REU Presentation - Justin Mickey Thomas...
Transcript of REU Presentation - Justin Mickey Thomas...
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
Overview of Today’s PresentationOverview of Today s Presentation
IntroductionIntroductionFabricationTestingTestingResults
Tensile relationshipsTensile relationshipsSoftening coefficients
ConclusionsConclusions
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
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
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
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
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
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
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
Form LayoutForm Layout
ConduitConduitStirrupsTiesTies
Casting PanelsCasting Panels
MixingMixing Slump Test2 Batches2 BatchesCylinder and Beam castingBeam castingVibrating
Cylinder and Beam TestsCylinder and Beam Tests
Cylinder Test:Cylinder Test:Compressive Strength
Beam Test:Crack StrengthCrack Strength
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
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
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
The Universal Element TesterThe Universal Element Tester
37 hydraulic in-yplane jacks
100 tons capacity per jack
Manual control
Computerized controlcontrol
Computerized Control SystemComputerized Control System
Custom controlCustom control boxes by Gardner systems
Capable of Load and Strain control
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
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
InstallationInstallation
Yoke AttachmentYoke Attachment
Pin InsertionPin Insertion
Jack AlignmentJack Alignment
LVDT MountingLVDT Mounting
TestingTesting
Sequential loadingSequential loadingTension in longitudinal directionCompression in transverse directionCompression in transverse direction
Purely axial loadingPurely axial loadingApplied stresses = principle stresses
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
TestingTesting
Monitor:Monitor:Real time stress-strain curvesCrackingCracking
Record crack width manuallyHold tension when ≥ 3/8 inHold tension when ≥ 3/8 in.
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
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
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
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
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
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
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
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
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
Softening CoefficientsSoftening Coefficients
Peak stress-softening coefficientg
'p
fσ
ζσ =
Peak strain-softening coefficientcf
ζσ
εζ p=
Previous research predicts0ε
ζ ε
1=εζ
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
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
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:
30
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
Results: Softening CoefficientsResults: Softening Coefficients
TEF-1TEF 1
497.0=σζ 782.0=εζ
TEF-5
7460ζ579.0=σζ 746.0=εζ
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
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
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+
=
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
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
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
AcknowledgementsAcknowledgements
Thanks to Norm Hoffman, Dr. Mo, Dr. Hsu, Gerald McTigret, and everyone out at South g , yPark