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
ii
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
JoshMassey ARE679HThesis 5/9/12
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
JoshMassey ARE679HThesis 5/9/12
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.
JoshMassey ARE679HThesis 5/9/12
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
JoshMassey ARE679HThesis 5/9/12
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
JoshMassey ARE679HThesis 5/9/12
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).
JoshMassey ARE679HThesis 5/9/12
5
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
JoshMassey ARE679HThesis 5/9/12
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
JoshMassey ARE679HThesis 5/9/12
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)
JoshMassey ARE679HThesis 5/9/12
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.
JoshMassey ARE679HThesis 5/9/12
9
3.2.2 Panel Tests by Muttoni PrevioustestswereconductedbyAurelioMuttonietal.atEcole
PolytechniqueFederaledeLausanneinSwitzerland.Thetestscomparedstrengthof
aseriesof12panelscastinthelaboratoryand4panelsextractedfromanactual
bridgegirderinthefield.ThelaboratorypanelsincludedspecimenswithbothHDPE
andsteelducts,someofwhichwereinjectedwithgroutandsomeleftempty.These
werecomparedtotwopanelswithnoductpresent,whichservedascontrols
(Muttoni,734).
JoshMassey ARE679HThesis 5/9/12
10
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
JoshMassey ARE679HThesis 5/9/12
11
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
JoshMassey ARE679HThesis 5/9/12
12
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
JoshMassey ARE679HThesis 5/9/12
13
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.
JoshMassey ARE679HThesis 5/9/12
14
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.
JoshMassey ARE679HThesis 5/9/12
15
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
ηd(Failure/Control)
δ (DuctDiameter/WebThickness)
AASHTO2010SegmentalShear
Figure4:UngroutedDuctResults
CodeReductionFactor
Conservative
Unconservative
1 ∙
JoshMassey ARE679HThesis 5/9/12
16
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
ηd(Failure/Control)
δ (DuctDiameter/WebThickness)
FSELdata
PreviousResearch
ACI318‐08
AASHTO2010GeneralShear
AASHTO2010SegmentalShear 1 ∙
JoshMassey ARE679HThesis 5/9/12
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
ηd(Failure/Control)
δ (DuctDiameter/WebThickness)
FSELDataPreviousResearchACI318‐08AASHTO2010GeneralShearAASHTO2010SegmentalShear
Figure7:PlasticDuctResults
1 ∙
JoshMassey ARE679HThesis 5/9/12
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
ηd(Failure/Control)
δ (DuctDiameter/WebThickness)
Steel‐Grouted Plastic‐GroutedSteel‐Ungrouted Plastic‐Ungrouted
JoshMassey ARE679HThesis 5/9/12
19
Figure9:DirectComparisonof5,7and9InchPanelData
Whenthereisaductpresentinthemember,thefailuremodeisasplitting
failurewhichisafunctionofthetensilestrengthofconcreteandtheeffectiveheight
oftheshearregionasshowninFigure10.Whennoductispresent,thefailuremode
isacrushingtypefailure,whichisgovernedbythecompressivestrengthofthe
concreteandthewidthofthewebregion.Thesefailuremodesarenotlinearly
dependentononeanother,andthereforeareducedwebwidthisnotaneffective
wayofmodelingthereductioninstrengthduetothepresenceofaduct.Futurecode
provisionsshouldthereforehaveadifferentform,whichtakesintoaccountthe
tensilefailuremode.
JoshMassey ARE679HThesis 5/9/12
20
6 Conclusions
Moreinformationonthebehaviorofpost‐tensionedbeamswillberequiredas
splicedgirderbridgesbecomemoreprevalentintheUnitedStates.Currentcode
equationsmaybeunconservative,andneedtoberecalibratedtoaccuratelydepict
thestrengthofmemberswithincreasedwebthicknesses,aswellasbeamswhich
useplasticductsratherthansteel.Itwasshownthatthematerialwhichtheductis
madefromdoesnotaffectsignificantlystrengthwithoutpresenceofgrout.
FurthertestingiscurrentlybeingconductedatFergusonStructuralEngineeringLab
tocorrelatedatacollectedfromfull‐scalepanelteststofull‐scalebeams.Thesedata
willbeusedtoformulatenewequationstobesuggestedtoorganizationswho
dictatebuildingcodessuchastheACIandAASHTO.
Figure10:ComparisonofCrushingandSplittingFailureModes
JoshMassey ARE679HThesis 5/9/12
21
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.
JoshMassey ARE679HThesis 5/9/12
22
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%
Set3: P8 24.125 7.0625 9.39 Steel Grouted 3 0.424 720.7 59%
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%
Set4: P5 23.9375 7.125 8.17 Plastic Grouted 3 0.421 401.6 39%
Set4: P6 24.0625 7.125 8.6 Steel Grouted 3 0.421 606.9 53%
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: P8 24 7.125 3.62 Plastic Grouted 3 0.421 414.3 81%
Set5: P5 24 7.125 3.62 Steel Grouted 3 0.421 422.8 82%
Set5: P7 24 7.125 3.62 Steel Grouted 3 0.421 524.9 102%
Set5: P9 24 7.125 3.62 Steel Grouted 3 0.421 560.5 109%
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%
Set8: P7 24 7.125 11.16 Plastic Grouted 3 0.421 535.5 32%
Set9: P2 23.9375 7.125 10.19 Contr 0 0.000 1475.0 93%
Set9: P3 24.0625 7.0625 10.19 Plastic Grouted 3 0.424 548.7 34%
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: P6 23.875 7.25 9.25 Steel Grouted 3 0.414 785.1 54%
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%
JoshMassey ARE679HThesis 5/9/12
23