# MODELS FOR TENSION STIFFENING AND DEFLECTIONS OF GFRP-RC

Πολεοδομικά Έργα

29 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

156 εμφανίσεις

HarshaSooriyaararachchi
BSc.Eng.(SL), MEng.(Tokyo), PhD(Sheffield,UK)
Supervised by
Prof. Kypros Pilakoutas
Dr. EwanByars
Department of Civil and Structural Engineering, University of Sheffield,
Sheffield, United Kingdom
MODELS FOR TENSION
STIFFENING AND
DEFLECTIONS OF GFRP-RC
Outline
•Introduction
•Problem definition
•Methodology
-Direct tension studies to quantify
Tension stiffening effect
•Modelling tension behaviour GFRP-RC
•Modelling Deflections
•Conclusions and remarks
Introduction: GFRP RC in Construction
Tension Stiffening in Design Codes
In ACI
eff
EI
kPl
3

Branson’s equation for
eff
I

−+

=
3
a
cr
cr
3
a
cr
geff
M
M
1I
M
M
II
0.0E+00
5.0E+07
1.0E+08
1.5E+08
2.0E+08
2.5E+08
012345
Ma/Mcr
I
eff

(mm
4
)
g
I
%5.0ρ
=
cr
I
Δerror
= Experimental Deflection minus
the Deflection by Branson’s
Equation, both at service level
(courtesy Toutanjiet al. (2003), Construction and
Building Material)
0
2
4
6
8
10
12
00.20.40.60.811.21.4
Rainforcement ratio (%)
Yost
Masmoudi et. al.
Benmokrane et.
error
Δ
(mm)

−+

=
3
a
cr
cr
3
a
cr
dgeff
M
M
1I
M
M
βII
ACI 440 approach

+=1
s
f
bd
E
E
αβ
5.0=
b
α

Rebar
type
Beam

Cover
(mm)
Reinforcement
Rein. Ratio
bh/As
=
ρ
(%)
cu
f

(MPa)
Failure
mode
B1 31
1∅12.7 mm
0.57 91 Bar failure
B2 31
1∅12.7 mm
0.57 46 Con. Crushing
GFRP
B3 31
2∅12.7 mm
1.15 46 Con. Crushing
Test on deflections –beam series
Tests on deflections –beam series (B3)
15.1ρ
=
0
10
20
30
40
50
60
0102030405060
Cental deflections (mm)
Experiment (B3)
ACI 440 (B3)
Central
Tests on deflections –beam series (B2)
57.0ρ
=
0
10
20
30
40
50
60
0102030405060
Cental deflections (mm)
Experiment (B2)
ACI 440 (B2)
Central
Tests on deflections –beam series (B1)
57.0ρ
=
0
10
20
30
40
50
60
0102030405060
Cental deflections (mm)
Experiment (B1)
ACI 440 (B1)
Central
750
120
2100
120
125
125
600
750
Variable during
construction
500
Transverse
rebars

Rebar
type
Slab

Cover,
(mm)
Reinforcement
Reinforcement
Ratio
bh/As
=
ρ
(%)
Concrete Cylinder
strength “MPa”
S1 27.5
5∅6mm
0.24 43
S2 31
5∅9.53mm
0.59 39
GFRP
S3 40
5∅19.05mm
2.38 39
Tests on deflections –Slab series
Test on deflections –beam series (S3)
38.2ρ
=
200
500
0
10
20
30
40
50
60
70
010203040506070
Cental Deflection (mm)
Experiment (S3)
ACI 440 (S1)
Central
Test on deflections –beam series (S2)
59.0ρ
=
200
500
0
10
20
30
40
50
0102030405060708090100110
Cental Deflection (mm)
Experiment (S2)
ACI 440 (S2)
Central
Test on deflections –beam series (S1)
24.0ρ
=
200
500
0
5
10
15
20
25
30
010203040506070
Cental Deflection (mm)
Experiment (S1)
ACI 440 (S1)
Central
Tension Stiffening for FRP Design
0.0E+00
5.0E+07
1.0E+08
1.5E+08
2.0E+08
2.5E+08
012345
Ma/Mcr
I
eff
(mm
4
)
ACI Barrons
ACI 440
Alsayed et al. A
Alsayed et al. B
Faza et al.
g
I
cr
I
•No general agreement on tension stiffening

−+

=
3
a
cr
cr
3
a
cr
geff
M
M
1I
M
M
II

−+

β=
3
a
cr
cr
3
a
cr
dgeff
M
M
1I
M
M
II
ACI Branson’s
ACI 440

−+

=
55
a
cr
cr
55
a
cr
geff
M
M
1I
M
M
II
..
Alsayedet. al A

−=
cr
a
creff
M
M
15
2
401II.
creff
II
=
Alsayedet. al B
3
M
M
1
cr
a
<<
ecr
ecr
m
I15I8
II23
I
+
=
Fazaet. al B
effe
IACII=
,
Research Approach
•Study the tension stiffening effect at fundamental level
•Develop a suitable way to incorporate tension
stiffening in deflection
Studying tension stiffening alone was important at the time as it is
necessary for Modelling GFRP-RC using FE Method based on
smeared crack approach.
Definition-Tension Stiffening
Tension stiffening of concrete is defined as:
the ability of concrete to carry tension between cracks and provide
extra stiffness for RC in tension.
Tension stiffening effect
•Serviceability often governs GFRP-RC design
•Tension stiffening is very important for the determination of
deflections and crack widths at low load levels
Average Strain
Average Stress
Bare bar response
RC response

Test results bar stress Vs overall strain
Average stress strain behaviour of concrete
0
200
400
600
800
05000100001500020000
Strain (Microstrain)
Stress (MPa)
C90/13/150
C50/13/150
13mm Bar
0
0.5
1
1.5
2
2.5
3
3.5
05000100001500020000
Strain (Microstrian)
Stress (MPa)
C90/13/150
C50/13/150
Strain Softening Behaviour Concrete
Parametric Study
100 mm
150 mm
200 mm
SpecimenConcrete
strength
Bar DiameterDimension
b×d×l
Reinforcement
ratio
C50/13/1004612.7100×100×1500
150×150×1500
200×200×1500
100×100×1500
150×150×1500
C50/19/1504619.1150×150×15001.27
200×200×1300
150×150×1300
200×200×1300
200×200×1300
1.26
C50/13/1504612.70.56
C50/13/2004612.70.32
C90/13/1009112.71.26
C90/13/1509112.70.56
C50/19/2004619.10.72
C90/19/1504619.11.27
C90/19/2009119.10.72
C50/19/200N9119.10.72
)'(
C
f
)(
ρ
)(
φ
0
0.005
0.01
0.015
0.02
0
200
400
600
800
1000
Strain (
ε
)
Bar Stress (MPa)
Bare bar
CEB-FIP C50/13/100
Experiment C50/13/100
ACI 224 C50/13/100
0
0.005
0.01
0.015
0.02
0
200
400
600
800
1000
Strain (
ε
)
Bar Stress (MPa)
CEB-FIP C50/13/150
Bare bar
ACI 224 C50/13/100
Experiment C50/13/150

−ε=ε
2
f
scr
sm
f
f
K1

+−
ρ

==
ft
f
cr
scr
n1
1
f
A
P
f
CEB
cr
3
a
cr
g
3
a
cr
e
A
P
P
1A
P
P
A

−+

=
cr
3
a
cr
gd
3
a
cr
e
A
P
P
1A
P
P
A

−+β

=
ACI
Original
Modified to account
for weak FRP bond
Reduced cross sectional area
Composite strain for given bar strain
100 mm
150 mm
Prediction of tension stiffening effect
-Code based approach
0
0.005
0.01
0.015
0.02
0
200
400
600
800
1000
Strain (
ε
)
Bar Stress (MPa)
Modified CEB-FIP C50/13/150
Bare bar
Experiment C50/13/150
Modified CEB-FIP C50/13/100
Experiment C50/13/100
Model for Tension Stiffening effect of GFRP-RC

−=
2
f
scr
sm
f
f
5.01
εε
0
0.005
0.01
0.015
0.02
0
0.2
0.4
0.6
0.8
1
Strain (
ε
)
Normalised Stress
Normalised C50/13/150
Modifeid CEB-FIP Model
Normalised C90/13/150
0
0.005
0.01
0.015
0.02
0
0.2
0.4
0.6
0.8
1
Strain (
ε
)
Normalised Stress
Experiment C50/13/100
Experiment C90/13/100
Modified CEB-FIP Model
150 mm
100 mm
Verification of the model for much wider data set

r1
ψ

r2
ψ

2
ψ

1
ψ

m
ψ

r
M

Curvature
ψ

rredr
MM.
,
β
=

Moment (M)
TS
ψ
Δ

TS2m
ψ
Δ
ψ
ψ

=
1
ψ
ψ
=
m
M
M
β)ψψ(ψΔ
r
r1r2TS
−=
2
122
)(

−−=
M
M
r
m
βψψψ
ψ
2
212
)(

−−=
D
rD
M
M
aaaa
β
2
212
5.0)(

−−=
D
rD
M
M
aaaa
Moment curvature relationship
Simplified deflection relationship
Incorporating Tension stiffening effect for deflection
–Simplified approach
0
10
20
30
40
50
60
70
0102030405060708090100
Central deflection (mm)
Experiment (S3)
Proposed model (S3)
Experiment (S2)
Proposed model (S2)
Experiment (S1)
Proposed model (S1)
Comparing experimental results with
Simplified approach-Slabs
Comparing experimental results with
Simplified approach-Beams
0
10
20
30
40
50
60
0102030405060
Cental deflections (mm)
Experiment (B1)
Proposed model (B1)
Experiment (B2)
Proposed model (B2)
Experiment (B3)
Proposed model (B3)
Central
FEM analysis using tension stiffening model
Comparing Experimental results with FEA (Beams)
0
10
20
30
40
50
60
0102030405060
Cental deflections (mm)
Experiment (B1)
Experiment (B2)
Experiment (B3)
ABAQUS FE Analysis (B1)
ABAQUS FE Analysis (B2)
ABAQUS FE Analysis (B3)
Central
Comparing experimental results with FEA (Slabs)
0
10
20
30
40
50
60
70
0102030405060708090100110
Cental Deflection (mm)
Experiment (S2)
ABAQUS FE analysis (S2)
Experiment (S1)
ABAQUS FE analysis (S1)
Experiment (S3)
ABAQUS FE analysis (S3)
Central
Conclusions and Remarks
•Existing ACI equation are not suitable for predicting tension
stiffening effect or deflections
•Study proposes accurate model to account for tension
stiffening effect
•Simplified version of deflection predictions are also shown
possible with the proposed equation
•With the proposed tension stiffening model accurate consistent
deflection predictions is possible.
•Direct tension test is used to study the tension stiffening effect

−=
2
f
scr
fcf
f
f
5.01
εε
2
D
rD
212
M
M
5.0)aa(aa

−−=