Tension Stiffening in GFRP RC Beamsci.group.shef.ac.uk/CI_content/FRP/ECF06_RAS.pdfECF16 - Shah...

Tension Stiffening in GFRP RC Beams

Raed Al Sunna(1,2), Kypros Pilakoutas (1),

Peter Waldron(1) and Tareq Al Hadeed(2)

(1) University of Sheffield - UK(2) Royal Scientific Society - Jordan

ECF16 - Shah Symposium (MMMCP)July 3-7, 2006 – Alexandroupolis, Greece


OUTLINE

- Methodology

- Experimental Programme

- Experimental Results

- Background

- Conclusions

BACKGROUND

Serviceability-controlled design

ACI 440.1R-03

IStructE (1999)- Steel RC equations applicable

( ) gcr

crgdcre IMMIIII

a

≤⎥⎥⎦

⎤

⎢⎢⎣

⎡−+=

3

β

⎥⎦

⎤⎢⎣

⎡+= 1

s

fbd E

Eαβ

αb = bond coefficient = 0.5

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40 45 50Midspan Deflection, mm

Forc

e, k

NBG2a

ACI 318

ACI 440.1 R

linear cracked section

β d =0.6, (α b = 0.5)



Key Variables- Reinforcement Ratio

- Modulus of Elasticity

- Bond Characteristics

Other Variables- Concrete cover

- Concrete Strength

- Rebar diameter

BACKGROUND

Ribbed

Ribbed

Braided

Indented

Sand coated

Indented

Helically wrapped



BACKGROUND



NN

L

4

5

3

2

1AsAc c

s

AA

=ρ

ρβ

s

ctm

Ef

1.3Ncr

Ncr

s

ectm

Ef α

ρρα

s

ectm

E

f )6.0( + LLstrain, Average Δ

1 = uncracked stage2 = crack formation stage 3 = stabilized cracking stage4 = yield stage 5 = bare steel rebar

Load, N

fctm = tensile strength of concreteEs = steel modulus Ec = concrete modulus αe = modular ratio = Es / Ec

Load-strain relationship of a steel RC tie (fib 1999)

Experimental:- Structural tests:

(Beams and Slabs, CFRP and GFRP)

- Material tests (Concrete and rebars)

Analytical:- Sectional analysis

- Finite element analysis

METHODOLOGY



76725

0

2300

125

2Ø6mm

125766 767

stirrups,Ø8mm/75mm

2Ø6mm

25m

mto

bar

s

150

stirrups,Ø8mm/75mm

250

EXPERIMENTAL PROGRAMME (GFRP RC Beams)



-

Equal stiffness ofrebars

Equal area ofrebars

Equal flexural capacity

Relation to control steel beam

0.00688

0.0391

0.00772

0.00432

Reinforcement ratio

2∅12

4∅19.05

2∅12.7

2∅9.53

Rebar details

BSbBSa

BS

BG3bBG3a

BG3

BG2bBG2a

BG2

BG1bBG1a

BG1

Beam designation

Series designation

Steel

GFRP

Rebar type




6504200019.056004150012.70650425009.53GFRP

Tensile strength, (MPa)

Modulus of elasticity, (MPa)

Nominal diameter,

(mm)

Rebar type

Steel tubeFRP

rebar Epoxy

Plastic end-piece

Grips of tension

machine




1 2 3 4

15

5 6 7 8 9 10 11 12 13 14

Strain Gauge on RebarStrain Gauge on concrete

Midspan forced crack

Anticipated natural crack

90mm

Anticipated natural crack

90mm

18mm 22.5

mm

Detail of 10 strain gauges, No. (5-14), at

midspan zone.

1/3 shear span

Straight arrangement

Helical arrangement




Dial Gauge

LVDT

12 3

4 5

8

7

6




EXPERIMENTAL RESULTS

Beam BG2a

02000400060008000

1000012000140001600018000

0 250 500 750 1000 1250Distance From Support, mm

Reb

ar S

train

, m

icro

stra

in

80.0 kN

60.0 kN

40.0 kN

20.3 kN (just afteradjacent crack)14.0 kN (just afterfirst crack) 13.3 kN (beforecracking)

Crack Locations

Beam BG2a

0102030405060708090

0 2000 4000 6000 8000 10000 12000 14000 16000Rebar Strain, microstrain

Load

, kN

Strain Gauge 10Strain Gauge 9Strain Gauge 8Strain Gauge 7Strain Gauge 6Strain Gauge 5Cracked-section analysis

109 876 5

Beam BG2a

0102030405060708090

-4000 -3500 -3000 -2500 -2000 -1500 -1000 -500 0Concrete Strain, microstrain

Load

, kN

Strain Gauge 15

Cracked-Section Analysis

Beam BG2a

0102030405060708090

0 0.02 0.04 0.06 0.08Curvature, m-1

Load

, kN

curvature derived from experimental strainsCracked-section analysis



Beam BG2a

0102030405060708090

-50 -40 -30 -20 -10 0Midspan Deflection, mm

Load

, kN

LVDT L6

Cracked-section analysis

Flexural deflections derived fromexperimental curvatures

Beam BG2a

0.00

100.00

200.00

300.00

400.00

500.00

600.00

0 2000 4000 6000 8000 10000 12000 14000 16000

strain, in microstrain

Stre

ss a

t cra

ck, i

n M

Pa

strain at crack

average strain between cracks

Beam BG2a

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

025050075010001250

Distance From Support, mm

Aver

age

Bon

d S

tress

, MPA

80.7365.8355.0534.4822.42

Beam BG2a

0

1

2

3

4

5

6

7

8

0 2000 4000 6000 8000 10000 12000 14000

Average strain, microstrain

Ave

rage

Bon

d, M

Pa

1st crack at crack inducer

two cracks adjacent to crack inducer

Stabilized cracking phase




Beam BG2a

0102030405060708090

0 0.5 1 1.5 2 Crack Width, mm

Load

, kN

LVDT L8

calculated from rebar strains

Measured at bottom concretefibre

Load = 20.8 kNAverage crack width = 0.13 mmStandard Deviation = 0.06

Note: Crack widths in flexure zone, at the bottom concrete fibre.




BC2a

BC2a

BC2a

BC2a




Beams BG, BS

0

20

40

60

80

100

120

140

0 10 20 30 40 50Midspan Deflection [mm]

Load

[kN

]

BG1aBG1bBG2aBG2bBG3aBG3bBSaBSb

ρf = 0.0043

ρf = 0.0077

ρf = 0.039


ρs = 0.0068



TENSION STIFFENING ANALYSIS



Beam Series BG

0

100

200

300

400

500

600

700

0 2000 4000 6000 8000 10000 12000 14000 16000

Average strain, microstrain

Stre

ss a

t cra

ck, M

pa

BG1bBG2aBG3bnaked 9.53 mm rebarnaked 12.7 mm rebarnaked 19 mm rebar




Beginning ofstabilized cracking phase

End ofstabilized cracking phase

Stabilized cracking

phase Beam

ID

Naked rebar modulus, Ef,

“MPa”

Effective Modulus, Eeff,

“MPa” Eeff/ Ef

Effective Modulus, Eeff,

“MPa”

Eeff/ Ef

Average Eeff/ Ef

BG3b 41970 47715 1.14 44548 1.06 1.1 BG2a 41600 49889 1.20 44636 1.07 1.14 BG1b 42750 492280 1.15 45370 1.06 1.11

Tension Stiffening in the Stabilised Cracking Phase

1.6 1.39For steel RC, ρ=1%

For steel RC, ρ=10% 1.31 1.03




NN

L

43

2

1

A

B

AfAc c

f

AA

=ρ

strength tensile concrete ctm

f =

modulus elasticrebar FRP=fE

modulus elastic concrete=cE

ratiomodular c

fe E

E==α

1.3Ncr

Ncr

f

ectm

Ef α

)1( load cracking

ραectmc

crfA

N+=

=

LL

strain, AverageΔ

))((

modulusrebar effective

LL

A

NE

f

eff

Δ=

=

Bpoint at 1.05Apoint at 1.2

f

f

EE

==

1 = uncracked stage 2 = crack formation stage 3 = stabilized cracking stage 4 = naked rebar

NLoad,

Proposed load-strain relationship of a GFRP RC tension tie



Tests of GFRP RC tension ties by Sooriyaararachchi

0

100

200

300

400

500

600

700

800

0 5000 10000 15000 20000

Average rebar strain, microstrain

Reb

ar st

ress

, MPa

Test C52/150/19Test C52/100/13Naked rebarProposed relationship




Midspan Deflection of Beam BG3


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30Midspan Deflection, mm

Load

, kN

Experimental / LVDT L6

Proposed relationship

FINITE ELEMENT ANALYSIS



Beam BG2a

0102030405060708090

-50 -40 -30 -20 -10 0Midspan Deflection, mm

Load

, kN

LVDT L6

Cracked-section analysis

Flexural deflections derived fromexperimental curvaturesFE Analysis

Beam BG2a

02000400060008000

1000012000140001600018000

0 250 500 750 1000 1250Distance From Support, mm

Reb

ar S

train

, m

icro

stra

in

80.0 kN

60.0 kN

40.0 kN

20.3 kN (just after adjacentcrack)14.0 kN (just after first crack)

13.3 kN (before cracking)

FE Analysis

FE Analysis

Crack Locations

Beam BG2a

0102030405060708090

0 2000 4000 6000 8000 10000 12000 14000 16000Rebar Strain, microstrain

Load

, kN

Strain Gauge 10Strain Gauge 9Strain Gauge 8Strain Gauge 7Strain Gauge 6Strain Gauge 5Cracked-section analysisFE Analysis

109 876 5

Beam BG2a

0102030405060708090

-4000 -3500 -3000 -2500 -2000 -1500 -1000 -500 0Concrete Strain, microstrain

Load

, kN

Strain Gauge 15

Cracked-Section Analysis

FE Analysis

FINITE ELEMENT ANALYSIS



CONCLUSIONS

Behaviour of GFRP RC beams:Deflection of GFRP RC is mainly caused by flexural curvatures.

Shear-induced deflections may not be negligible for low reinforcement ratios and deep-penetrating wide cracks.

The response of the compressive concrete zone requires further consideration due to the increased localised effect of cracks.

GFRP RC show good bond.

CSA predicts the maximum rebar strain at a crack, underestimatesthe extreme-fibre concrete strain, and when shear induced deformations are sizeable may not provide an upper-bound deflection.



CONCLUSIONS

Tension Stiffening of GFRP RC beams:Contrary to steel RC, the amount of GFRP reinforcement may have negligible effect on tension stiffening in the stabilised cracking phase

(ρ>0.4%, or ρeff>1.25%)

An average Eeff (1.10 E) offers a reasonable approximation for the whole stabilised cracking phase.

Tension stiffening in GFRP is lower than steel RC, which is due to the high levels of rebar strain involved.

An initial tension stiffening relationship is proposed but needs to be expressed more fundamentally.



ACKNOWLEDGEMENTS

The Higher Council for Science and Technology (Jordan)

The Royal Scientific Society (Jordan)

The University of Sheffield (UK)

The Karim Rida Said Foundation (UK)



Tension Stiffening in GFRP RC Beamsci.group.shef.ac.uk/CI_content/FRP/ECF06_RAS.pdfECF16 - Shah...

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