Structural Implication Tensioned Prestressed Concrete

Structural Implication of Post‐Tensioned Ducts in Prestressed Concrete Girders

By Josh Massey

First Reader: _________________ Oguzhan Bayrak

Second Reader: _________________

James Jirsa

JoshMassey ARE679HThesis 5/9/12

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TABLE OF CONTENTS

1 INTRODUCTION 1

2 SPLICED GIRDER TECHNOLOGY 2

2.1 Basic Description ...................................................................................................................... 2

2.2 Comparison to Segmental Box Girders ..................................................................................... 2

2.3 Benefits of Spliced Girder Technology ...................................................................................... 3

2.4 Applications ............................................................................................................................. 3

3 LITERATURE REVIEW 5

3.1 Shear Strength of Post‐Tensioned Members ............................................................................. 5

3.1.1 Shear Strength Modeling ..................................................................................................... 5

3.1.2 Effects of Post‐Tensioning Ducts on Shear Strength .............................................................. 6

3.1.3 Relevant Parameters ........................................................................................................... 6

3.1.4 Need for HDPE Duct Data ..................................................................................................... 7

3.2 Results from Literature ............................................................................................................ 8

3.2.1 Current Code Provisions ...................................................................................................... 8

3.2.2 Panel Tests by Muttoni ........................................................................................................ 9


iii

4 EXPERIMENTAL PROGRAM 10

4.1 Specimen Design .................................................................................................................... 10

4.2 Casting ................................................................................................................................... 11

4.3 Test Setup .............................................................................................................................. 12

4.4 Variables Tested .................................................................................................................... 13

4.4.1 Grouted Versus Ungrouted Ducts ....................................................................................... 13

4.4.2 Plastic Versus Steel Ducts .................................................................................................. 13

4.4.3 Size Effects ........................................................................................................................ 13

5 RESULTS 14

5.1 Ungrouted Ducts .................................................................................................................... 14

5.2 Steel Ducts ............................................................................................................................. 16

5.3 Plastic Ducts .......................................................................................................................... 17

5.4 Size Effects ............................................................................................................................. 18

6 CONCLUSIONS 20

8 BIBLIOGRAPHY 21

APPENDIX A: TABULATED RESULTS 22


1

1 Introduction

Prestressed concrete girders are used extensively to support bridge decks in

highway bridges. Themaximum length of a typical prestressed concrete girder is

generallylimitedtowhatcanbetransportedsafelybytruckstotheconstructionsite

– approximately 160 feet.With the use of post‐tensioned strands placed in ducts

castintothegirders,multiplepretensionedconcretegirderscanbesplicedtogether

to form a continuous member along the length of a bridge, allowing greater

structural continuity and more efficient use of materials. However, due to the

location of the ducts in the relatively thinweb regionsof the girders, new failure

modescancontroltheshearstrengthofthemembers.Thestructuralimplicationsof

corrugated steel and plastic ducts cast in the web regions of spliced Tx‐Girders

under the effects of compressive loading are studied in this report. Splicedgirder

technologyisdetailedinchapter2.AliteraturereviewofcurrentU.S.provisionsfor

designof splicedgirdersandhowtheyaremodeled isprovided inChapter3.The

experimental program is described in chapter 4. The experimental results and

conclusionsarediscussedinchapters5and6respectively.


2

2 Spliced Girder Technology

2.1 Basic Description

Splicing isessentiallyamethodwherebygirders thatwouldnormallybe too

heavy or large to transport may be created on‐site from precast segments. Once

spliced together using cast‐in‐place concrete, the structure is generally post‐

tensionedtoimprovethestructuralperformanceofthesplicedregions(Castrodale

&White, 5). Since their first use inNorthAfrica in 1944, over 250 spliced girder

bridgeshavebeenerected. IntheUnitedStates,splicingtechnologyhasbeenused

mostcommonlyinFlorida,Washington,Oregon,andColorado,thoughafairnumber

ofbridgeshavebeenbuiltinotherstates(Castrodale&White,17).

2.2 Comparison to Segmental Box Girders

Spliced girder construction is essentially similar to segmental box girder

construction,butseveraldistinctdifferencessetthemapart.Bothmethodsusepost‐

tensionedstrands ingroutedducts tocreatecontinuousmembers from individual

precastpieces.However,precastsegmentsinsplicedgirderconstructiontendtobe

muchlongercomparedtotheoverallspanlength,aregenerallyI‐orU‐shaped,and

are referred to as “girder segments.” Also, segmental box girders are generally

splicedusingmatchcasting,wherebythesurfacestobesplicedinthefieldarecast

withshearkeysdesigned to fit together.Thismethod is lesspreferable tocast‐in‐

placesplicingwhenusinggirdersegmentsduetoopposinganglesintheendregions

induced by camber resulting from eccentric pretensioning force in the individual

girdersegments.Boxgirdersalsotendtohaveanintegralfullwidthdeck,whereas


3

spliced girders are topped with a cast‐in‐place deck after erection (Castrodale &

White,10).

2.3 Benefits of Spliced Girder Technology

When used properly, the spliced girder method can increase span lengths,

reduce overall structural depth and increase construction speeds, in addition to

improving overall aesthetics. Longer spans can allow designers to reduce the

amount of supporting piers, thus diminishing material costs, increasing driver

safety, andhelping to avoidobstacles orwaterwaysbeneath the structure.Useof

precast segments also decreases the amount of falsework and on‐site workers

required,effectivelyreducingconstructiontimeandcosts(Castrodale&White,5).

2.4 Applications

Thereareseveralreasonswhydesignersmaychoosetousesplicedgirdersfora

givenprojectwhetheritisasimpleorcontinuousspanbridge.Ifasimplespanisto

beused,splicedgirdersareoftenmoreeconomicalwhenfull‐lengthprecastgirders

would bedifficult to erect or be transported to the site. In locationswhere roads

leadingtotheconstructionsitewouldbeunabletosupporttheweightorlengthof

trucks carrying a full‐length girder, breaking the girders into smallerpieces tobe

assembledon‐sitemayallow theuseofprecast concretegirders.Contractorsmay

choose touse splicedgirder segments toallowuseof a smaller,moreeconomical

craneduringconstruction,oriflocallyavailableequipmentwouldbeunabletolifta

full‐lengthgirderintoplace.Theprogramrequirementsofsomesituations,suchas

single‐point urban interchanges, call for aminimized girder depth. Use of spliced


4

girder technologycanalleviate transportationproblemsof suchgirderscausedby

theextensivelengthandaddedweightcausedbydecreasingthedepth.Continuous

spanbridgeswithintermediatesupportsarethemosttypicalapplicationofspliced

girders.These include full‐spangirders,whichare joinedabove interior supports;

partialspangirders,whicharesplicedbothbetweenandat interiorsupports;and

haunchedgirders(Castrodale&White,6).Haunchedgirdershavevaryingstructural

depthsthatexpandnearsupportingpiersbyincreasingtheheightofeithertheweb

regionorbottomflangeof themember.Due to the immenseheightandweightof

suchmembers, theyaregenerallyonly feasibleabovenavigablewaterwayswhere

theycanbeassembleddirectlyfromabarge(Castrodale&White,37).


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3 Literature Review

3.1 Shear Strength of Post‐Tensioned Members

3.1.1 Shear Strength Modeling

Strutandtiemodelingisamethodofdeterminingthestrengthofa

reinforcedconcretememberbytreatingthebeamasatrussconsistingofseriesof

concretestruts,whichtransmitcompressiveforces;andsteelties,whichtransmit

tensileforces.Shearstrengthiscomputedbydisregardingthetensilestrengthof

concrete,andassumingcompressiveforceswillbecarriedbyconcretestruts

orientedat45°tothelongitudinalaxis,whichareresistedbytheverticalsteel

stirrupsloadedintension.Ithasbeenshownthattrussmodelswhichassumean

angleof45°areveryconservative,butaretypicallypreciseenoughfordesign

purposes(445R,5).

Compressionfieldtheory(CFT)isamoreadvancedformofstrutandtie

modelingwhichtakesintoaccounttheactualangleatwhichthediagonalstruts

form.TheanglecanbederivedfromMohr’scircleofstrain,andisafunctionofthe

ratioofsteelreinforcementtotheareaofconcreteinboththelongitudinaland

transversedirections(445R,6).

Modifiedcompressionfieldtheory(MCFT)isafurtherrefinementofstrut

andtiemodelingwhichtakesadvantageofcrackedconcrete’slimitedtensile

strength.Themethodalsotakesintoconsiderationthepossibilityoffailuredueto

highlocalizedstressesatcracklocations,aswellastheinfluenceofshearforceson


6

thelongitudinalreinforcement(445R,9).ThoughMCFTcanpredicttheactual

strengthofagivensectiontoahighlevelofprecision,theprocedureisgenerally

viewedtobetootediousfortypicaldesignwork.

3.1.2 Effects of Post‐Tensioning Ducts on Shear Strength

Theintroductionofapost‐tensioningductintothewebregionofagirder

createsanareaoftensilestressaboveandbelowtheductduetothedivergenceof

compressivestressflowaroundtheduct.Thesetensileregionstypicallycausesmall

crackstoformatthetopandbottomoftheduct,whichadvanceoutwardfromthe

ductasloadisincreased,resultinginasplittingfailureofthespecimen(Muttoni,

729).Thereducedstrengthoftheshearsectionistypicallymodeledinoneoftwo

ways:areducedeffectivewidthofweb,orareducedcompressivestrengthofthe

concreteitself(Muttoni,308).

3.1.3 Relevant Parameters

Themainparametersaffectingtheshearstrengthofpost‐tensionedgirders

aretheductmaterial,thestiffnessofthegrout,whetherornottheductisgrouted,

andtheratioofductwidthtotheoverallwebthickness.Posttensioningductsare

commonlyavailableinsteelorhigh‐densitypolyethylene(HDPE)plastic.Plastic

ductsarelesscostlytomanufacture,butresultinalowerstrengththansteelducts

becauseofthelackofbondattheconcrete‐plasticinterface.Thestiffnessofgrout

usedrelativetothestiffnessoftheconcretealsoaffectsthestrengthofthesection.If

thestiffnessofthegroutismuchlowerthanthatofthesurroundingconcrete,more

stresswilltendtoflowthroughthesurroundingconcrete,increasingtheresulting


7

tensilestressaboveandbelowtheduct(Figure1a).If

thestiffnessofthegroutisgreaterthanthatofthe

surroundingconcrete,morestresswilltendtoflow

throughductitself,creatingtensilestressfarther

awayfromthelocationoftheduct(Figure1b).Ducts

withgroutstrengthmostlikethesurrounding

concretewillhavethegreateststrength,because

stressiscarriedmoreuniformlyacrossthethickness

oftheweb.Similarly,ungroutedductsgreatlyreduce

theperformanceofthesection,becausenostress

canbecarriedthroughtheopenductregion.

3.1.4 Need for HDPE Duct Data

Currently,thereisverylittledataontheeffectsofplasticductsonshear

strengthofconcretegirders.Becauseconcretebindstosteelwhilecuring,some

stresscanbetransferredthroughtheductratherthanthroughthesurrounding

concrete,thusincreasingthestrengthofthesection.However,concretewillnot

bindtohigh‐densitypolyethylene,andthereforenostresscanbetransferredatthe

concrete‐HDPEinterface.Becauseofthis,sectionswithHDPEandsteelductswill

havedifferentstrengthcharacteristics,asconfirmedbyprevioustesting(Muttoni,

731).Currentcodeprovisionsdonotdistinguishbetweensteelandplasticductsin

strengthreductioncalculations.

(a) (b)

Figure1:ComparisonofStiffGrout(a)andSoftGrout(b)


8

3.2 Results from Literature

3.2.1 Current Code Provisions

IntheUnitedStates,theprincipalcodesforreinforcedandprecast

concretestructuresareAASHTO,whichgovernstheconstructionofhighway

bridges,andACI318,whichgovernsconcretebuildingdesign.The2010editionof

AASTHOhastwoprovisionsforthecalculationofshearstrengthofmemberswith

imbeddedpost‐tensioningducts:section5.8.6.1forsegmentalconstruction,and

section5.8.2.9forgeneralconstruction.ACIcurrentlyhasnoprovisionsforthe

effectofductsonshearcapacity.InAASHTOLRFD,thereductionfactorsare

implementedbyuseofaweb‐widthreductionfactoroftheform:

1 ∙ Equation1

where istheinnerductdiametertowebthicknessratio,and isafactorto

accountforlossofstrengthduetoductpresence.Forgeneralconstruction, is

equalto½forungroutedductsand¼forgroutedducts.Forsegmental

construction, isequalto1forungroutedductsand½forgroutedducts.The

segmental factorsarehigherduetoalackofredundancyinsegmentalboxgirder

construction,whichcallsforahigherfactorofsafety.


9

3.2.2 Panel Tests by Muttoni PrevioustestswereconductedbyAurelioMuttonietal.atEcole

PolytechniqueFederaledeLausanneinSwitzerland.Thetestscomparedstrengthof

aseriesof12panelscastinthelaboratoryand4panelsextractedfromanactual

bridgegirderinthefield.ThelaboratorypanelsincludedspecimenswithbothHDPE

andsteelducts,someofwhichwereinjectedwithgroutandsomeleftempty.These

werecomparedtotwopanelswithnoductpresent,whichservedascontrols

(Muttoni,734).


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4 Experimental Program

4.1 Specimen Design

Becauseofthelargecostsassociatedwithfull‐scalebeamtesting,full‐scale

webtestswereconductedinordertodeterminethestrengthcharacteristicsofweb

sectionswithsteelandplasticductscomparedtothatofanormalweb.Full‐scale

webspecimensconsistof24”squarepanelsofvaryingwidthtorepresentweb

regionsofdifferentthicknesses.Allpanelscontain#4deformedbarsasrepresented

inFigure.Specimenswithsteelorplasticductscasthorizontallyinthecenterofthe

panelwerecomparedtocontrolspecimenscontainingnoducts.

Figure2:TypicalPanelReinforcement


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4.2 Casting

PanelswerecastatFergusonStructuralEngineeringLabusing30‐footlong

sideformsbolteddowntotwolayersof3/4‐inchplywoodsupportedby4x4lumber

spacedatregularintervals.Partitionformsheldtheductsinplaceduringcasting

separatedindividualpanelsasshowninFigure3.Reinforcementwasheldintoplace

bytyingthemto#2bars,whichweresetintothepartitionforms.Oncetheconcrete

hadhardened,panelswereremovedfromtheformsandsetasideforfurthercuring.

Afterroughlytwoweeks,thepanelswerepositionedwiththeductoriented

verticallyandfilledwithgroutand0.5inchstrandstorepresentpost‐tensioning

steel.Thenumberofstrandsdifferedwitheachsizeofduct,with7strandsin2.5

inchducts,9strandsin3inchducts,and12strandsin3‐5/8inchducts.Thestrands

wereonlyplacedtoaugmentthestiffnessoftheductregion,andwerenotstressed

duringgroutplacement.

Figure3:PanelForms


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4.3 Test Setup

PaneltestswereperformedusingthetestsetupshowninFigure4.The

resistingframeconsistedoftwolargebeamssalvagedfromapriorproject,which

wererestrainedby8steelrods3inchesindiameter.Twohydraulicramswitha

combinedcapacityof4millionpoundswereusedtocreatecompressiveforce,

whichwastransmittedtothepanelusingahighstiffnesstransferbeam.The

transferbeamwasallowedtoslidebyattaching4”by6”piecesofTeflontothe

undersideofthetransferbeam,whichweresupportedbytwopiecesofTeflonglued

tothetopofthetrackbeam.

Figure2:TestingFrame

(a)TopView

(b)SideView


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4.4 Variables Tested

4.4.1 Grouted Versus Ungrouted Ducts

Ductsaregenerallygroutedtopreventtheintrusionofwaterintothetendon,

whichcouldcausecorrosivedamageinstrands.Beforegroutisplaced,thelarge

voidinthewebsectioncreatedbytheductgreatlyreducesthestrengthofthe

member.Bytestingbothgroutedandungroutedspecimens,theirstrengthcanbe

comparedtothatofanunreducedsection,i.e.onewithnoduct.

4.4.2 Plastic Versus Steel Ducts

Becauseconcreteisabletoformabondwithasteelduct,someloadisableto

betransferredintotheductwhengroutispresent.HDPEductsdonotformabond

withtheconcreteandthereforehavedifferentstrengthcharacteristics.Current

codesdonotdistinguishbetweenthem.

4.4.3 Size Effects

Varyingthicknessesofpanelsweretestedtoexploretheeffectsofincreasing

thewebthicknessonstructuralperformance.Thewebsofbulbteegirderscan

easilybemadewiderbyincreasingthedistancebetweensideformsduringcasting.

Theeffectsofwebwidthonoverallstrengthwerecompareddirectlybycasting5,7

and9inchpanelsinoneset.


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5 Results

5.1 Ungrouted Ducts

Whennogroutispresentintheduct,thestrengthofthesectionwasfoundto

beinsignificantlyaffectedbytheductmaterial.Figure5iskeyfigurewhichexplains

theplotsgiveninfigures6through9.ResultsfrombothdatacollectedatFerguson

StructuralEngineeringLab(AppendixA)andpreviousresearchareplottedagainst

thereductionfactorthatwouldbegivenbyACIandAASHTOprovisions,whichwere

discussedinSection3.2.1.Anydatapointsthatfallbelowthelinesrepresentingthe

variouscodeequationswouldbedesignedunconservatively,i.e.theirmodeled

strengthwouldbegreaterthanthatwhichwillbeactuallyattainedinthefield.

AscanbeseeninFigure6,neitherthegeneralorsegmentalprovisionsfor

ungroutedductsadequatelyaccountforthereductioninstrengthduetoanopen

voidbeingpresentinthewebregionofagirder.Becauseavastmajorityofthedata

pointshaveanactualstrengthbelowwhatthecodewouldapplytothesection,any

beamdesignedusingthoseprovisionswouldbedesignedunconservatively.


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Figure3:KeyFigure

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6

ηd(Failure/Control)

δ (DuctDiameter/WebThickness)

FSELData‐Plastic

FSELData‐Steel

PreviousResearch‐Steel

ACI318‐08

AASHTO2010GeneralShear

AASHTO2010SegmentalShear

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6



AASHTO2010SegmentalShear

Figure4:UngroutedDuctResults

CodeReductionFactor

Conservative

Unconservative

1 ∙


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5.2 Steel Ducts

Thoughsteelductswereshowntoperformbetterthanplasticducts,current

reductionfactorsstillmaynotadequatelyaccountforthestrengthreductioncaused

bytheirpresence.Thevastmajorityofpreviousresearchdatawasconductedusing

steelducts.Ourresultsgenerallyagreedwiththesedata,withtheexceptionofafew

outliers,notincludedontheplot,whichmayhavehaddefectswithinthepanelsor

non‐uniformloadingconditions.Theseresultsindicatethatcurrentreduction

factorsmaynotbeadequatetoaccuratelypredicttheshearstrengthofgirderswith

post‐tensionedducts.

Figure5:SteelDuctResults

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6



FSELdata

PreviousResearch

ACI318‐08

AASHTO2010GeneralShear

AASHTO2010SegmentalShear 1 ∙


17

5.3 Plastic Ducts

Priortoourtesting,verylittlelaboratorydatawasavailableontheeffectsof

plasticducts.GiveninFigure7isourexperimentaldataaswellasdatafrom

previousresearch.Becausecurrentcodesdonotaccountforthedifferencebetween

steelandplasticducts,theirstrengthisnotaccuratelymodeledbycurrentcode

provisions.Asexpected,ourcomparisonofsteelductstoplasticducts,givenin

Figure8,foundthatthoughtheductmaterialhadlittleeffectonthestrengthwhen

leftungrouted,ductswhichweregroutedhadsignificantlyhigherstrengthswith

steelductsthanplasticducts.Thisismostlikelybecauseconcretecanforma

chemicalbondwiththesteelductasitcures,allowingamechanismtotransmit

someoftheloadfromthesurroundingconcreteintotheductregion.WhenaHDPE

ductisused,theconcretecannotformabondwiththeduct,andthereforecan

transfermuchlessloadthroughthegroutinsidetheduct.Inordertomodelthis

behaviormoreaccurately,differentfactorsshouldbeimplementedtodistinguish

betweenplasticandsteelducts.

Figure6:PlasticDuctResults

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6



FSELDataPreviousResearchACI318‐08AASHTO2010GeneralShearAASHTO2010SegmentalShear

Figure7:PlasticDuctResults

1 ∙


18

Figure8:ComparisonofPlasticandSteelDuctData

5.4 Size Effects

Inonespecificsetofpanels,5,7,and9inchpanelsweredirectlycompared

againsteachotherusingbothplasticandsteelducts.Thoughdesignersusing

currentcodeprovisionswouldpredictanincreaseinrelativestrengthastheduct

diametertoweb‐thicknessratioisdecreased,ourresults,giveninFigure9,show

thatwhenthewebthicknessisincreased,therelativestrengthactuallydecreased.

Thisisbecausecurrentcodeequationsuseareducedwebwidthtoaccountforthe

presenceofaduct,whichdoesnottakeintoaccountthedifferentfailuremodesof

webregionswithandwithoutducts.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.3 0.35 0.4 0.45 0.5



Steel‐Grouted Plastic‐GroutedSteel‐Ungrouted Plastic‐Ungrouted


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Figure9:DirectComparisonof5,7and9InchPanelData

Whenthereisaductpresentinthemember,thefailuremodeisasplitting

failurewhichisafunctionofthetensilestrengthofconcreteandtheeffectiveheight

oftheshearregionasshowninFigure10.Whennoductispresent,thefailuremode

isacrushingtypefailure,whichisgovernedbythecompressivestrengthofthe

concreteandthewidthofthewebregion.Thesefailuremodesarenotlinearly

dependentononeanother,andthereforeareducedwebwidthisnotaneffective

wayofmodelingthereductioninstrengthduetothepresenceofaduct.Futurecode

provisionsshouldthereforehaveadifferentform,whichtakesintoaccountthe

tensilefailuremode.


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6 Conclusions

Moreinformationonthebehaviorofpost‐tensionedbeamswillberequiredas

splicedgirderbridgesbecomemoreprevalentintheUnitedStates.Currentcode

equationsmaybeunconservative,andneedtoberecalibratedtoaccuratelydepict

thestrengthofmemberswithincreasedwebthicknesses,aswellasbeamswhich

useplasticductsratherthansteel.Itwasshownthatthematerialwhichtheductis

madefromdoesnotaffectsignificantlystrengthwithoutpresenceofgrout.

FurthertestingiscurrentlybeingconductedatFergusonStructuralEngineeringLab

tocorrelatedatacollectedfromfull‐scalepanelteststofull‐scalebeams.Thesedata

willbeusedtoformulatenewequationstobesuggestedtoorganizationswho

dictatebuildingcodessuchastheACIandAASHTO.

Figure10:ComparisonofCrushingandSplittingFailureModes


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8 Bibliography

AASHTO.LRFDBridgeDesignSpecifications.Washington,D.C.:American

AssociationofStateHighwayandTransportationOfficials,2007.ACI318.BuildingCodeRequirementsforStructuralConcrete.FarmingtonHills:

AmericanConcreteInstitute,2008.ACI‐ASCEJointCommittee445.RecentApproachestoShearDesignofStructural

Concrete.FarmingtonHills:AmericanConcreteInstitute,2000Castrodale,R.W.,&White,C.D.(2004).ExtendingSpanRangesofPrecast

PrestressedConcreteGirders(ReportNo.517).RetrievedfromNationalCooperativeHighwayResearchProgramwebsite:http://www.national‐academies.org/trb/bookstore

Hawkins,NeilM.,andDanielA.Kuchma.NCHRPReport579:ApplicationofLRFD

BridgeDesignSpecificationstoHigh‐StrengthStructuralConcreteShearProvisions.NationalCooperativeHighwayResearchProgram,WashingtonD.C.:TransportationResearchBoard,2007.

Hawkins,NeilM.,DanielA.Kuchma,RobertF.Mast,M.LeeMarsh,andKarl‐Heinz

Reineck.NCHRPReport549:SimplifiedShearDesignofStructuralConcreteMembers.NationalCooperativeHighwayResearchProgram,Washington,D.C.:TransportationResearchBoard,2005.

Muttoni,A.,Burdet,O.L.,&Hars,E.(2006).Effectofducttypeonshearstrengthof

thinwebs.ACIStructuralJournal,103(5),729‐35.Muttoni,A.,&Ruiz,M.F.(2008).Shearstrengthofthin‐webbedpost‐tensioned

beams.ACIStructuralJournal,105(3),308‐317.Ronald,H.D.(2001).Designandconstructionconsiderationsforcontinuouspost‐

tensionedbulb‐teegirderbridges.PCIJournal,2001(May‐June),44‐66.


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Appendix A: Tabulated Results

Set and Specimen Number

Actual Specimen Width (in)

Actual Specimen Thickness

(in)

Concretef’c (ksi)

Duct Type

Grout Presence

Inner Duct Diam. (in)

Diameter to

Thickness Ratio

Failure Load (kips)

Failure Load Normalized Against

Control (ηd)

Set1: P5 24 5 6.23 Contr 0 0 625.2 100%

Set1: P7 24 5 6.23 Plastic Grouted 2.37 0.474 409.6 66%

Set1: P9 24 5 6.23 Plastic Grouted 2.37 0.474 403.3 65%

Set1: P4 24 5 6.23 Steel Ungroute 2.5 0.5 267.7 43%

Set1: P6 24 5 6.23 Steel Grouted 2.5 0.5 504.0 81%

Set1: P8 24 5 6.23 Steel Grouted 2.5 0.5 536.3 86%

Set3: P5 23.9375 7 9.39 Contr 0 0 1192.7 100%Set3: P1 24 7.0625 9.39 Plastic Grouted 3 0.424 506.0 42%

Set3: P2 24.125 7.0625 9.39 Plastic Grouted 3 0.425 499.9 41%

Set3: P3 24.125 7 9.39 Plastic Ungroute 3 0.428 294.2 24%

Set3: P6 24.0625 7 9.39 Plastic Grouted 3 0.428 482.4 40%

Set3: P4 23.9375 7 9.39 Steel Ungroute 3 0.428 298.8 25%

Set3: P7 23.9375 7.0625 9.39 Steel Grouted 3 0.425 778.6 65%


Set4: P1 23.875 7.125 8.17 Contr 0 0 1016.9 100%Set4: P2 24 7.125 8.6 Contr 0 0.000 1143.5 100%



Set5: P1 23.75 7 3.62 Contr 0 0 515.4 103%Set5: P2 24 7.0625 3.62 Contr 0 0.000 493.9 97%

Set5: P4 24.125 7 3.62 Plastic Grouted 3 0.428 302.8 60%

Set5: P6 24 7.125 3.62 Plastic Grouted 3 0.421 328.9 64%


Set5: P5 24 7.125 3.62 Steel Grouted 3 0.421 422.8 82%



Set7: P1 23.9375 7 10.15 Contr 3 0.428 1217.0 100%Set7: P2 23.9375 7 10.62 Contr 3 0.429 1219.3 100%

Set7: P8 24.1875 7.0625 10.62 Plastic Grouted 2 3/8 0.336 529.4 43%

Set8: P1 23.875 7.125 11.16 Contr 0 0 1643.4 100%Set8: P2 23.875 7 11.16 Contr 0 0.000 1653.7 100%

Set8: P3 24.3125 7.0625 11.16 Plastic Grouted 3 3/8 0.477 456.1 28%


Set9: P2 23.9375 7.125 10.19 Contr 0 0.000 1475.0 93%


Set11: P1 24 9.25 9.25 Contr 0 0 1354.6 96%Set11: P2 24.125 9.1875 9.25 Plastic Grouted 3.375 0.367 528.2 38%

Set11: P3 24.125 9.25 9.25 Steel Grouted 3.375 0.364 750.3 53%

Set11: P4 24 7.25 9.25 Contr 0 0 1461.5 100%


Set11: P7 24.125 5.125 9.25 Contr 0 0.000 842.0 100%

Set11: P8 24.125 5.25 9.25 Plastic Grouted 2.375 0.452 518.2 62%

Set11: P9 24.1875 5.1875 9.25 Steel Grouted 2.375 0.457 709.5 84%


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Structural Implication Tensioned Prestressed Concrete