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Constitutive Relationships of Softening Coefficients forConstitutive Relationships of Prestressed Steel Fiber
Reinforced Concrete in Tension
Softening Coefficients for Prestressed Steel Fiber Reinforced Concrete
Justin Mickey
_______________________________
Thomas Kelleher
______________________________
NSF REU Summer Scholars
University of Houstony
August, 2008
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Overview of Today’s PresentationOverview of Today s Presentation
IntroductionIntroductionFabricationTestingTestingResults
Tensile relationshipsTensile relationshipsSoftening coefficients
ConclusionsConclusions
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RelevanceRelevance
Want to predict behavior of prestressed steelWant to predict behavior of prestressed steel fiber reinforced concrete (prestressed SFRC)Applications include: pp
Shear wallsBox bridgesgNuclear containment vesselsOff-shore structures
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RelevanceRelevance
Why steel fiber?Why steel fiber?Reduce or eliminate need for traditional shear reinforcement (stirrups)( p )Less time and labor cost associated with stirrup placement and fabrication p p
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Previous ResearchPrevious Research
Researchers at UH have studied:Researchers at UH have studied:Reinforced ConcreteSteel Fiber Reinforced ConcreteSteel Fiber Reinforced ConcretePrestressed Reinforced Concrete
Currently studying behavior of prestressedCurrently studying behavior of prestressed steel fiber reinforced concrete
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ObjectivesObjectives
For Prestressed SFRC:For Prestressed SFRC:Constitutive relationship in tensionSoftening coefficientsSoftening coefficients
For both we want to:For both we want to:Calculate experimentalCompare w/ previous theoreticalCompare w/ previous theoreticalPropose model
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Mix DesignMix Design
Type I/II CementType I/II Cement
Cement: Water ratio of 1:0 6Cement: Water ratio of 1:0.6
Target Compressive Strength of 6 ksiTarget Compressive Strength of 6 ksi
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Steel Fiber ReinforcementSteel Fiber Reinforcement
TEF-1: 0.5% by weightDramix® ZP305 1 2”x0 022” diameter fibersDramix® ZP305 1.2 x0.022 diameter fibers
TEF 5: 1 5% by weightTEF-5: 1.5% by weightDramix® RC80/60 1.4”x0.03” diameter fibers
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Steel ReinforcementSteel Reinforcement
Transverse Direction:Transverse Direction:10 grade 60 #4 steel rebar
t 2
Longitudinal Direction:TEF 1 : 10 TEF 5 : 5TEF-1 : 10 TEF-5 : 5
0.6 diameter grade 70 steel prestressing tendons
1prestressing tendons
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Form LayoutForm Layout
ConduitConduitStirrupsTiesTies
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Casting PanelsCasting Panels
MixingMixing Slump Test2 Batches2 BatchesCylinder and Beam castingBeam castingVibrating
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Cylinder and Beam TestsCylinder and Beam Tests
Cylinder Test:Cylinder Test:Compressive Strength
Beam Test:Crack StrengthCrack Strength
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What is Prestressing?What is Prestressing?
Improved tensileImproved tensile properties
Residual compressive stress crf
Tensile stress Not to scalecσ
Decompression
Stage T1
cεcεcrε
Stage T2
Compressivestrain
Tensile strain
cxεeco p ess o
)( ii εσ
Stage UC
cσCompressivestress
),( cici εσ
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Prestressing ProcessPrestressing ProcessHydraulic Jack ε σ pif
piεSpecime Concrete
FForce per T d
y
Load Cell
ciε ciσ p pin Force Tendon
TEF-1 -0.000177 -0.8620 ksi
-330 kips 33 kips 152.1 ksi
0.005244
TEF-5 -0.000099 (-0.4317 ksi)
(-165.7 kips)
33.15 kips 152.7 ksi
0.005267Load Cell
TEF-5: LVDTs
ksi) kips) ksi
TEF 5: LVDTs
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Plate AttachmentPlate Attachment
Half-inch steel platesHalf inch steel plates
Prevent cracking outside the measurablePrevent cracking outside the measurable area
Provide bracing for imbedded steel rebar
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The Universal Element TesterThe Universal Element Tester
37 hydraulic in-yplane jacks
100 tons capacity per jack
Manual control
Computerized controlcontrol
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Computerized Control SystemComputerized Control System
Custom controlCustom control boxes by Gardner systems
Capable of Load and Strain control
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Load ControlLoad Control
Load CellsLoad Cells
Real time load readingsReal time load readings
Computer automaticallyComputer automatically adjusts hydraulic pressurep essu e
Useful pre-yieldingUseful pre yielding
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Strain ControlStrain Control
LVDTs(Linear Variable Differential Transformer)
Si l lifiSignal amplifier
Pressure adjustmentsPressure adjustments based on strain readingsg
Allows for postyeilding y gdata acquisition
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InstallationInstallation
Yoke AttachmentYoke Attachment
Pin InsertionPin Insertion
Jack AlignmentJack Alignment
LVDT MountingLVDT Mounting
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TestingTesting
Sequential loadingSequential loadingTension in longitudinal directionCompression in transverse directionCompression in transverse direction
Purely axial loadingPurely axial loadingApplied stresses = principle stresses
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TestingTesting
Loading SequenceLoading Sequence
Test Segment
Description Duration Tensile End Goal
Compressive End GoalSegment
1 Elastic Tensile 15 min. 15 kips 0
2 Release 5 min. 0 0
3 Elastic Compressive 15 min. 0 15 kips
4 Release 5 min. 0 0
5 Tensile 60 min. 45 kips 05 Tensile 60 min. 45 kips 0
6 Tensile mode switch from load-control to strain-control
7 Tensile 60 min. 1.0% strain 0
8 Compressive 90 min. 1.0% strain 85 kips
9 Compressive ~60 min 1.0% strain Failure
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TestingTesting
Monitor:Monitor:Real time stress-strain curvesCrackingCracking
Record crack width manuallyHold tension when ≥ 3/8 inHold tension when ≥ 3/8 in.
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Results: Cylinder/Flexural DataResults: Cylinder/Flexural Data
Obtain properties of concreteObtain properties of concrete6 cylinders & 2 flexural specimens tested for each panelp
Panel E0ε'f fTEF-1 50.6 MPa (7.34 ksi) 0.00239 33.67 GPa (4883 ksi) 824 psi
cE0εcf rf
TEF-5 40.1 MPa (5.82 ksi) 0.00214 29.98 GPa (4348 ksi) 1668 psi
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Results: Tensile BehaviorResults: Tensile Behavior
TEF-1TEF 1
TEF-1 Tension
1.2
1.4
1.6
0.6
0.8
1
Stre
ss (k
si)
0 2
0
0.2
0.4
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012
-0.2
Strain
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Results: Tensile BehaviorResults: Tensile Behavior
TEF-5TEF 5
TEF-5 Tensile
1.2
1.4
1.6
0.6
0.8
1
Stre
ss (k
si)
0 2
0
0.2
0.4
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012
-0.2
Strain
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Results: Tensile BehaviorResults: Tensile Behavior
Embedded Steel Tendon ContributionEmbedded Steel Tendon Contribution
Ef ε= spsps Ef ε=
51
5
⎥⎤
⎢⎡
⎟⎞
⎜⎛ ′′
′′= sps
ps
E
Ef
ε
ε
1⎥⎥
⎦⎢⎢
⎣⎟⎟⎠
⎞⎜⎜⎝
⎛
′+
pu
sps
fE ε
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Results: Tensile BehaviorResults: Tensile Behavior
Prestressed Concrete Steel Fiber Concrete
ciciccc E σεεσ +−′= )(
)( cxccc E εεσ −′′= )(E εσ ′=
5.0
⎟⎞
⎜⎛ ε )3.04.0( Wf−
⎟⎞
⎜⎛ ε
)( ccc E εσ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
c
crcrc f
εε
σc
crcrc f ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
εε
σ
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Results: Tensile BehaviorResults: Tensile Behavior
Proposed Equations:Proposed Equations:
E σεεσ +−′= )(
)(E εεσ ′′=
ciciccc E σεεσ +−= )(
)*02.063.0( Wf−⎞⎛
)( cxccc E εεσ −=
)( f
c
crcrc f ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
εε
σ
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Results: Tensile BehaviorResults: Tensile Behavior
Graphical Comparison of Steel TendonsGraphical Comparison of Steel Tendons
TEF-1 TEF-5TEF-1 TEF-5TEF-1 Steel Tension
300
TEF-5 Steel Tension300
150
200
250
s (k
si)
Experimental 150
200
250
ss (k
si)
Experimental
50
100
150
Stre
ss ExperimentalTheoretical
50
100
Stre
s ExperimentalTheoretical
0-0.001 0.001 0.003 0.005 0.007 0.009 0.011 0.013 0.015
Strain
0-0.001 0.001 0.003 0.005 0.007 0.009 0.011 0.013 0.015
Strain
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Results: Tensile BehaviorResults: Tensile Behavior
Graphical Comparison of ConcreteGraphical Comparison of Concrete
TEF-1 TEF-5TEF-1 TEF-5TEF-1 Concrete Tension
0.9
TEF-5 Concrete Tension
0.9
0 3
0.5
0.7
ksi)
Th i l0.3
0.5
0.7
(ksi
)Theoretical
-0.1
0.1
0.3
-0.0010 0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060
Stre
ss (k Theoretical
Experimental
-0.1
0.1
-0.0010 0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0080
Stre
ss
Experimental
-0.5
-0.3
Strain-0.5
-0.3
Strain
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Softening CoefficientsSoftening Coefficients
Tensile loadingTensile loadingStrains and cracksConcrete weaker in compressionConcrete weaker in compression
Softening coefficients measure this effect atSoftening coefficients measure this effect at given tensile strain
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Softening CoefficientsSoftening Coefficients
Peak stress-softening coefficientg
'p
fσ
ζσ =
Peak strain-softening coefficientcf
ζσ
εζ p=
Previous research predicts0ε
ζ ε
1=εζ
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Factors Affecting Softening Coefficients
Positive effects:Positive effects:% Volume of steel fibers,Aspect ratio, ff DL
fVAspect ratio,
Negative effects:
ff DL
Negative effects:Tensile strainPrestressing steel ratio, plρg , plρ
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Factors Affecting Softening Coefficients
Specimen
TEF-1 0.5% 1.2 in. 0.022 in. 54.5 0.59% 1.0%
plρfV fL fD ff DL lε
Expect TEF 5 to have larger coefficient
TEF-5 1.5% 1.4 in. 0.03 in. 46.7 0.295% 0.9%
Expect TEF-5 to have larger coefficient
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Calculating Softening CoefficientsCalculating Softening Coefficients
Compressive Stress-Strain CurvesCompressive Stress Strain CurvesTEF-1:TEF-5:
2.25=pσ 001712.0=pε
2.23=pσ 001594.0=pεTEF-5:
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TEF-1 TEF-5
2.23pσ pε
15
20
25
ss (M
Pa)
5
10Stre
s
0-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Strain
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Results: Softening CoefficientsResults: Softening Coefficients
TEF-1TEF 1
497.0=σζ 782.0=εζ
TEF-5
7460ζ579.0=σζ 746.0=εζ
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Comparison to TheoreticalComparison to TheoreticalComparison of Stress-Softening Coefficients, σζ
Specimen Tensile Strain
Predicted RC
Predicted Prestressed RC
Predicted SFRC
Experimental Prestressed SFRC
TEF-1 1.0% 0.257 0.365 0.537 0.497
TEF-5 0.9% 0.277 0.420 0.649 0.579
Experimental values seem consistent
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Theoretical for Prestressed RCTheoretical for Prestressed RC
Wang (2006)Wang (2006)
( ) ( ) ( ) 9.01 ≤′= βεζ σ ffff c
Where:
( ) 908.5≤′ff d
'f 'f MP
( )11ε =f
( ) 9.0'≤=
c
cf
ff and cf cf MPa
( )1
1 4001 εε
+f
( ) −= 1β
βf ( )°24
βf
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Theoretical for SFRCTheoretical for SFRC
Mansour (2004):Mansour (2004):Incorporated steel fiber index
M lti li d ti f RC b f t fffff DLVW =
Multiplied equation for RC by factor of
to get:)43.01( fW+
ζ)43.01(9.0 +
= fW
lεζ σ 2501+
=
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Theoretical for Prestressed SFRCTheoretical for Prestressed SFRC
Propose adding a factor to prestressed RCPropose adding a factor to prestressed RC based on steel fiber index:
( ) bmWWf ff +=
Giving:
( ) bmWWf ff +
Giving:
( ) ( ) ( ) ( ) 9.01 ≤′= fc Wfffff βεζ σ
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Theoretical for Prestressed SFRCTheoretical for Prestressed SFRC
Calculating experimental ( )fWfCalculating experimental
Specimen Experimental
TEF-1 0 2727 0 4973 0 8153 0 5345 1 0 4358 1 141
fW σζ ( )cff ′ ( )1εf ( )βf ( ) ( ) ( )βε ffff c 1′ ( )fWf
( )ff
Linear regression:
TEF-1 0.2727 0.4973 0.8153 0.5345 1 0.4358 1.141
TEF-2 0.7000 0.5793 0.9 0.5547 1 0.4992 1.160
Linear regression:
( ) 129.10452.0 += ff WWf ff
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ConclusionsConclusions
CalculatedCalculatedTensile stress-strain relationshipsValues of softening coefficientsValues of softening coefficients
Results appear consistentProposed models for prestressed SFRCProposed models for prestressed SFRC
Based on previous researchMore data neededMore data needed
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AcknowledgementsAcknowledgements
Thanks to Norm Hoffman, Dr. Mo, Dr. Hsu, Gerald McTigret, and everyone out at South g , yPark