalls4.5.1 General

Allretainingwallsshallincludeseismicdesignloadcombinations.ThedesignaccelerationforretainingwallsshallbedeterminedinaccordancewiththeAASHTOSEISMIC.Oncethedesignaccelerationisdetermined,thedesignershallfollowtheapplicabledesignspecificationrequirementslistedinAppendix8.1-A1:

ExceptionstothecasesdescribedinAppendix8.1-A1mayoccurwithapprovalfromtheWSDOTBridgeDesignEngineerand/ortheWSDOTGeotechnicalEngineer.



4.6 AppendicesAppendix4-B1 DesignExamplesofSeismicRetrofits

Appendix4-B2 SAP2000SeismicAnalysisExample


Design Examples Appendix 4-B1 of Seismic Retrofits

DesignExample–RestrainerDesignFHWA-HRT-06-032Seismic Retrofitting Manual for Highway Structures: Part 1 - Bridges,Example8.1RestrainerDesignbyIterativeMethod

WSDOT Bridge Design Manual M 23-50.06 Page 4-B1-1 July 2011

Design Examples Appendix 4-B1 of Seismic Retrofits

Design Example – Restrainer DesignFHWA-HRT-06-032 Seismic Retrofitting Manual for Highway Structures: Part 1 - Bridges, Example 8.1 Restrainer Design by Iterative Method

= 12.00 '' Seat Width (inch)= 2.00 '' concrete cover on vertical faces at seat (inch)

"G" = 1.00 ''

F.S. = 0.67 safety factor against the unseating of the span

= 176.00 ksi restrainer yield stress (ksi)= 10,000 restrainer modulus of elasticity (ksi)= 18.00 ' restrainer length (ft.)= 1.00 '' restrainer slack (inch)= 5000.00 the weight of the less flexible frame (kips) (Frame 1)= 5000.00 the stiffness of the more flexible frame (kips) (Frame 2)= 2040 the stiffness of the less flexible frame (kips/in) (Frame 1)= 510 the stiffness of the more flexible frame (kips/in) (Frame 2) OK= 4.00 Target displacement ductility of the frames= 386.40 acceleration due to gravity (in/sec2)= 0.05 design spectrum damping ratio= 1.75 short period coefficient= 0.70 long period coefficient= 0.28 effective peak ground acceleration coefficient= 0.05 '' converge tolerance

Calculate the period at the end of constant design spectral acceleration plateau (sec)

= 0.7 / 1.75 = 0.4 sec

Calculate the period at beginning of constant design spectral acceleration plateau (sec)

= 0.2 * 0.4 = 0.08 sec

expansion joint gap (inch). For new structures, use maximum estimated opening.

1K

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Design Examples of Seismic Retrofits Chapter 4

Page 4-B1-2 WSDOT Bridge Design Manual M 23-50.06 July 2011

Step 1: Calculate Available seat width,= 12 - 1 - 2 * 2 = 7 '' 0.67 * 7 = 4.69 ''

Step 2: Calculate Maximum Allowable Expansion Joint Displacement and compare to the available seat width.= 1 + 176 * 18 * 12 / 10000 = 4.8 '' > = 4.69 '' NG

Step 3: Compute expansion joint displacement without restrainersThe effective stiffness of each frame are modified due to yielding of frames.

= 2040 / 4 = 510 kip/in= 510 / 4 = 127.5 kip/in

The effective natural period of each frame is given by:

= 2 * PI() *( 5000 / ( 386.4 * 510) )^0.5 = 1 sec.

= 2 * PI() *( 5000 / ( 386.4 * 127.5) )^0.5 = 2 sec.

The effective damping and design spectrum correction factor is:= 0.05 + ( 1 - 0.95 /( 4 ) ^ 0.5 - 0.05 * (4 ) ^ 0.5 ) / PI() = 0.19= 1.5 / ( 40 * 0.19 + 1 ) + 0.5 = 0.68

Determine the frame displacement from Design Spectrum= 1.00 sec. = 0.699

= 2.00 sec. = 0.350

Modified displacement for damping other than 5 percent damped bridges

= ( 1 / ( 2*PI()))^2 * 0.68* 0.699 * 386.4 = 4.65 ''

= ( 2 / ( 2*PI()))^2 * 0.68* 0.35 * 386.4 = 9.3 ''

the frequency ratio of modes, = 2 / 1 = 2

The cross-correlation coefficient,

= (8 * 0.19 ^2)*(1 + 2 )*( 2 ^(3/2))/((1 - 2 ^2)^2 + 4* 0.19 ^2* 2 *(1+ 2 )^2) = 0.2

The initial relative hinge displacement

= ( 4.65 ^2 + 9.3 ^2 - 2 * 0.2 * 4.65 * 9.3 ) ^ 0.5 = 9.52 '' >=2/3 Das = 4.69 ''

Restrainers are required

The relative displacement of the two frames can be calculated using the CQC combination of the two frame displacement as given by equation (Eq. 3)

effK ,1effK ,2

asDasD

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Chapter 4 Design Examples of Seismic Retrofits


Step 4: Estimate the Initial restrainer stiffness

= ( 510 * 127.5 ) / ( 510 + 127.5 ) = 102 kip/in

= 102 * ( 9.52 - 4.8 ) / 9.52 = 50.54 kip/in

Adjust restrainer stiffness to limit the joint displacement to a prescribed value .This can be achieve by using Goal Seek on the Tools menu.

Goal SeekSet Cell $J$104 Cell Address forTo Value

By Changing Cell $D$104 Cell address for initial guess

Apply the Goal Seek every time you use the spreadsheet and Click OK

= 193.21 kip/in (Input a value to start) = 0.00 ''

Step 5: Calculate Relative Hinge Displacement from modal analysis.

Frame 1 mass = 5000 / 386.4 = 12.94 kip. Sec2 / inFrame 2 mass = 5000 / 386.4 = 12.94 kip. Sec2 / in

= 510.00 kip/in = 127.50 kip/in

Solve the following quadratic equation for natural frequencies

= 12.94 * 12.94 = 167.44

= - 12.94 * ( 127.5 + 193.21 ) - 12.94 * ( 510 + 193.21 ) = -13249.52

= 510 * 127.5 + ( 510 + 127.5 ) * 193.21 = 188197.22

The roots of this quadratic are= (-( -13249.52) +(( -13249.52) ^2-4* 167.44 * 188197.22 )^0.5)/( 2*167.44 ) = 60.57

= (-(-13249.52-((-13249.52)^2-4*167.44*188197.22)^0.5)/(2*167.44) = 18.56

The natural frequencies are= 7.78 rad/sec = 4.31 rad/sec

The corresponding natural periods are= 0.81 sec. = 1.46 sec.

For mode 1, = 7.78 rad/sec = 60.57= 510 + 193.21 - 12.94 * 60.57 = -80.61

The relative value (modal shape) corresponding

= 193.21 / -80.61 = -2.397

It is customary to describe the normal modes by assigning a unit value to one of the amplitudes.For the first mode, set = 1.00 then = -2.40The mode shape for the first mode is

-2.401.00

1m2m

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Design Examples of Seismic Retrofits Chapter 4

Page 4-B1-4 WSDOT Bridge Design Manual M 23-50.06 July 2011

For mode 2, = 4.31 rad/sec = 18.56= 510 + 193.21 - 12.94 * 18.56 = 463.11

The relative value

= 193.21 / 463.11 = 0.417

For the 2nd mode, set = 1.00 then = 2.40The mode shape for the 2nd mode is

1.002.40

Calculate the participation factor for mode " 1 "

12.94 * -2.4 + 12.94 * 1 = -18.08

= ( 510 + 193.21 ) * (-2.4) ^2 - 2* 193.21 * -2.4 * 1 + ( 127.5 + 193.21 ) * ( 1 ) ^2 = 5286.98

1 - -2.4 = 3.4

-18.08 / 5286.98 * 3.4 = -0.0116 sec.2

Calculate the participation factor for mode " 2 "

12.94 * 1 + 12.94 * 2.4 = 43.96

= ( 510 + 193.21 ) * (1) ^2 - 2* 193.21 * 1 * 2.4 + ( 127.5 + 193.21 ) * ( 2.4 ) ^2 = 1619.53

2.4 - 1 = 1.4

43.96 / 1619.53 * 1.4 = 0.0379 sec.2

Determine the frame displacement from Design Spectrum= 0.81 sec. = 0.867

= 1.46 sec. = 0.480

2 222

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Chapter 4 Design Examples of Seismic Retrofits


Calculate new relative displacement at expansion joint

-0.0116 * 0.68 * 0.867 * 386.4 = -2.64 ''

0.0379 * 0.68 * 0.48 * 386.4 = 4.77 ''

The effective period ratio

= 1.46 / 0.81 = 1.81

The cross-correlation coefficient,= (8 * 0.19 ^2)*(1+ 1.81 )*( 1.81 ^(3/2))/((1 -1.81 ^2)^2+4* 0.19 ^2* 1.81 *(1+1.81 )^2) = 0.26

= ( ( -2.64)^2 + ( 4.77)^2+2* 0.26 * ( -2.64 ) * (4.77))^0.5 = 4.8 ''>4.8 ''

= 4.8 - 4.8 = 0 ''

OK Go to Step 7 and calculate the number of restrainers

Step 7: Calculate number of restrainers

= 4.80 '' = 193.21 kip/in = 176.00 ksi= 0.222 in^2

= ( 193.21 * 4.8 ) / ( 176 * 0.222 ) = 23.74 restrainers

eff

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36 WSDOT Bridge Design Manual M 23-50.17 June 2017WSDOT Bridge Design Manual M23-50.04 Page 4-B2-1

August 2010

SAP2000 Seismic Appendix 4-B2 Analysis Example

1. IntroductionThisexampleservestoillustratetheprocedureusedtoperformnonlinearstatic“pushover”analysisinboththelongitudinalandtransversedirections inaccordancewiththeAASHTO Guide Specifications for LRFD Seismic Bridge Design usingSAP2000. Afullmodelofthebridgeisusedtocomputethedisplacementdemandfromaresponse-spectrumanalysis. Toperformthepushoveranalysisinthelongitudinaldirection,theentirebridgeis pushedinordertoincludetheframeactionofthesuperstructureandadjacentbents. Toperformthepushoveranalysisinthetransversedirection,a bentisisolatedusingtheSAP2000“stagedconstruction”feature. Theexamplebridgeissymmetric andhasthreespans. ItisassumedthereaderhassomepreviousknowledgeofhowtouseSAP2000. ThisexamplewascreatedusingSAP2000version14.2.0.

Note: Byproducingthisexample,theWashingtonStateDepartmentofTransportationdoesnotwarrantthatthe SAP2000softwaredoesnotincludeerrors. TheexampledoesnotrelieveDesignEngineersoftheirprofessionalresponsibilityforthesoftware’s accuracy andisnotintendedtodoso. Design Engineers shouldverifyallcomputerresultswithhandcalculations.

Brief Table of Contents of Example:

1. Introduction..............................................................................................................................1

2. ModelSetup .............................................................................................................................22.1 OverviewofModel ....................................................................................................22.2 FoundationsModeling ...............................................................................................32.3 MaterialsModeling ....................................................................................................62.4 ColumnModeling ......................................................................................................152.5 CrossbeamModeling .................................................................................................192.6 SuperstructureModeling............................................................................................202.7 GravityLoad Patterns ................................................................................................22

3. DisplacementDemandAnalysis ..............................................................................................233.1 ModalAnalysis ..........................................................................................................233.2 Response-SpectrumAnalysis.....................................................................................273.3 DisplacementDemand ...............................................................................................32

4. DisplacementCapacityAnalysis .............................................................................................344.1 HingeDefinitionsandAssignments ..........................................................................344.2 PushoverAnalysis......................................................................................................41

5. CodeRequirements ..................................................................................................................665.1 P-Δ Capacity Requirement Check .............................................................................665.2 MinimumLateralStrengthCheck .............................................................................675.3 StructureDisplacementDemand/CapacityCheck.....................................................695.4 MemberDuctilityRequirementCheck ......................................................................735.5 ColumnShearDemand/CapacityCheck ...................................................................795.6 BalancedStiffnessandFrameGeometryRequirementCheck ..................................83

Appendix 4-B2 SAP2000 Seismic Analysis Example



SAP2000 Seismic Analysis Example

Page 4-B2-2 WSDOT Bridge Design Manual M23-50.04August 2010

2. ModelSetup2.1 OverviewofModelThisexampleemploysSAP2000. Thesuperstructureismodeledusingframe elementsforeachofthegirdersandshellelementsforthedeck. Shellelementsarealsousedtomodeltheend,intermediate, andpierdiaphragms. Non-prismaticframesectionsareusedtomodelthecrossbeamssincetheyhavevariabledepth. TheX-axisisalongthebridge’s longitudinalaxis andtheZ-axisisvertical. TheunitsusedforinputsintoSAP2000throughoutthisexamplearekip-in.Thefollowingsummarizesthebridgebeingmodeled:

• Allspansare145’inlength• (5)linesofprestressedconcretegirders(WF74G)with9’-6”ctcspacing• 8”deckwith46’-11”towidth• Girdersarecontinuousandfixedtothecrossbeamsattheintermediatepiers• (2)5’diametercolumnsatbents• Combinedspreadfootings– 20’Lx40’W x5’Dateachbent• Abutmentlongitudinalisfree,transverseisfixed

Figure2.1-1showsaviewofthemodelinSAP2000.

Wireframe3-DViewof ModelFigure 2.1-1




WSDOT Bridge Design Manual M23-50.04 Page 4-B2-3August 2010

2.2 FoundationsModeling2.2.1 IntermediatePiers

Eachbentissupportedbyacombinedspreadfootingthatis20’Lx40’Wx5’D. Thesefootingsaremodeledusingsprings. RigidlinksconnectthebasesofthecolumnstoacenterjointthatthespringpropertiesareassignedtoasshowninFigure2.2.1-1.

Wireframe2-DViewofBentFigure 2.2.1-1

ThesoilspringsweregeneratedusingthemethodforspreadfootingsoutlinedinChapter7oftheWashington State Department of Transportation Bridge Design Manual. TheassumedsoilparameterswereG=1,700 ksf and ν = 0.35. Thespringvaluesusedinthemodelforthespreadfootingsare showninTable2.2.1-1.

DegreeofFreedom StiffnessValueUX 18,810 kip/inUY 16,820 kip/inUZ 18,000 kip/inRX 1,030,000,000 kip-in/radRY 417,100,000 kip-in/radRZ 1,178,000,000 kip-in/rad

JointSpringValuesforSpreadFootingsTable 2.2.1-1

Figure2.2.1-2 showsthespreadfootingjointspringassignments (Assign menu > Joint > Springs).





SpreadFootingJointSpring AssignmentsFigure 2.2.1-2

Thespringsusedinthedemandmodel(response-spectrummodel)arethesameasthespringsusedinthecapacitymodel(pushovermodel). It is alsobeacceptabletoconservativelyusefixed-basecolumnsforthecapacitymodel.

2.2.2 Abutments

ThesuperstructureismodeledasbeingfreeinthelongitudinaldirectionattheabutmentsinaccordancewiththepoliciesoutlinedintheWashington State Department of Transportation Bridge Design Manual. Theabutmentsarefixedinthetransversedirection inthisexampleforsimplification. However,pleasenotethattheAASHTO Guide Specifications for LRFD Seismic Bridge Design requirethestiffnessofthetransverseabutments bemodeled. Sincethere arefivegirderlinesinsteadofaspineelement,thejointsattheendsofthegirdersattheabutmentsallhavejointrestraintsassignedtothem. ThegirderjointrestraintassignmentsattheabutmentsarelistedinTable2.2.2-1.

DegreeofFreedom FixityUX FreeUY FixedUZ FixedRX FreeRY FreeRZ Free

JointFixityforGirderJointsatAbutmentsTable 2.2.2-1





Figure2.2.2-1showsthegirderjointrestraintsattheabutments(Assign menu > Joint > Restraints).

GirderJointRestraint AssignmentsatAbutmentsFigure 2.2.2-1





2.3 MaterialsModelingSAP2000’s defaultconcretematerialpropertieshaveelasticmodulibasedonconcretedensitiesof144psf. TheelasticmodulioftheconcretematerialsusedinthisexamplearebasedontheWashingtonStateDepartmentofTransportation’spolicyonconcretedensities tobeusedinthecalculations ofelasticmoduli. PleaseseethecurrentWSDOT Bridge Design Manual andBridge Design Memorandums. In Version14 ofSAP2000,nonlinearmaterialpropertiesforCaltranssectionsarenolongerdefinedinSectionDesigner andarenowdefinedinthematerialdefinitionsthemselves. Table2.3-1 lists the materialdefinitionsusedinthemodelandtheelementstheyareappliedto (Define menu > Materials).

MaterialName MaterialType SectionPropertyUsedFor

MaterialUnitWeight(pcf)ForDeadLoad

ForModulusofElasticity

4000Psi-Deck Concrete Deck 155 150

4000Psi-Other Concrete Crossbeams&Diaphragms 150 145

5200Psi-Column Concrete Columns 150 1457000Psi-Girder Concrete Girders 165 155

A706-Other Rebar RebarOtherThanColumns 490 -

A706-Column Rebar ColumnRebar 490 -

MaterialPropertiesUsedinModelTable 2.3-1

The“5200Psi-Column”and“A706-Column” materialdefinitionsarecreatedtodefinetheexpected,nonlinearpropertiesofthecolumnsection.

TheMaterialPropertyDataforthematerial“4000Psi-Deck” isshowninFigure2.3-1 (Define menu > Materials > select 4000Psi-Deck > click Modify/Show Material button).





MaterialPropertyDataforMaterial“4000Psi-Deck”Figure 2.3-1

TheMaterialPropertyDataforthematerial“4000Psi-Other”isshowninFigure2.3-2(Define menu > Materials > select 4000Psi-Other > click Modify/Show Material button).

MaterialPropertyDataforMaterial“4000Psi-Other”Figure 2.3-2





TheMaterialPropertyDataforthematerial“7000Psi-Girder” isshowninFigure2.3-3 (Define menu > Materials > select 7000Psi-Girder > click Modify/Show Material button).

MaterialPropertyDataforMaterial “7000Psi-Girder”Figure 2.3-3





TheMaterialPropertyDataforthematerial“5200Psi-Column” isshownFigure2.3-4 (Define menu > Materials > select 5200Psi-Column > click Modify/Show Material button).

MaterialPropertyDataforMaterial“5200Psi-Column”Figure 2.3-4

WhentheSwitch To Advanced Property Display boxshowninFigure2.3-4 ischecked , thewindowshowninFigure2.3-5 opens.

AdvancedMaterialPropertyOptionsforMaterial“5200Psi-Column”Figure 2.3-5

ByclickingtheModify/Show Material Properties buttoninFigure2.3-5, thewindowshowninFigure2.3-6 opens.





AdvancedMaterialPropertyDataforMaterial“5200Psi-Column”Figure 2.3-6

ByclickingtheNonlinear Material Data buttoninFigure2.3-6, thewindowshowninFigure2.3-7 opens.

NonlinearMaterialDataforMaterial“5200Psi-Column”Figure 2.3-7

NotethatinFigure2.3-7 theStrain At Unconfined Compressive Strength, f’c andtheUltimate Unconfined Strain Capacity aresettothevaluesrequiredinSection8.4.4oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design. TheseunconfinedpropertiesareparametersusedindefiningtheManderconfinedconcretestress-straincurveofthecolumncore. Itisseen





thatundertheStress-Strain Definition Options, Mander isselected. ByclickingtheShowStress-Strain Plot buttoninFigure2.3-7, a plotsimilartothatshownFigure2.3-8 isdisplayed.

Material Stress-StrainCurvePlotforMaterial“5200Psi-Column”Figure 2.3-8

Figure2.3-8 showsboththeconfinedandunconfinednonlinearstress-strainrelationships. Theusershouldverifythattheconcretestress-straincurvesareasexpected.

TheMaterialPropertyDataforthematerial“A706-Other”isshowninFigure2.3-9 (Define menu > Materials > select A706-Other > click Modify/Show Material button).



MaterialPropertyDataforMaterial“A706-Other”Figure 2.3-9

TheMaterialPropertyDataforthematerial“A706-Column” isshowninFigure2.3-10(Define menu > Materials > select A706-Column > click Modify/Show Material button).

MaterialPropertyDataforMaterial“A706-Column”Figure 2.3-10





MaterialPropertyDataforMaterial“A706-Other”Figure 2.3-9

TheMaterialPropertyDataforthematerial“A706-Column” isshowninFigure2.3-10(Define menu > Materials > select A706-Column > click Modify/Show Material button).

MaterialPropertyDataforMaterial“A706-Column”Figure 2.3-10





WhentheSwitch To Advanced Property Display boxinFigure2.3-10 ischecked, thewindowshowninFigure2.3-11 opens.

AdvancedMaterialPropertyOptionsforMaterial “A706-Column”Figure 2.3-11

ByclickingtheModify/Show Material Properties button inFigure2.3-11, thewindowshowninFigure2.3-12 opens.

AdvancedMaterialPropertyDataforMaterial“A706-Column”Figure 2.3-12

InFigure2.3-12, theMinimum Yield Stress, Fy = 68 ksiandtheMinimum Tensile Stress,Fu = 95 ksiasrequiredperTable8.4.2-1oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design. SAP2000usesFy andFu insteadofFye andFue togeneratethenonlinearstress-strain curve. Therefore,theFye andFue inputsinSAP2000donotserveapurposeforthisanalysis. ByclickingtheNonlinear Material Data buttoninFigure2.3-12,thewindowshowninFigure2.3-13 opens.





NonlinearMaterialDataforMaterial“A706-Column”Figure 2.3-13

InFigure2.3-13,itisseenthatundertheStress-Strain Curve Definitions Options, Park isselected. AlsotheboxforUse Caltrans Default Controlling Strain Values ischecked. ByclickingtheShow Stress-Strain Plot buttoninFigure2.3-13 theplot showninFigure2.3-14 isdisplayed.

Material Stress-StrainCurvePlotforMaterial“A706-Column”Figure 2.3-14

InFigure2.3-14, the strain at which the stress begins to decrease is εRsu,whichtheusershouldverifyforcorrectness.





2.4 ColumnModelingThereare twocolumnsateachbent. Thecolumns arefivefeetindiameterandhave(24)#10barsforlongitudinalsteel,which amountstoasteel-concretearearatioofabout1%. Inthehingezones,thecolumnshaveconfinementsteelconsistingof#6spiralbarswitha3.5 inchspacing.

Thecolumnelementshaverigidendoffsetsassignedtothematthefootingsandcrossbeams.Thenetclearheightofthecolumnsis29’-2”. Thecolumnsaresplitintothreeframeelements.Section5.4.3oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design requiresthatcolumnsbesplitintoaminimumofthreeelements.

Figure2.4-1showstheframesectionpropertydefinitionforthecolumnelements(Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button).

FrameSectionPropertyDefinitionfor FrameSection“COL”Figure 2.4-1

ByclickingtheSection Designer buttoninFigure2.4-1,thewindowshowninFigure2.4-2opens. The“COL” framesectionis definedusingaroundCaltransshapeinSectionDesigner asshowninFigure2.4-2.





SectionDesignerViewofFrameSection“COL”Figure 2.4-2

Byright-clickingonthesectionshowninFigure2.4-2,thewindowshownin Figure2.4-3opens.Figure2.4-3showstheparameterinputwindowfortheCaltransshapeisshowninFigure2.4-2.





CaltransSectionPropertiesforFrameSection “COL”Figure 2.4-3

ByclickingtheShow buttonfortheCore Concrete inFigure2.4-3,thewindowshowninFigure2.4-4 opens.





ConcreteModelforCoreofFrameSection“COL”Figure 2.4-4

Figure2.4-4 showstheManderconfinedstress-strainconcretemodelforthecore ofthecolumn.Theusershouldverifythattheconcretestress-straincurveisasexpected.





2.5 Crossbeam ModelingThecrossbeams are modeledasframeelementswithnon-prismaticsectionpropertiesduetothevariabledepthofthe sections (Define menu > Section Properties > Frame Sections). Thecrossbeamelementshavetheirinsertionpointssettothetopcenter (Assign menu > Frame > Insertion Point). Thepierdiaphragmabovethecrossbeamismodeledwithshellelements. Anextruded viewofthebentisshowninFigure2.5-1.

Extruded2-DViewofBentFigure 2.5-1





2.5 Crossbeam ModelingThecrossbeams are modeledasframeelementswithnon-prismaticsectionpropertiesduetothevariabledepthofthe sections (Define menu > Section Properties > Frame Sections). Thecrossbeamelementshavetheirinsertionpointssettothetopcenter (Assign menu > Frame > Insertion Point). Thepierdiaphragmabovethecrossbeamismodeledwithshellelements. Anextruded viewofthebentisshowninFigure2.5-1.

Extruded2-DViewofBentFigure 2.5-1



2.6 Superstructure ModelingThegirdersareWashingtonStateDepartmentofTransportationWF74Gs. Theframesectiondefinitionforsection“WF74G”isshowninFigure2.6-1 (Define menu > Section Properties > Frame Sections > select WF74G > click Modify/Show Property button).

FrameSectionParameterInputforFrameSection“WF74G”Figure 2.6-1

Thegirdersareassignedinsertionpointssuchthattheyconnect tothesamejointsasthedeckelementsbutarebelowthedeck. Sincethedeckis8 inches thickandthegapbetweenthetopofthegirderandthesoffitofthedeckis3 inches,theinsertionpointis7 inches (8 in./2+3 in.)abovethetopofthegirder. Figure2.6-2showsthegirderframeelementinsertionpointassignments(Assign menu > Frame > Insertion Point).





GirderFrameElementInsertionPointAssignmentsFigure 2.6-2

Linksconnectthegirderstothecrossbeamswhichmodelsthefixedconnectionbetweentheseelements. SeethescreenshotshowninFigure2.6-3.

Wireframe3-DViewofBentandSuperstructureIntersectionFigure 2.6-3

The superstructureisbrokenintofivesegments perspan. Section5.4.3oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design requiresthataminimumoffoursegments perspanbeused.





2.7 GravityLoadPatternsTherearethree deadloadpatternsinthemodel: “DC-Structure”, “DC-Barriers”, and“DW-Overlay”. The“DC-Structure” caseincludestheselfweightofthestructuralcomponents. The“DC-Barriers” caseincludesthedeadloadofthebarriers,whichisappliedasanarealoadtotheoutermostdeckshells. The“DW-Overlay” caseincludesthefutureoverlayloadsappliedtothedeckshells. Thedead loadpatterndefinitionsareshownFigure2.7-1 (Define menu > Load Patterns).

Dead LoadPatternDefinitionsFigure 2.7-1

Thedesignershouldverifytheweightofthestructureinthemodelwithhandcalculations.





3. DisplacementDemandAnalysis3.1 ModalAnalysis3.1.1 MassSource

Allofthedeadloadsare consideredascontributingmassforthemodalload case. AdisplayofthemasssourcedefinitionwindowfromSAP2000isshowninFigure3.1.1-1 (Define menu > Mass Source).

MassSourceDefinitionFigure 3.1.1-1

3.1.2 CrackingofColumns

Section5.6oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design providesdiagramsthatcanbeusedtodeterminethecrackedsectionpropertiesofthecolumns. However,SAP2000’sSectionDesignercanbeusedtocomputetheeffectivesectionproperties. IfusingSectionDesigner,thedesignershouldverifythatthemethodofcalculationconformstoAASHTO Guide Specifications of LRFD Seismic Bridge Design. Thecolumnaxialdeadloadatmid-heightisapproximately 1,250 kips without includingtheeffectsofthe constructionstaging. Forthebridgeinthisexample,theinclusionofstagingeffectswouldcausetheaxialloadinthecolumnstovarybylessthantenpercent. Suchasmallchangeinaxialloadwouldnotsignificantlyaltertheresultsofthisanalysis. However,therearesituationswheretheinclusionofconstructionsequence effectswillsignificantlyaltertheanalysis. Therefore,engineeringjudgmentshouldbeusedwhendecidedwhetherornottoincludetheeffectsofstaging. ByhavingSectionDesignerperformamoment-curvatureanalysisonthecolumnsectionwithanaxialloadof1,250 kips,itisfoundthatICrack=212,907 inch4. Thegrossmomentofinertiais628,044 inch4 (ascalculatedbySAP2000). Therefore,theratiois212,907/628,044 = 0.34. Themoment-curvatureanalysisisshowninFigure3.1.2-1 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve).





MomentCurvatureCurveforFrameSection“COL”atP=-1250 kipsFigure 3.1.2-1

ItcanbeseeninFigure3.1.2-1thatconcretestraincapacitylimitstheavailableplasticcurvature.DesignersshouldverifythatSAP2000’sbilinearizationisacceptable. ThepropertymodifiersarethenappliedtothecolumnframeelementsasshowninFigure3.1.2-2 (Assign menu > Frame > Property Modifiers).

FramePropertyModificationFactorforColumnFrame ElementsFigure 3.1.2-2

Thetorsionalconstantmodifieris0.2forcolumnsasrequiredbySection5.6.5oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design.





3.1.3 LoadCaseSetup

The“MODAL” load caseusesRitzvectorsandisdefinedinSAP2000asshowninFigure3.1.3-1 (Define menu > Load Cases > select MODAL > click Modify/Show Load Case button).

LoadCaseDataforLoadCase“MODAL”Figure 3.1.3-1

3.1.4 Verificationof MassParticipation

Section5.4.3oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design requires aminimumof90%massparticipationinbothdirections. Forthisexample,themassisconsideredtobethesameinbothdirectionseventhoughtheenddiaphragmsarefreeinthelongitudinaldirectionandrestrained inthetransversedirection. BydisplayingtheModal Participating Mass Ratios tableforthe“MODAL”loadcaseitisfoundthattheX-direction(longitudinal)reachesgreaterthan90%massparticipationonthefirstmodeshape,whiletheY-direction(transverse)reachesgreaterthan90%massparticipationbythe seventeenthmodeshape. Thisimpliesthattheminimumcoderequirementscouldbemetbyincludingonlyseventeenmodeshapes.TheModal Participating Mass Ratios tableisshowninFigure3.1.4-1 (Display menu > Show Tables > check Modal Participating Mass Ratios > click OK button).





ModalParticipatingMassRatiosforLoadCase“MODAL”Figure 3.1.4-1

Figure3.1.4-1alsoshowsthatthefirstmodeintheX-direction(longitudinal)hasaperiodof0.95 secondsandthefirstmodeintheY-direction(transverse)hasperiodof0.61 seconds. Thedesignershouldverifyfundamentalperiodswithhandcalculations. Thedesignershouldalsovisuallyreviewtheprimarymodeshapestoverifytheyrepresentrealisticbehavior.





3.2 Response-SpectrumAnalysis3.2.1 SeismicHazard

ThebridgeislocatedinRedmond,Wash. Themappedspectralaccelerationcoefficientsare:

PGA=0.396gSs =0.883gS1 =0.294g

AsiteclassofE isassumedforthisexampleandthesitecoefficientsare:

FPGA = 0.91Fa = 1.04Fv = 2.82

Therefore,theresponse-spectrumisgeneratedusingthefollowingparameters:

As =FPGA*PGA=0.361 gSDS =Fa*Ss = 0.919 gSD1 =Fv*S1 = 0.830 g

SinceSD1 isgreaterthanor equalto0.50,perTable3.5-1oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design theSeismicDesignCategoryisD.

3.2.2 Response-SpectrumInput

ThespectrumisdefinedfromafilecreatedusingtheAASHTOEarthquakeGroundMotionParameterstool. Ascreenshotoftheresponse-spectrumas inputted inSAP2000isshowninFigure3.2.2-1 (Define menu > Functions > Response Spectrum > select SC-E > click ShowSpectrum button).





ResponseSpectrumFunctionDefinitionfromFileforFunction“SC-E”Figure 3.2.2-1

WhentheConvert to User Defined buttonisclicked,thefunctionappearsasshowninFigure3.2.2-2.

ResponseSpectrumFunctionDefinition forFunction“SC-E”Figure 3.2.2-2





Havingtheresponse-spectrumfunctionstoredas“UserDefined”isadvantageousbecausethedataisstoredwithinthe.SDBfile. Therefore,ifthe.SDBfileistransferredtoadifferentlocation(differentcomputer),theresponse-spectrumfunctionwillalsobemoved.

3.2.3 LoadCaseSetup

Tworesponse-spectrumanalysiscasesaresetupinSAP2000: oneforeachorthogonaldirection.

3.2.3.1 LongitudinalDirection

Theload casedata fortheX-directionisshowninFigure3.2.3.1-1 (Define menu > Load Cases > select EX > click Modify/Show Load Case button).

LoadCaseDataforLoadCase“EX”Figure 3.2.3.1-1

3.2.3.2 Transverse Direction

TheloadcasedatafortheY-directionisshownFigure3.2.3.2-1 (Define menu > Load Cases > select EY > click Modify/Show Load Case button).





LoadCaseDataforLoad Case “EY”Figure 3.2.3.2-1

3.2.4 Response-SpectrumDisplacements

ThecolumndisplacementsinthisexamplearetrackedatJoint33,whichislocatedatthetopofacolumn. Sincethebridgeissymmetric,allofthecolumnshavethesamedisplacementsin theresponse-spectrumanalyses.


Thehorizontaldisplacementsatthetops ofthecolumns fromtheEXanalysiscaseareU1=7.48inches andU2 = 0.00 inches. ThisisshowninFigure3.2.4.1-1 asdisplayedinSAP2000(Display menu > Show Deformed Shape > select EX > click OK button).





JointDisplacementatJoint33forLoadCase“EX”Figure 3.2.4.1-1


Thehorizontaldisplacementsatthetops ofthecolumns fromtheEYanalysiscaseareU1=0.17inches andU2=3.55 inches. ThisisshowninFigure3.2.4.2-1 asdisplayedinSAP2000(Display menu > Show Deformed Shape > select EY > click OK button).

JointDisplacementatJoint33forLoadCase“EY”Figure 3.2.4.2-1





3.3 DisplacementDemand3.3.1 DisplacementMagnification

DisplacementmagnificationmustbeperformedinaccordancewithSection4.3.3oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design.

ComputeTs andT*:

Ts = SD1 /SDS= 0.830 / 0.919= 0.903 sec.

T* = 1.25 Ts= 1.25 * 0.903= 1.13 sec.


ComputemagnificationfortheX-direction (Longitudinal):

TLong = 0.95 sec. (seesection3.1.4)

T* /TLong = 1.13 / 0.95= 1.19 >1.0=>Magnificationisrequired

Rd_Long = (1 – 1/μD)*(T* / T) + 1 / μD= (1 – 1/6)*(1.19)+1/6 (Assume μD =6)= 1.16


ComputemagnificationfortheY-direction (Transverse):

TTrans = 0.61 sec. (seesection3.1.4)

T*/TTrans = 1.13 /0.61= 1.85 >1.0=>Magnificationisrequired

Rd_Trans = (1 – 1/μD) * (T* / T) + 1 / μD= (1 – 1/6)*(1.85)+1/6 (Assume μD =6)= 1.71

3.3.2ColumnDisplacementDemand

Section4.4oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design requiresthat100%plus30%ofthedisplacementsfromeachorthogonalseismicloadcasebecombinedtodeterminethedisplacementdemands.ThedisplacementsaretrackedasJoint33,whichislocatedatthetopofacolumn.






FortheX-direction(100EX+30EY):

UX(duetoEX)=7.48in.

UX(duetoEY)=0.17in.

Therefore,

ΔLD_Long = 1.0 * Rd_Long * 7.48+0.3 * Rd_Trans * 0.17

= 1.0*1.16*7.48+0.3*1.71*0.17=8.76in. =>ThisisthedisplacementdemandfortheX-Dir

3.3.1.2 TransverseDirection

FortheY-direction(100EY+30EX):

UY(duetoEY)=3.55in.

UY(duetoEX)=0.00in.

Therefore,

ΔLD_Trans = 1.0 * Rd_Trans * 3.55+0.3*Rd_Long * 0.00

= 1.0 * 1.71 * 3.55 +0.3*1.16*0.00=6.07in.=>ThisistheDisplacementDemandfortheY-Dir





4. DisplacementCapacityAnalysis4.1 PlasticHingeDefinitionsandAssignments4.1.1 ColumnInflectionPoints

Thetopsand bottomsofallcolumnshaveenoughmomentfixityinalldirectionstocauseplastichinging,whichmeansthecolumnswillexhibitbehaviorsimilartoafixed-fixedcolumn. Theplasticmomentcapacitiesofthecolumnsunderdeadloadswillbeusedtoapproximatethelocationofthecolumninflectionpoints. Therefore,theaxialloads(duetodeadload)atthetopandbottomofthecolumnsmustbedetermined. Duetothesymmetryofthebridgeinthisexample,theaxialloadsarethesameforallofthecolumns,whichwillnotbetrueformostbridges. Figure4.1.1-1showstheaxialforcediagramfortheDC+DWloadcaseasdisplayedinSAP2000(Display menu > Show Forces/Stresses > Frames/Cables > select DC+DW > select Axial Force > click OK button).

FrameAxialForceDiagramforLoadCase“DC+DW”Figure 4.1.1-1

FromtheaxialloadsdisplayedfortheDC+DWloadcaseitisdeterminedthattheaxialforceatthebottomofthecolumnisapproximately1,290 kipsandtheaxialforceatthetopofthecolumnisapproximately1,210 kips(seesection3.1.2ofthisexampleforadiscussionontheinclusionofconstructionsequenceeffectsoncolumnaxialloads). Itisexpectedthatthe differenceinaxialloadbetweenthetopsandbottomsofthecolumnswillnotresultinasignificantdifferenceintheplasticmoment. However,onsomebridgestheaxialloads atthetopsandbottomsofthecolumnsmaybesubstantiallydifferentorthecolumnsectionmayvaryalongitsheightproducingsignificantlydifferentplasticmomentsateachend.





Themoment-curvatureanalysisofthecolumnbaseisshowninFigure4.1.1-2(Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button >click Section Designer button > Display menu > Show Moment-Curvature Curve).


ItisseeninFigure4.1.1-2thattheplasticmomentcapacityatthebaseofthecolumnis79,186kip-inches (withonlydeadloadapplied).

Themoment-curvatureanalysisofthecolumntopisshowninFigure4.1.1-3(Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button >click Section Designer button > Display menu > Show Moment-Curvature Curve).






ItisseeninFigure4.1.1-3thattheplasticmomentcapacityatthetop ofthecolumnis77,920kip-inches (withonlydeadloadapplied).

Theclearheightofthecolumnsis350 inches;therefore:

L1 = Lengthfrompointofmaximummomentatbaseofcolumntoinflectionpoint(in.)= 350 xMp_col_base /(Mp_col_base +Mp_col_top)= 350x79186 /(79186 +77920)= 176 in.

L2 = Lengthfrompointofmaximummomentattopofcolumntoinflectionpoint(in.)= 350 – L1= 350 – 176= 174 in.

4.1.2 PlasticHingeLengths

Theplastichingelengthsmustbecomputedatboththetopsandbottomsofthecolumnsusingtheequations inSection4.11.6oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design. Thehingelengthiscomputedasfollows:

Lp =0.08L+0.15fyedbl ≥ 0.3fyedbl





Where:L = lengthofcolumnfrompointofmaximummomenttothepointof moment

contraflexure(in.)= L1 atthebaseofthecolumns(L1Long = L1Trans = 176 in.)= L2 atthetopofthecolumns(L2Long = L2Trans = 174 in.)

fye = expectedyieldstrengthoflongitudinalcolumnreinforcingsteelbars(ksi)= 68ksi(ASTMA706bars).

dbl = nominaldiameteroflongitudinalcolumnreinforcingsteelbars(in.)= 1.27 in. (#10 bars)

Lp1 = Plastichingelengthatbaseofcolumn= 0.08*176 +0.15*68*1.27 ≥ 0.3*68*1.27= 27.03 ≥ 25.91= 27.0 in.

Lp2 = Plastichingelengthattopofcolumn= 0.08*174 +0.15*68*1.27≥ 0.3*68*1.27= 26.87 ≥ 25.91= 26.9 in.

Inthisexample, theplastichingelengthsinbothdirections are thesamebecause thelocationsoftheinflectionpointsinboth directionsarethesame. Thiswillnotalwaysbethecase,suchaswhenthereisasinglecolumnbent.

4.1.3 AssignPlasticHinges

Inordertoassigntheplastichingestothecolumnelements, therelativelocationsoftheplastichingesalongthecolumnframeelementsmustbecomputed.

Forthebases ofthecolumns:

RelativeLength= [FootingOffset+(HingeLength/2)]/ElementLength= [30+(27.0 /2)]/146= 0.30

Forthetops ofthecolumns:

RelativeLength= [ElementLength– XbeamOffset– (HingeLength/2)]/ElementLength= [146– 58 – (26.9 / 2)]/146= 0.51

ThehingesatthebasesofthecolumnsareassignedatrelativedistancesasshowninFigure4.1.3-1(Assign menu > Frame > Hinges).





FrameHingeAssignmentsforColumnBasesFigure 4.1.3-1

ByselectingtheAuto P-M3 HingePropertyinFigure4.1.3-1 andclickingtheModify/Show Auto Hinge Assignment Data button,thewindowshowninFigure4.1.3-2opens. Figure4.1.3-2 showstheAuto Hinge Assignment Data formwithinputparametersforthehingesatthebasesofthecolumnsinthelongitudinaldirection. Duetotheorientationoftheframeelementlocalaxes,theP-M3hingeactsinthelongitudinaldirection.

AutoHingeAssignmentDataforColumnBasesinLongitudinalDirectionFigure 4.1.3-2

ByselectingtheAuto P-M2 HingePropertyinFigure4.1.3-1 andclickingtheModify/Show Hinge Assignment Data buttoninFigure4.1.3-1,thewindowshowninFigure4.1.3-3opens.Figure4.1.3-3showsthe Auto Hinge Assignment Data form withinputparametersforthehingesatthebases ofthecolumnsinthetransversedirection. Duetotheorientationoftheframeelementlocalaxes,theP-M2hingeactsinthetransversedirection.





AutoHingeAssignmentDataforColumnBasesinTransverseDirectionFigure 4.1.3-3

InFigures4.1.3-2and4.1.3-3itisseenthattheHinge Length issetto27.0 inches,theUse Idealized (Bilinear) Moment-Curvature Curve boxischecked,andtheDrops Load After Point E optionisselected.

ThehingesatthetopsofthecolumnsareassignedatrelativedistancesasshowninFigure4.1.3-4(Assign menu > Frame > Hinges).

FrameHingeAssignmentsforColumnTopsFigure 4.1.3-4

ByselectingtheAuto P-M3 HingeProperty inFigure4.1.3-4 andclickingtheModify/Show Auto Hinge Assignment Data button,thewindowshowninFigure4.1.3-5opens. Figure4.1.3-5showstheAuto Hinge Assignment Data formwithinputparametersforthehingesatthetopsofthecolumnsinthelongitudinaldirection. Duetotheorientationoftheframeelementlocalaxes,theP-M3hingeactsinthelongitudinaldirection.





AutoHingeAssignmentDataforColumnTopsinLongitudinalDirectionFigure 4.1.3-5

ByselectingtheAuto P-M2 HingePropertyinFigure4.1.3-4 andclickingtheModify/Show Hinge Assignment Data button,thewindowshowninFigure4.1.3-6opens. Figure4.1.3-6showstheAuto Hinge Assignment Data formwithinputparametersforthehingesatthetopsofthecolumnsinthetransversedirection. Duetotheorientationoftheframeelementlocalaxes,theP-M2hingeactsinthetransversedirection.

AutoHingeAssignmentDataforColumnTopsinTransverseDirectionFigure 4.1.3-6

InFigures4.1.3-5and4.1.3-6itisseenthattheHinge Length issetto26.9 inches,theUse Idealized (Bilinear) Moment-Curvature Curve boxischecked,andtheDrops Load After Point E optionisselected.





4.2 PushoverAnalysis4.2.1 LateralLoadDistributions


Thelateralloaddistributionusedinthisexampleforthepushoveranalysisinthelongitudinaldirectionisadirecthorizontalaccelerationonthestructuremass. Also,thedeadloadcanbeappliedaspreviouslydefinedsincetheentirestructureispresentduringthepushoveranalysis. Itshouldbenotedthatalateralloaddistributionproportionaltothefundamentalmodeshapeinthelongitudinaldirectionisalsoacceptableprovidedthatatleast75%ofthestructuremassparticipatesinthemode. ThisrecommendationisderivedfromprovisionsinFEMA 356:Prestandard and Commentary for the Seismic Rehabilitation of Buildings.


Thelateralloaddistributionusedinthisexampleforthepushoveranalysisin thetransversedirection consistsofahorizontalloadappliedattheequivalentofthecentroidofthesuperstructure. Thisloaddistributionisused tomimicadirecthorizontalaccelerationonthesuperstructuremass. Theloadisappliedthiswaybecause thebentisisolated usingstagedconstructionandthesuperstructureisnotpresentforthetransversepushoverloadcase. Asmentionedabove,alateralloaddistributionproportionaltothefundamentalmodeshapeinthetransversedirectionisalsoacceptableprovidedthatatleast75%ofthestructuremassparticipatesinthemode.

Aspecialloadpatternmustbecreatedforthecolumndeadloadssincetheentirestructureisnotinplaceduringthepushoveranalysis. Anewloadpatterncalled“Dead-Col_Axial”isaddedasshowninFigure4.2.1.2-1 (Define menu > Load Patterns).

“Dead-Col_Axial”LoadPatternDefinitionFigure 4.2.1.2-1

Thecolumnaxialloads are1,250 kips (averageoftopandbottom). Thecolumndeadloadmomentsinthetransversedirectionaresmallandcanbeneglected. Figure4.2.1.2-2showsthejointforcesassignmentwindowforthe“Dead-Col_Axial”loadpattern (Assign menu > Joint Loads > Forces).





JointForceAssignmentforLoadPattern“Dead-Col_Axial”Figure 4.2.1.2-2

AftertheforcesdefinedinFigure4.2.1.2-2havebeenassigned,theycanbeviewedasshowninFigure4.2.1.2-3.

WireframeViewofAssignedForcesforLoadPattern“Dead-Col_Axial”Figure 4.2.1.2-3

Todefinethetransversepushoveranalysislateralloaddistribution,a newloadpatterncalled“Trans_Push”isaddedasshowninFigure4.2.1.2-4 (Define menu > Load Patterns).





“Trans_Push”LoadPatternDefinitionFigure 4.2.1.2-4

Sincethesuperstructureisnotdefined asaspineelement,thereis nojointintheplaneofthebentlocatedatthecentroidofthesuperstructure. Therefore,theloaddistributionforthetransversepushoveranalysisisanequivalenthorizontalloadconsistingofapointloadandamomentappliedatthecentercrossbeam joint. Thecentroidofthesuperstructureislocated58.83inches abovethecenterjoint. Asaresult, a jointforcewithahorizontalpointloadof100kipsandamomentof100*58.83=5,883kip-inches isused. Specialcareshouldbetakentoensurethat theshearandmomentareappliedintheproperdirections. ThejointforcesareassignedtothecrossbeamcenterjointasshowninFigure4.2.1.2-5 (Assign menu > Joint Loads > Forces).

JointForceAssignmentforLoadPattern“Trans_Push”Figure 4.2.1.2-5

AftertheforcesdefinedinFigure4.2.1.2-5 havebeenassigned,theycanbeviewedasshowninFigure4.2.1.2-6.





WireframeViewofAssignedForcesforLoadPattern“Trans_Push”Figure 4.2.1.2-6

4.2.2 LoadCaseSetup


Thedeadload(DC+DW)mustbeappliedpriortoperformingthepushoveranalysis. Todosointhelongitudinaldirection,anewloadcaseiscreatedcalled“LongPushSetup”. Inthisloadcase,thedeadload(DC+DW)isappliedandthecaseisrunasa nonlinearanalysis. Byrunningtheloadcaseasanonlinearanalysistype, anotherloadcasecancontinuefromitwith theloadsstoredinthestructure.

TheLoad Case Data formforthe“LongPushSetup”loadcaseisshowninFigure4.2.2.1-1(Define menu > Load Cases > select LongPushSetup > click Modify/Show Load Case button).





LoadCaseDataforLoadCase“LongPushSetup”Figure 4.2.2.1-1

ItisseeninFigure4.2.2.1-1that theInitial Conditions aresettoZero Initial Conditions – Start from Unstressed State, theLoad Case Type isStatic, theAnalysis Type issettoNonlinear,andtheGeometric Nonlinearity Parameters aresettoNone.

Anewloadcaseisnowcreatedcalled“LongPush”,whichwillactuallybethepushoveranalysiscase. TheLoad Case Data formforthe“LongPush”loadcaseisshowninFigure4.2.2.1-2(Define menu > Load Cases > select LongPush > click Modify/Show Load Case button).





LoadCaseDataforLoadCase“LongPush”Figure 4.2.2.1-2

ItisseeninFigure4.2.2.1-2thattheInitial Conditions aresettoContinue from State at End of Nonlinear Case “LongPushSetup”, theLoad Case Type isStatic, theAnalysis Type isNonlinear,andtheGeometric Nonlinearity Parameters aresetto None. Under Loads Applied,theLoad Type issettoAccel intheUX directionwithaScale Factor equalto-1. ApplyingtheaccelerationinthenegativeX-directionresultsinanegative baseshear and positiveX-directiondisplacements.

ByclickingtheModify/Show buttonfortheLoad Application parametersinFigure4.2.2.1-2,thewindowshowninFigure4.2.2.1-3opens. ItisseeninFigure4.2.2.1-3thattheLoad Application Control issettoDisplacement Control, theLoad to a Monitored Displacement Magnitude of valueissetat 11 inches whichisgreater thanthelongitudinaldisplacementdemandof8.76 inches. Also,theDOF beingtrackedisU1 at Joint 33.

LoadApplicationControlforLoadCase“LongPush”Figure 4.2.2.1-3





ByclickingtheModify/Show buttonfortheResults Saved inFigure4.2.2.1-2, thewindowshowninFigure4.2.2.1-4opens. ItisseeninFigure4.2.2.1-4thattheResults Saved optionissettoMultiple States, theMinimum Number of Saved States issetto22,whichensuresthatastepwilloccurforatleasteveryhalf-inch ofdisplacement. Also,theSave positive Displacement Increments Only boxischecked.

ResultsSavedforLoadCase“LongPush”Figure 4.2.2.1-4


Aswiththelongitudinaldirection,thedeadloadmustbeappliedpriortoperformingthepushoveranalysisinthetransversedirection. However,forthetransversedirection,asinglebentwillbeisolatedusingstagedconstructionpriortoperformingthepushoveranalysis. Todoso,theelementsatPier2areselectedandthenassignedtoa group (Assign menu > Assign to Group). Figure4.2.2.2-1showstheGroup Definition forthegroup“Pier2” (Define menu > Groups > select Pier2 > click Modify/Show Group button).

GroupDefinitionforGroup“Pier2”Figure 4.2.2.2-1

Toisolatethebentandapplythestaticloadstothecolumns,astagedconstructionloadcasecalled“TransPushSetup”iscreated (Define menu > Load Cases > select TransPushSetup > click Modify/Show Load Case button). The“TransPushSetup”analysiscasehastwostages,onetoisolatethebent,andonetoapplythecolumnaxialloads. Notethesetwostagescouldbe





combinedintoonestagewithoutalteringtheresults. Stage1ofthe“TransPushSetup”loadcasedefinitionisshowninFigure4.2.2.2-2.

Stage1LoadCaseDataforLoadCase“TransPushSetup”Figure 4.2.2.2-2

ItisseeninFigure4.2.2.2-2thattheonlyelementsaddedarethoseinthegroup“Pier2”,theInitial Conditions aresettoZero Initial Conditions – Start from Unstressed State, theLoad Case Type isStatic, theAnalysis Type issettoNonlinear Staged Construction,andtheGeometric Nonlinearity Parameters aresettoNone. Stage2ofthe“TransPushSetup”load casedefinitionisshowninFigure4.2.2.2-3.





Stage2LoadCaseDataforLoadCase“TransPushSetup”Figure 4.2.2.2-3

ItisseeninFigure4.2.2.2-3thattheloadpattern“Dead-Col_Axial”isapplied.

Anewloadcaseisnowcreatedcalled“TransPush”,whichwillactuallybethepushoveranalysiscase. TheLoad Case Data formforthe“TransPush”loadcaseisshowninFigure4.2.2.2-4(Define menu > Load Cases > select TransPush > click Modify/Show Load Case button).





LoadCaseDataforLoadCase“TransPush”Figure 4.2.2.2-4

ItisseeninFigure4.2.2.2-4thattheInitial Conditions aresettoContinue from State at End of Nonlinear Case “TransPushSetup”,theLoad Case Type isStatic,theAnalysis Type isNonlinear,andtheGeometric Nonlinearity Parameters aresettoNone. Under Loads Applied,theLoad Type issettoLoad Pattern withtheLoad Name settoTrans_Push and the Scale Factor isequalto1.

ByclickingtheModify/Show buttonfortheLoad Application parametersinFigure4.2.2.2-4,thewindowshowninFigure4.2.2.2-5 opens. ItisseeninFigure4.2.2.2-5 thattheLoad Application Control issettoDisplacement Control,theLoad to a Monitored Displacement Magnitude of valueissetat10 inches,whichislargerthanthetransversedisplacementdemandof6.07 inches. Also, theDOF beingtrackedisU2 at Joint 33.

LoadApplicationControlforLoadCase“TransPush”Figure 4.2.2.2-5





ByclickingtheModify/Show buttonfortheResults Saved inFigure4.2.2.2-4,thewindowshowninFigure4.2.2.2-6opens. ItisseeninFigure4.2.2.2-6thattheResults Saved optionissettoMultiple States,theMinimum Number of Saved States issetto20, whichensuresthatastepwilloccurforatleasteveryhalf-inchofdisplacement. Also, theSave positive Displacement Increments Only boxischecked.

ResultsSavedforLoadCase“TransPush”Figure 4.2.2.2-6

4.2.3 LoadCaseResults


ThesystempushovercurveforthelongitudinaldirectionisshowninFigure4.2.3.1-1(Display menu > Show Static Pushover Curve). Thepointonthecurvewherethebaseshearbeginstodecreaseindicatesthedisplacementatwhichthefirstplastichingereachesitscurvaturelimitstate andisthedisplacementcapacityofthestructure.

PushoverCurveforLoadCase“LongPush”Figure 4.2.3.1-1





Figures4.2.3.1-2through4.2.3.1-13 showthedeformedshapeofthestructureatvariousdisplacementsfortheloadcase“LongPush” (Display menu > Show Deformed Shape > selectLongPush > click OK button). Notethattheplastichingecolorschemetermssuchas“IO”,“LS”,and“CP”areinreference toperformancebaseddesignofbuildingstructures. However,forCaltransplastichinges,thecolorsarediscretizedevenlyalongtheplasticdeformation.Therefore,thecolorschemestillprovidesavisualrepresentationofthehingeplasticstrainprogressionthatisuseful.

ViewofDeformedShapefortheLoadCase“LongPush”atUX=0.0 in.Figure 4.2.3.1-2





ViewofDeformedShapefortheLoad Case“LongPush”atUX=4.9 in.Figure 4.2.3.1-7






View ofDeformedShapefortheLoadCase“LongPush”atUX=10.7 in.Figure 4.2.3.1-13


Thesystempushovercurveforthetransverse directionisshowninFigure4.2.3.2-1(Display menu > Show Static Pushover Curve). Thepointonthecurvewherethebaseshearbeginstodecreaseindicatesthedisplacementatwhichthefirstplastichingereachesitscurvaturelimitstate andisthedisplacementcapacityofthestructure.





PushoverCurveforLoadCase“TransPush”Figure 4.2.3.2-1

Figures4.2.3.2-2through4.2.3.2-13 showthedeformedshapeofthestructureatvariousdisplacementsfortheloadcase“TransPush” (Display menu > Show Deformed Shape > selectTransPush > click OK button). Notethattheplastichingecolorschemeterms suchas“IO”,“LS”,and“CP”areinreferencetoperformance-baseddesignofbuildingstructures. However,forCaltransplastichinges,thecolorsarediscretizedevenlyalongtheplasticdeformation.Therefore,thecolorschemestillprovidesavisualrepresentationofthehingeplasticstrainprogressionthatisuseful.





ViewofDeformedShapefortheLoadCase“TransPush”atUY=0.0 in.Figure 4.2.3.2-2







ViewofDeformedShapefortheLoadCase“TransPush”atUY= 5.1 in.Figure 4.2.3.2-7





5. CodeRequirements5.1 P-Δ CapacityRequirementCheckTherequirementsofsection4.11.5oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbesatisfiedoranonlineartimehistoryanalysisthatincludesP-Δ effects mustbeperformed. Therequirementisasfollows:

PdlΔr ≤ 0.25 MpWhere:

Pdl = unfactoreddeadloadactingonthecolumn(kip)= 1,250 kips

Δr = relativelateraloffsetbetweenthepointofcontraflexureandthefurthestendoftheplastichinge(in.)= ΔL

D /2 (Assumedsincetheinflectionpointislocatedatapproximatelymid-heightofthecolumn. Iftherequirementsarenotmet,amoreadvancedcalculation of Δr willbeperformed)

Mp = idealizedplasticmomentcapacityofreinforcedconcretecolumnbaseduponexpectedmaterialproperties(kip-in.)

= 78,560 kip-in. (SeeFigure3.1.2-1)

5.1.1 LongitudinalDirection

0.25Mp= 0.25 * 78,560= 19,640 kip-in.

Δr = ΔLD_Long /2

= 8.76 /2= 4.38 in.

PdlΔr = 1,250 * 4.38= 5,475 kip-in. < 0.25Mp =19,640 kip-in. =>Okay

5.1.2 TransverseDirection

Δr = ΔLD_Trans /2

= 6.07 /2= 3.04 in.

PdlΔr = 1,250 kips*3.04= 3,800 kip-in. < 0.25Mp =19,640 kip-in. =>Okay





5.2 MinimumLateralStrengthCheckTherequirementsofSection8.7.1oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbesatisfied. Therequirementisasfollows:

Mne ≥ 0.1Ptrib (Hh +0.5Ds) / ΛWhere:

Mne = nominalmomentcapacityofthecolumnbaseduponexpectedmaterialpropertiesasshowninFigure8.5-1 oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design (kip-in.)

Ptrib = greaterofthedeadloadpercolumnorforce associatedwiththetributaryseismicmasscollectedatthebent(kip)

Hh = theheightfromthetopofthefootingtothetopofthecolumnortheequivalentcolumnheightforapileextension(in.)

= 34.0 * 12 (Topoffootingtotopofcrossbeam)= 408in.

Ds = depthofsuperstructure(in.)= 7.083 * 12= 85in.

Λ = fixityfactor (SeeSection4.8.1oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design)

= 2forfixedtopandbottom

DeterminePtrib:

Sincetheabutmentsarebeingmodeledasfreeinthelongitudinaldirection,alloftheseismicmassiscollectedatthebentsinthelongitudinaldirection. Therefore,theforceassociatedwiththetributaryseismicmasscollectedatthebentisgreaterthanthedeadloadpercolumn andiscomputedasfollows:

Ptrib = WeightofStructure/#ofbents/#ofcolumnsperbent= 6,638 /2/2= 1,660 kips

Note that amoresophisticatedanalysistodeterminethetributaryseismicmasswouldbenecessaryif thebridgewerenotsymmetricandthebentsdidnothaveequalstiffness.

DetermineMne:

Section8.5oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design definesMneastheexpectednominalmomentcapacitybasedontheexpectedconcreteandreinforcingsteelstrengths whentheconcretestrainreachesamagnitudeof0.003. SectionDesignerinSAP2000canbeusedtodetermineMne byperformingamoment-curvatureanalysisanddisplayingthemomentwhentheconcretereachesastrainof0.003. Themoment-curvature diagramforthecolumnsectionisshowninFigure5.2-1withvaluesdisplayedataconcretestrainof0.002989(Define menu > Section Properties > Frame Sections > select COL > click Modify/Show





Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve).

Moment-CurvatureCurve forFrameSection “COL” at εc =0.003Figure 5.2-1

ItisseeninFigure5.2-1 thatMne = 73,482 kip-inches.

PerformCheck:

0.1Ptrib (Hh +0.5Ds) / Λ = 0.1*1,660 *(408 +0.5*85)/2= 37,392 kip-in. < 73,482 kip-in. = Mne =>Okay





5.3 StructureDisplacementDemand/Capacity CheckTherequirementsofSection4.8oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbesatisfied. Therequirementisasfollows:

ΔLD < ΔL

CWhere:

ΔLD = displacementdemandtakenalongthelocalprincipalaxisoftheductile

member(in.)

ΔLC = displacement capacity taken along the local principal axis corresponding to ΔL

Doftheductilemember(in.)

5.3.1 LongitudinalDirection

Fromsection3.3.2.1,thedisplacementdemandinthelongitudinaldirectionisΔLD_Long = 8.73

inches.

Determine ΔLC_Long:

ThedisplacementcapacitycanbedeterminedfromthepushovercurveasshowinFigure5.3.1-1(Display menu > Show Static Pushover Curve).

PushoverCurveforLoadCase“LongPush”Figure 5.3.1-1

Thedisplacementatwhichthefirsthingeruptures(fails)isthedisplacementcapacityofthestructure andisalsothe pointatwhichthebaseshearbeginstodecrease. ItcanbeseeninFigure5.3.1-1thatthebasesheardoesnotdecrease untila displacementofapproximately 11 inches.Thissuggests thedisplacementcapacityofthebridge inthelongitudinaldirectionisgreaterthan





thedisplacementdemand. Toconfirmthis,thetableshowninFigure5.3.1-2canbedisplayedbyclickingFile menu > Display Tables inFigure5.3.1-1.

PushoverCurveTabularDataforLoadCase“LongPush”Figure 5.3.1-2

Figure5.3.1-2showsthestep,displacement,baseforce,andhingestatedataforthelongitudinalpushoveranalysis. Bydefinition,hingesfailiftheyareinthe“BeyondE”hingestate. InFigure5.3.1-2itcanbeseenthatstep23isthefirststepany hingesreachthe“BeyondE”hingestate.Therefore, ΔL

C_Long = 10.69 inches andthefollowingcanbestated:

ΔLC_Long = 10.69 in. > ΔL

D_Long = 8.76 in. => LongitudinalDisplacementDemand/CapacityisOkay

5.3.2 TransverseDirection

FromSection3.3.2.2 ofthisexample,thedisplacementdemand inthetransversedirectionisΔL

D_Trans = 6.07 inches.

Determine ΔLC_Trans:

ThedisplacementcapacitycanbedeterminedfromthepushovercurveasshowinFigure5.3.2-1(Display menu > Show Static Pushover Curve).





PushoverCurveforLoadCase“TransPush”Figure 5.3.2-1

Asmentionedabove,thedisplacementatwhichthefirstplastichingeruptures(fails)isthedisplacementcapacityofthestructure andisalsothepointatwhichthebaseshearbeginstodecrease. ItcanbeseeninFigure5.3.2-1 thatthebasesheardoesnotdecreaseuntiladisplacementofapproximately 9.5 inches. Thissuggeststhedisplacementcapacityofthebridgeinthetransversedirectionisgreaterthanthedisplacementdemand. Toconfirmthis,thetableshowninFigure5.3.2-2 canbedisplayedbyclickingFile menu > Display Tables inFigure5.3.2-1.





PushoverCurveTabularDataforLoadCase“TransPush”Figure 5.3.2-2

Figure5.3.2-2 showsthestep,displacement,baseforce,andhingestatedataforthetransversepushoveranalysis. Recallthetransversepushoveranalysisonlyincludesasinglebent. Bydefinition,hingesfailiftheyareinthe“BeyondE”hingestate. InFigure5.3.2-2 itcanbeseenthatstep21isthefirststepanyhingesreachthe“BeyondE”hingestate. Therefore, ΔL

C_Trans =9.51 inches andthefollowingcanbestated:

ΔLC_Trans = 9.51 in.>ΔL

D_Trans = 6.07 in. => TransverseDisplacementDemand/CapacityisOkay





5.4 MemberDuctilityRequirement CheckTherequirementsforhingeductilitydemandsinSection4.9oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbemetforallhingesinthestructure. Thememberductilitydemandmaybecomputedasfollows:

μD ≤ 6(formultiplecolumnbents)Where:

μD = ductilitydemand= 1 + Δpd / Δyi

Δyi = idealizedyielddisplacement(doesnotincludesoileffects)(in.)= φyi * L2 /3

L = lengthfrompointofmaximummomenttotheinflectionpoint(in.)

φyi = idealizedyieldcurvature(1/in.)

Δpd = plasticdisplacementdemand(in.)= θpd *(L– 0.5*Lp)

θpd = plasticrotationdemanddeterminedbySAP2000(rad.)

Lp = plastichingelength(in.)

Therefore:μD = 1 + 3 * [θpd / (φyi *L)]*(1– 0.5 * Lp /L)

Thisexamplewillexplicitlyshowhowtocomputetheductilitydemandforthelowerhingeofthetrailingcolumnbeingdeflectedinthetransversedirection. Theductilitydemandsfortheremaininghingesarepresentedintabularformat.

DetermineL:

Thelocations oftheinflectionpointswereapproximatedpreviouslytodeterminethehingelengths. However,nowthatthepushoveranalysishasbeenperformed,theactualinflectionpointscanbedetermined.

Figure5.3.2-2showsthatatstep13thedisplacementis6.11inches,whichisslightlygreaterthanthedisplacementdemand. Figure5.4-1showsthecolumnmoment2-2diagramat step13 oftheTransPushloadcaseasdisplayedinSAP2000(Display menu > Show Forces/Stresses > Frames/Cables > select TransPush > select Moment 2-2 > select Step 13 > click OK button).





Frame Moment 2-2DiagramforLoadCase“TransPush” at Step 13Figure 5.4-1

Fromthisinformationitisfoundthattheinflectionpointis59 inches abovethelowerjointonthemiddlecolumnelementandthefollowingiscomputed:

L = Lengthfrompointofmaximummomentatbaseofcolumntoinflectionpoint= LengthofLowerElement– FootingOffset+59= 146 – 30+59= 175 in.

Determine θpd:

Sincethedisplacementofthebentatstep13isgreaterthanthedisplacementdemand,theplasticrotationatstep13isgreaterthanor equaltotheplasticrotationdemand. The plasticrotationateachstepcanbefounddirectlyfromthehingeresults inSAP2000. Thenameofthelowerhingeonthetrailingcolumnis1H1. Figure5.4-2showstheplasticrotationplotofhinge1H1atstep13 oftheTransPushloadcase(Display menu > Show Hinge Results > select hinge 1H1 (Auto P-M2) > select load case TransPush > select step 13 > click OK button).





Hinge“1H1”PlasticRotationResultsforLoadCase“TransPush”atStep13Figure 5.4-2

Figure5.4-2showsthattheplasticrotationforhinge1H1is0.0129 radians. Therefore θpd =0.0129 radians.

Determineφyi:

Theidealizedyieldcurvaturewillbefoundby determiningtheaxialloadinthehingeatfirstyieldandtheninputtingthatloadintoSectionDesigner. Theaxialloadatyieldcanbefoundbyviewingthehingeresults atstep4 (whenthehingefirstyields). Figure5.4-3showstheaxialplasticdeformationplotofhinge1H1atstep4 oftheTransPushloadcase(Display menu > Show Hinge Results > select hinge 1H1 (Auto P-M2) > select load case TransPush > select step 4 > select hinge DOF P > click OK button).





Hinge“1H1”AxialPlasticDeformationResultsforLoadCase“TransPush”atStep 4

Figure 5.4-3

Figure5.4-3showsthattheaxialloadinhinge1H1atstep4 oftheTransPushloadcaseis-432kips. ThatloadcannowbeenteredintoSectionDesignertodeterminetheidealizedyieldcurvature, φyi. Themoment-curvaturediagramforthecolumnsectionwithP=-432 kipsisshowninFigure5.4-4(Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve).





Moment-CurvatureCurve forFrameSection“COL”atP=-432 kipsFigure 5.4-4

Figure5.4-4showsthatPhi-yield(Idealized)=.00009294. Therefore: φyi = 0.00009294 inches-1.

Theductilitydemandinthetransversedirectionforthelowerhingeinthetrailingcolumncannowbecalculatedasfollows:

μD = 1 + 3 * [θpd / (φyi *L)]*(1– 0.5 * Lp /L)Where:

L = 175in.

φyi = 0.00009294 in.-1

θpd = 0.0129 rad.

Lp = 27.0 in.

Therefore:μD = 1+3*[0.0129 /(0.00009294 *175)]*(1– 0.5 * 27.0 /175)

= 3.2 <6=>okay

TheductilitydemandsandrelatedvaluesforallcolumnhingesareshowninTable5.4-1.





PushoverDirection

ColumnandHingeLocation

HingeName

YieldStep

AxialLoadatYield

φyi θpd Lp L μD

(Long/Trans) (-) (-) (#) (kips) (1/in.) (rad.) (in.) (in.) (-)

Longitudinal TrailingLower 1H2 5 -1222 .0000889 .0207 27.0 175 4.7

Longitudinal TrailingUpper 3H2 6 -1135 .00008926 .0204 26.9 175 4.6

Longitudinal LeadingLower 7H2 6 -1354 .00008851 .0195 27.0 175 4.5

Longitudinal LeadingUpper 9H2 8 -1277 .0000887 .0168 26.9 175 4.0

Transverse TrailingLower 1H1 4 -432 .00009294 .0129 27.0 175 3.2

Transverse TrailingUpper 3H1 5 -305 .00009292 .0118 26.9 175 3.0

Transverse LeadingLower 4H1 6 -2226 .00009185 .0104 27.0 175 2.8

Transverse LeadingUpper 6H1 7 -2253 .00009186 .00902 26.9 175 2.6

DuctilityDemandsforAllColumnHingesTable 5.4-1

Table5.4-1showsthatallhingeductilitydemandsarelessthan6.





5.5 ColumnShearDemand/CapacityCheckThecolumnshearrequirementsinSection8.6oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbemetforallcolumnsinthestructure.

φsVn ≥ Vu

Where:φs = 0.9Vn = nominalshearcapacity(kips)

= Vc +Vs

ConcreteShearCapacity:Vc = concretecontributiontoshearcapacity (kips)

= vcAeWhere:

Ae = 0.8AgAg = grossareaofmembercross-section(in.2)

vc ifPu iscompressive:vc = 0.032 α’ [1 + Pu /(2Ag)]f’c1/2 ≤ min ( 0.11 f’c1/2 , 0.047 α’ f’c1/2)

vc otherwise:vc = 0

Forcircularcolumnswithspiralreinforcing:

0.3 ≤ α’ = fs /0.15+3.67- µD ≤ 3fs = ρsfyh ≤ 0.35ρs = (4Asp)/(sD’)

Where:Pu = ultimatecompressiveforceactingonsection(kips)Asp = areaofspiral(in.2)s = pitchofspiral(in.)D’ = diameterofspiral(in.)fyh = nominalyieldstressofspiral(ksi)f’c = nominalconcretestrength(ksi)µD = maximumlocalductilitydemandofmember

SteelShearCapacity:

Vs = steelcontributiontoshearcapacity(kips)Vs = (π / 2) (Asp fyh D’)/s

Thisexamplewillexplicitlyshowhowtoperformthesheardemand/capacitycheckforthetrailingcolumnbeingdeflectedinthetransversedirection. Thesheardemand/capacitychecksfortheremainingcolumnsarepresentedintabularformat.

DetermineVu:





Figure5.5-1showsthecolumnsheardiagramfortheTransPushloadcaseasdisplayedinSAP2000(Display menu > Show Forces/Stresses > Frames/Cables > select TransPush >select Shear 3-3 > select Step 13 > click OK button).

FrameShear3-3DiagramforLoadCase“TransPush”atStep13Figure 5.5-1

FromFigure5.5-1itisdeterminedthattheplasticshearinthetrailingcolumnis389 kips.Section8.6.1statesthatVu shallbedeterminedonthebasisofVpo,whichistheshearassociatedwiththeoverstrengthmoment,Mpo,definedinSection8.5oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design. ForASTMA706reinforcementtheoverstrengthmagnifieris1.2,andsotheshearfortheSAP2000modelmustbemultipliedbythisfactor.

Therefore:Vu = λmo Vp

Where:λpo = 1.2Vp = 389 kips

andVu = 1.2 * 389

= 467 kips

DetermineVc:

Figure5.5-2showsthecolumnaxialloaddiagramfortheTransPushloadcaseasdisplayedinSAP2000(Display menu > Show Forces/Stresses > Frames/Cables > select TransPush >select Axial Force > select Step 13 > click OK button).





Frame AxialForce DiagramforLoadCase“TransPush”atStep13Figure 5.5-2

FromFigure5.5-2 itisdeterminedthattheaxialforceinthetrailingcolumnis-247 kips.

Therefore:Pu = 247 kipsAg = π * 602 /4

= 2827.4in.2

Ae = 0.8Ag= 0.8 * 2827.4= 2262in.2

Asp = 0.44in.2s = 3.5in.

D’ = 60 – 1.5 – 1.5 – 0.75= 56.25in.

fyh = 60ksif’c = 4ksiρs = (4Asp)/(sD’)

= (4*0.44)/(3.5*56.25)= 0.0089

fs = ρsfyh ≤ 0.35= 0.0089 * 60 ≤ 0.35= 0.54 ≤ 0.35= 0.35 ksi





µD = 3.2(seeSection5.4ofthisexample)

0.3 ≤ α’ = fs /0.15+3.67- µD ≤ 3= 0.35/0.15+3.67– 3.2 ≤ 3= 0.35/0.15+3.67– 3.2 ≤ 3= 2.8 ≤ 3

α’ = 2.8

vc = 0.032 α’ [1 + Pu /(2Ag)]f’c1/2 ≤ min ( 0.11 f’c1/2 , 0.047 α’ f’c1/2)= 0.032*2.8*[1+247 /(2*2827.4)]41/2 ≤ min(0.11*41/2,0.047*2.8*41/2)= 0.187 ≤ min (0.22 , 0.263)= 0.187 ksi

Vc = vcAe= 0.187 * 2262= 423 kips

DetermineVs:Vs = (π / 2) (Asp fyh D’)/s

= (π / 2) (0.44 * 60 * 56.25)/3.5= 666 kips

Determine φsVn:

φsVn = φs (Vc +Vs)= 0.9*(423 +666)= 980 kips>Vu = 467 kips=> okay

ThesheardemandsandcapacitiesandrelatedvaluesforallcolumnsareshowninTable5.5-1.

PushoverDirection Column Vp Vu Pu µD α' vc Vc Vs φsVn

(Long/Trans) (-) (kips) (kips) (kips) (-) (-) (ksi) (kips) (kips) (kips)Longitudinal Trailing 484 581 1175 4.7 1.3 0.10 228 666 804Longitudinal Leading 497 596 1320 4.5 1.5 0.12 268 666 841Transverse Trailing 389 467 247 3.2 2.8 0.19 423 666 980Transverse Leading 580 696 2253 2.8 3.0 0.22 498 666 1047

ColumnShearDemandsandCapacitiesTable 5.5-1

Table5.5-1showsthattheshearcapacitiesaregreaterthanthesheardemandsforallcolumns.





5.6 BalancedStiffnessandFrameGeometryRequirement CheckThebalancedstiffnessandbalancedframegeometryrequirementsofSections4.1.2and4.1.3oftheAASHTO Guide Specifications for LRFD Seismic Bridge Design mustbemet. Duetothesymmetryofthisexample,theserequirementsareokaybyinspection. However,onmanybridgestheserequirementsmay highlyinfluencethedesign.



4.99 ReferencesAASHTO LRFD Bridge Design Specifications,6thEdition,2012

AASHTOGuide Specifications for LRFD Seismic Bridge Design,2ndEdition,2011

AASHTOGuide Specifications for Seismic Isolation Design,3rdEdition,2010

CaltransBridge Design Aids144JointShearModelingGuidelinesforExistingStructures,CaliforniaDepartmentofTransportation,August2008

FHWASeismic Retrofitting Manual for Highway Structures: Part 1 Bridges,PublicationNo.FHWA-HRT-06-032,January2006

McLean,D.I.andSmith,C.L.,Noncontact Lap Splices in Bridge Column-Shaft Connections,ReportNumberWA-RD417.1,WashingtonStateUniversity

WSDOTGeotechnical Design ManualM46-03,EnvironmentalandEngineeringProgram,GeotechnicalServices,WashingtonStateDepartmentofTransportation

http://www.dot.ca.gov/hq/esc/techpubs/manual/bridgemanuals/bridge-design-aids/bda.html





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