shear design equations for frp rc beamsci.group.shef.ac.uk/ci_content/frp/frprcs6_03_mg.pdf · beam...
TRANSCRIPT
Centre for Cement and Concrete
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Dr. Maurizio GuadagniniDr. Kypros Pilakoutas
Professor Peter Waldron
Centre for Cement and ConcreteDept. of Civil and Structural Engineering
The University of Sheffield, UK
SHEAR DESIGN EQUATIONSFOR FRP RC BEAMS
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OutlineOutline
• Shear resistance
• Predictive approaches
• Experimental investigation
• New approach
• Validation
• Conclusions
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strutstrut
tie
Ft
Strut and Tie
Arch
Truss
Shear Transfer MechanismsShear Transfer Mechanisms
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Shear ResistanceShear Resistance
V = Vc + VsConcrete
contributionEmpirical equation
concrete in compressionaggregate interlockdowel action
Contribution of shear r/ment+
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1000
2000
%
σ
ε
(MPa)
0 1 2 3
Reinforcing Steel
Prestressing Steel
AFRP
GFRP
CFRP
Shear and FRP r/mentShear and FRP r/ment
microstrain0 3000 6000 9000 12000 15000
Neu
tral a
xis
dept
h(m
m)
50
100
150
200
250
300
Steel RC sectionFRP RC section
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FRP SF F=FRP Sε ε=
FRP FRP FRP FRP S S S SF E A E A Fε ε= ⋅ ⋅ = ⋅ ⋅ =
FRPe FRP
S
EA AE
= ⋅
Predictive ApproachPredictive Approach
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Limiting Strain = 0.2% - 0.25%Predictive ApproachPredictive Approach
1000
2000
%
σ
ε
(MPa)
0 1 2 3
Reinforcing Steel
Prestressing Steel
AFRP
GFRP
CFRP
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• Are the shear mechanisms for steel and FRP RC similar?
• Is it correct to simply add the separate shear contributions from the concrete and reinforcement?
• Is the limiting strain concept valid?
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Experimental programmeExperimental programme
1st phase of testing
2nd phase of testing
Concrete shear
resistance
Shear link contribution
Vc
Vs
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1st Phase of testing1st Phase of testing
Steel RC Beams
AS = 434 mm2
GFRP RC Beams
AFRP = 452 mm2
1000
2300
1800
1000
2300
1800
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1st phase of testing1st phase of testing
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Experimental set-upExperimental set-up
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Displacement (mm)0 2 4 6 8 10 12 14 16 18 20
Load
(kN
)
0
20
40
60
80
100SB 40
GB 43
a/d ~ 3
Typical Load-displacement responseTypical Load-displacement response
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Displacement (mm)0 2 4 6 8 10 12 14 16 18 20
Load
(kN
)
020406080
100120140160180
GB 45
GB 43
GB 44
Load-displacement response forGFRP RC beamsLoad-displacement response forGFRP RC beams
� = shear diagonal failure
a/d ~ 3
a/d ~ 2
a/d ~ 1
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Location of straingage (mm)0 500 1000 1500 2000 2500
0
1000
2000
3000
4000
5000
6000
SB40 (90.59 kN)GB43 (54.16 kN)
Strain distribution along the flexural reinforcementStrain distribution along the flexural reinforcement
Strain approach
New strain level proposedM
icro
stra
in
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2nd phase of testing2nd phase of testing
GFRP linksCFRP links
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Experimental set-upExperimental set-up
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Experimental set-upExperimental set-up
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0 2000 4000 6000 8000
Load
(kN
)
020406080
100120140160
Strain in the flexural reinforcementStrain in the flexural reinforcement
Strain approach
New strain level proposed
Microstrain
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0 2000 4000 6000 8000
Load
(kN
)
020406080
100120140160
Strain in the shear reinforcementStrain in the shear reinforcement
Strain approach
New strain level proposed
Microstrain
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Displacement (mm)0 2 4 6 8 10
Shea
r for
ce (k
N)
0
10
20
30
40
50
60
70
estimatedconcrete
contribution25
00 μ
stra
in(f
lex.
r/m
ent)
2500
μst
rain
(fle
x. r/
men
t - 1
st pha
se)
4500 μstrain (shear r/ment)
2500 μstrain (shear r/ment)SB 40
estimatedshear r/mentcontribution
Decomposition of shear carrying mechanismsDecomposition of shear carrying mechanisms
Beam SB40R
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Displacement (mm)0 5 10 15 20 25 30 35
Shea
r for
ce (k
N)
0
10
20
30
40
50
60
70
estimatedconcrete
contribution
2500 μstrain(shear r/ment - 1st+2nd cycles)
4500 μstrain(shear r/ment - 1st+2nd cycles)
2500
μst
rain
flex.
r/m
ent
(1st p
hase
)
4500
μst
rain
flex.
r/m
ent
(1st
pha
se)
GB 43
estimatedshear r/mentcontribution
4500 μstrain(shear r/ment 3rd cycle)
Beam GB43R
Decomposition of shear carrying mechanismsDecomposition of shear carrying mechanisms
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SB 40 a/d ~ 3 SB 41 a/d ~ 2
GB 43 a/d ~ 3 GB 44 a/d ~ 2
@ 116 kN
@ 103 kN @ 160 kN
@ 180 kN
Types of Shear FailureTypes of Shear Failure
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Shear Crack Width GrowthShear Crack Width Growth
Beam SB40/R Beam GB43/R
Crack width (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0
Load
(kN
)
0
20
40
60
80
100
120
140
Shear crack - 1st
phaseShear crack - 2nd phase
SL
SA
wSLwm
Crack width (mm)0.0 0.5 1.0 1.5 2.0
Load
(kN
)0
20
40
60
80
100
120
140
2nd phase - 1st+2nd cycle2nd phase - 3rd cycle
SL - 3rd cycle
SA - 1st+2nd cycles
SA - 3rd cycle
SL - 1st+2nd cycles
1st phase
wSLwm
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Strain Approach & Sheffield ApproachStrain Approach & Sheffield Approach
Experimental data (kN)0 20 40 60 80 100 120 140 160
Pre
dict
edva
lues
(kN
)
0
20
40
60
80
100
120
140
160BS-8110 - Sheffield approachACI-318-99 - Sheffield approach
EC2-2001 (1stdraft) - Sheffield approach
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Shear reinforcement requirementShear reinforcement requirement
Normalized flexural stiffness E/5GPa)0.0 0.2 0.4 0.6 0.8 1.0 1.2
Rat
ioof
shea
rr-m
ent(
Stra
in/S
heffi
eld)
1.0
1.5
2.0
2.5
3.0
3.5
vd = 1 MPa
vd = 1.5 MPa
vd = 1.75 MPa
vd = 2 MPa
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• The strain in both the flexural and shear FRP r/ment can reach values that are much higher than those currently adopted
• Shear resisting mechanisms are mobilised in a similar way in both GFRP and steel RC beams and failure modes are characterised by similar behaviour
• The principle of strain control is accepted, but a new limit of 4,500 με is proposed
ConclusionsConclusions