Towards Unified Bond Modelling for the Structural Behaviour of GFRP-RC Kypros Pilakoutas
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Transcript of Towards Unified Bond Modelling for the Structural Behaviour of GFRP-RC Kypros Pilakoutas
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4th November 2005
Towards Unified Bond Modelling for the Structural Behaviour of GFRP-RC
Kypros PilakoutasHarsha Sooriyaararachchi
Maurizio Guadagnini
Centre for Cement and ConcreteDepartment of Civil and Structural Engineering, University of Sheffield,
Sheffield, United Kingdom
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GFRP bars
Use of GFRP for bridge deck construction(Franklin county bridge Virginia)
Stiffness of GFRP compared to Steel
0
200
400
600
800
0 5000 10000 15000
Strain (micro strain)
Str
es
s (
MP
a)
GFRP Bare bar
Steel bare bar
GFRP-RC in Construction
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Outline
• Hierarchy of bond modelling
• Macro level Modelling
• Meso level modelling
• Average bond stress slip relation
• Formulation of bond modelling using strain distribution
• Local bond stress-slip-strain relation
s
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Steel reinforcement FRP reinforcement
Hierarchy of bond Modelling
Macro-level modelling
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Steel reinforcement FRP reinforcement
Macro-level modelling
Hierarchy of bond Modelling
Meso-level modelling
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Steel reinforcement FRP reinforcement
Macro-level modelling
Meso-level modelling
Micro-level modelling
Hierarchy of bond Modelling
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Tension stiffening effect Average Strain
Av
era
ge
Str
es
s
Bare bar response
RC response
Tension stiffening of concrete is defined as: the ability of concrete to carry tension between cracks and provide
extra stiffness for RC in tension.
Macro Level Bond Modelling
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Test results bar stress Vs overall strain Average stress strain behaviour of concrete
0
200
400
600
800
0 5000 10000 15000 20000
Strain (Microstrain)
Str
es
s (
MP
a)
C90/13/150
C50/13/150
13mm Bar
0
0.5
1
1.5
2
2.5
3
3.5
0 5000 10000 15000 20000
Strain (Microstrian)
Str
es
s (
MP
a)
C90/13/150
C50/13/150
Strain Softening Behaviour Concrete
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Reinforced concrete in tension
Typical Test Results
c
f N
N
Strain of the composite specimen at
Strain of the bar at crack
Average Strain
Ave
rag
e S
tres
s
N
f
c
Sta
ge I
Pre
Cra
ckin
g
Sta
ge II
Cra
ck P
rop
agat
ion
Sta
ge III
Po
st C
rack
ing
Response of composite section
Bare bar response
Tension Stiffening Behaviour
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1st crack2nd 3rd
Internally strain gauged bar
0
2000
4000
6000Just before first crack (37 kN)
0
2000
4000
After second crack (43 kN)
0 200 400 600 800 1000 12000
2000
4000
Length along the bar (mm)
Ba
r s
tra
in
( )
After third crack (53 kN)
Strain Distribution while Cracking
Stage I
Stage II
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0 200 400 600 800 1000 12000
1000
2000
3000
4000
5000
6000
7000
510152025303641465156606670 kN
Length along the specimen (mm)
Str
ain
( )
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
5152025303641465156606670 kN
Length along the specimen (mm)
Sli
p (
mm
)
Post cracking slip and strain
Stage III
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Typical strain and bond stress distribution between cracks
650 700 750 800 850 900 950 10000
5000
10000
15000
20000
Distance between cracks # 1 & # 2 mm
Ba
rs s
tra
in
( )
35 kN
55 kN75 kN95 kN115 kN135 kN155 kN
35.8 kN
650 700 750 800 850 900 950 1000-15
-10
-5
0
5
10
15
Distance between cracks # 1 & # 2 mm
Bo
nd
str
ess
(MP
a)
55 kN
155 kN
Strain and bond between cracks
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Meso Level Bond Modelling
Direct tension test
Pullout test
Magnified images showing bond failure
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Average Bond Stress Vs. Slip
(a) (d) (b) (c)
0
1
2
3
4
5
6
7
8
9
10
11
12
0 0.5 1 1.5 2 2.5 3 3.5
Slip (mm)
Bo
nd
str
es
s (
MP
a)
19-45-5D - Loaded end
19-45-5D - Free end
Comparison of average bond stress slip behaviour for the two test in almost identical circumstances
0 0.5 1 1.5 2 2.5
0
1
2
3
4
5
6
7
8
9
10
11
12
a (0~150)
(b) (175~325)(d) (900~1050)
(d) (750~900)
(d) (750~900) (d) (750~900)
(c) (750~900)(a) (0~175)
Slip (mm)
Bo
nd
Str
ess
(N/m
m2 )
50%
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Stress Conditions During Testing
Direct tension test
Pull out test
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Bond Stress based on strain distribution
dxd
4dE fff
x
0 f dxs 115.2 kN
135.6 kN
155.7 kN
dxd
4dE fff
dxd f
x
0 f dxs
Str
ain
Distance between cracks
2262
2473
2677
2874
3079
3267
dxd
4dE fff
dxd f
free
x
0 f sdxs
Str
ain
Distance along the embedment length
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Local Bond Stress Slip Relationship
0 50 100 1500
5000
10000
15000
Distance from centre of the crack (mm)
Str
ian
( )
0 0.5 1 1.5 2
0
2
4
6
8
10
12
0
25
50
75100
125
150
175
Slip (mm)
Bo
nd
str
ess
(N
/mm2 )
0 50 100 1500
5000
10000
15000
Distance from centre of the crack (mm)
Str
ain
( )
0 0.5 1 1.5
0
2
4
6
8
10
12
12.5
37.5
62.587.5
112.5
137.5
Slip (mm)
Bo
nd
str
ess
(N
/mm
2 )
0 25 50 75 100
150
175
125
0 25 50 75 100
150
125
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0 50 100 1500
5000
10000
15000
Distance from centre of the crack (mm)
Str
ain
( )
dxd
4dE fff
dxd f
x
0 f dxs
x
f
0 0.1 0.2 0.3 0.4 0.5 0.60
2
4
6
8
10
*8474
940610464
1130312317
13241 14159
Different Slip at (mm)D
iffe
ren
t b
on
d s
tre
ss (
N/m
m2)
*f
f
s
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0 0.5 1 1.50
2
4
6
8
10
352
1196
2071
310039144854 5740
665375858474
940610464
1130312317
1324114159
Slip at different strain levels (mm)
Bo
nd
str
ess
(N/m
m2 )
Bond stresses slip at different strain
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0 0.5 1 1.50
1
2
3
4
5
6
7
8
9
10
1196
3100 48546653
847410464
12317
14159
Slip at different strain levels (mm)
Bo
nd
str
es
s (
N/m
m2)
00
e14 25053
.
)()( ..max
S.
1
251.
cal
icalS
Scal= Slip at peak bond stress at calibrated strain
cal = Referred strain for calibration
s Relation for BOND
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4th November 2005
0 0.5 1 1.5 2
0
2
4
6
8
10
0
25
25
50
50
7575
100
100
125125
150150
175
175
Local slip (mm)
Lo
cal
bo
nd
str
ess
(N/m
m2 )
Comparison of Results
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Local Bond Stresses in Pull-out 5D
0 20 40 60 80 100
0
1
2
3
4
length (mm)B
on
d s
tre
ss
(
N/m
m2)
0 20 40 60 80 100
0
200
400
600
800
Length (mm)
Str
ain
(
)
0 0.005 0.01 0.015 0.020
0.5
1
1.5
2
2.5
3
91mm
Slip at various section mm
Bo
nd
str
ess
(N
/mm
2)
19mm
38 mm
57 mm
76 mm
95.5mm
0 0.05 0.1 0.15 0.20
2
4
6
8
10
Slip at various sections mmB
on
d s
tre
ss
(N/m
m2)
19 mm
38 mm
57 mm
76 mm
95 mm
0 20 40 60 80 100
0
2
4
6
8
10
Length(mm)
Bo
nd
str
es
s
(N
/mm
2)
0 20 40 60 80 100
0
1000
2000
3000
Length (mm)
Str
ain
(
)
Grade 90
Grade 45
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Local Bond Stresses in Pull-out 10D
0 50 100 150 2000
2
4
6
8
10
12
length(mm)
Bo
nd
str
es
s
(N
/mm
2)
0 0.05 0.1 0.15 0.20
2
4
6
8
10
12
0mm
Slip at various section (mm)B
on
d s
tre
ss
(N/m
m2)
57mm76mm
96 mm
115 mm
134mm
153 mm
172mm
191mm
0 50 100 150 200
0
1000
2000
3000
4000
Length (mm)
Str
ain
(
)
0 50 100 150 2000
1
2
3
4
Length(mm)
Bo
nd
str
es
s
(N
/mm
2)
0 0.02 0.04 0.06 0.080
1
2
3
4
0mm
Slip at various section (mm)
Bo
nd
str
es
s
(N
/mm
2)
38.2mm57.3mm
95mm115 mm
134 mm
153 mm172mm
191mm
0 50 100 150 200
0
500
1000
1500
Length (mm)
Str
ain
(
)
Grade 90
Grade 45
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Comparisons of results
Local bond behaviour in pull out test 19/45/10D
0 0.02 0.04 0.06 0.080
0.5
1
1.5
2
2.5
3
3.5
4
Local slip mm
Bo
nd
str
ess
(N/m
m2 )
19.1 mm19 mm
57 mm57 mm
96 mm
96 mm
115 mm115 mm
134 mm
134 mm
153 mm
153 mm
171 mm171mm
191 mm
191mm
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4th November 2005
Conclusions
• -s- approach proposed
• Is Average bond stress slip relationship useful?
• Different levels of bond modelling
• More work to be done
• Bond stress profile changes with increasing load
• Testing conditions affect bond behaviour