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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

Overview of Today’s PresentationOverview of Today s Presentation

IntroductionIntroductionFabricationTestingTestingResultsConclusionsConclusions

RelevanceRelevance

Want to predict behavior of prestressed steelWant to predict behavior of prestressed steel fiber reinforced concrete (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 CementCement: Water ratio of 1:0.6Target 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”Dramix® ZP305 1.2 x0.022

diameter fibers

TEF-5: 1.5% by weightDramix® RC80/60Dramix® 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 : 5

t 2

TEF-1 : 10 TEF-5 : 50.6 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 preyieldingUseful preyielding

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 loadingApplied stresses = principle stressesApplied 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