theoretical modelling of frp strengthened concrete...
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Prof. Paolo S. Valvo
University of Pisa
2017-09-22
Theoretical modelling of FRP strengthened concrete beams
2
Outline
• Tests on CFRP strengthened beams (no GFRP)
• Experimental tests (October 2016)
• Finite element analysis (May 2017)
• Tests on CFRP + GFRP strengthened beams
• Finite element analysis (July 2017)
• Experimental tests (August 2017)
• Conclusions
3
Outline
• Tests on CFRP strengthened beams (no GFRP)
• Experimental tests (October 2016)
• Finite element analysis (May 2017)
• Tests on CFRP + GFRP strengthened beams
• Finite element analysis (July 2017)
• Experimental tests (August 2017)
• Conclusions
4
TESTS ON CFRP STRENGTHENED BEAMS
BEAM 3
Not strengthened beam
BEAM 2
CFRP passive beam
BEAM 1
CFRP pre-stressed beam
6
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
ANALYSIS OF BEAM 3 – Geometrical and mechanical properties
MECHANICAL PROPERTIES
Material Type
Design
strength
(MPa)
Elastic
modulus
(MPa)
Steel B500B 500 210000
Concrete C30/37 49 36889
Note: the design strength of concrete is obtained from
laboratory tests on small-scale samples, conveniently
corrected
Cross section of BEAM 3
200
300
2Φ16
2Φ16
7
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
STRESS-STRAIN CURVES FOR CONCRETE AND STEEL
0
20
40
60
80
100
120
0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160
ST
RE
SS
(M
Pa)
STRAIN
UNCONFINED CONCRETE CONFINED CONCRETE
0
100
200
300
400
500
600
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
ST
RE
SS
(M
Pa)
STRAIN
Stress-strain curves for concrete (compression) Stress-strain curve for steel
(tension and compression)
8
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
ANALYSIS OF BEAM 3 –Analysis results
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70 80 90
LO
AD
(kN
)
DEFLECTION AT MIDSPAN (mm)
CTH EXP RESULTS FEM ANALYSIS
10
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
MECHANICAL PROPERTIES
Material Type
Design
strength
(MPa)
Elastic
modulus
(MPa)
Steel B500B 500 210000
Concrete C30/37 49 36889
CFRP IM80C 2369 230000
Adhesive SK41 - 7100
Cross section of BEAM 2
200
300
2Φ16
2Φ16
ANALYSIS OF BEAM 2 – Geometrical and mechanical properties
Note: the CFRP design strength has been evaluated
from the ultimate strain observed during the
laboratory test
11
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
0
500
1000
1500
2000
2500
0.000 0.010 0.020 0.030 0.040 0.050 0.060
ST
RE
SS
(MP
a)
STRAIN
Stress-strain curve for CFRP laminates
(tension)
STRESS-STRAIN CURVE FOR CFRP
12
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
LO
AD
(kN
)
DEFLECTION AT MIDSPAN (mm)
CTH EXP RESULTS FEM ANALYSIS
ANALYSIS OF BEAM 2 –Analysis results
14
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
ANALYSIS OF BEAM 1 – Geometrical and mechanical properties
MECHANICAL PROPERTIES
Material Type
Design
strength
(MPa)
Elastic
modulus
(MPa)
Steel B500B 500 210000
Concrete C30/37 49 36889
CFRP IM80C 2369 230000
Adhesive SK41 - 7100
Cross section of BEAM 1
200
300
2Φ16
2Φ16
15
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
ANALYSIS OF BEAM 1 – Pre-stressing action on CFRP
0
10
20
30
40
50
60
70
80
90
100
0 500 1000 1500 2000 2500 3000 3500 4000 4500
PR
E-S
TR
ES
S (
kN
)
LENGTH (mm)
The prestress distribution is obtained from the
strain values measured during the laboratory tests
16
FEM ANALYSIS OF CFRP STRENGTHENED BEAMS
ANALYSIS OF BEAM 1 –Analysis results
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0
LO
AD
(kN
)
DEFLECTION AT MIDSPAN (mm)
CTH EXP RESULTS FEM ANALYSIS
17
COMPARISONS
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60 70 80 90
LO
AD
(kN
)
DEFLECTION AT MIDSPAN (mm)
FEM ANALYSIS
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70 80 90
LO
AD
(kN
)
DEFLECTION AT MIDSPAN (mm)
CTH EXPERIMENTAL RESULTS
BEAM 3 – No strengthening
BEAM 2 – Strengthening with
passive CFRP
BEAM 1 – Strengthening with
pre-stressed CFRP
BEAM 3 – No strengthening
BEAM 2 – Strengthening with
passive CFRP
BEAM 1 – Strengthening with
pre-stressed CFRP
FEM vs EXPERIMENTAL RESULTS
18
Outline
• Tests on CFRP strengthened beams (no GFRP)
• Experimental tests (October 2016)
• Finite element analysis (May 2017)
• Tests on CFRP + GFRP strengthened beams
• Finite element analysis (July 2017)
• Experimental tests (August 2017)
• Conclusions
19
CFRP + GFRP STRENGTHENED BEAMS
SPECIMEN 2
(CFRP pre-stressed laminates +
GFRP longitudinal panels)
SPECIMEN 1
(Not strengthened)
22
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
SPECIMEN 1 (Not strengthened)
Finite element modelCross section
23
SPECIMEN 2 (Strengthened with CFRP + GFRP)
Cross section and Finite element model
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
24
0
10
20
30
40
50
60
0.000 0.005 0.010 0.015 0.020 0.025
ST
RE
SS
(MP
a)
STRAIN
UNCONFINED CONCRETE CONFINED CONCRETE
0
100
200
300
400
500
600
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
ST
RE
SS
(M
Pa)
STRAIN
Stress-strain curves for concrete (compression) Stress-strain curve for steel
(tension and compression)
STRESS-STRAIN CURVES FOR CONCRETE AND STEEL
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
25
Stress-strain curve for CFRP laminates
(tension and compression)
0
500
1000
1500
2000
2500
3000
3500
0.000 0.010 0.020 0.030 0.040 0.050 0.060
ST
RE
SS
(M
Pa)
STRAIN
STRESS-STRAIN CURVE FOR CFRP
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
26
SPECIMEN 1 (Not strengthened)
Load F = 25 kN
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
27
SPECIMEN 1 (Not strengthened)
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
Load F = 100 kN
28
SPECIMEN 1 (Not strengthened)
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
Load F = 135 kN
29
SPECIMEN 2 (Strengthened with CFRP + GFRP)
Load F = 50 kN
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
30
SPECIMEN 2 (Strengthened with CFRP + GFRP)
Load F = 100 kN
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
31
SPECIMEN 2 (Strengthened with CFRP + GFRP)
Load F = 300 kN
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
32
SPECIMEN 2 (Strengthened with CFRP + GFRP)
Load F = 380 kN
SUPPORT
MIDSPAN
Model of half specimen
FEM ANALYSIS OF CFRP+GFRP STRENGTHENED BEAMS
33
FEM PREDICTIONS OF TEST RESULTS (July 2017)
Specimen 1 – Not Strengthened Specimen 2 – Strengthened with CFRP+GFRP
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30 35 40
LO
AD
(k
N)
DEFLECTION AT MIDSPAN (mm)
Yielding of steel
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 60 70 80 90L
OA
D (
kN
)
DEFLECTION AT MIDSPAN (mm)
Tensile failure of concrete
Yielding of steel
Tensile failure of concrete
Tensile failure of CFRP
34
EXPERIMENTAL TEST RESULTS (August 2017)
Specimen 1 – Not Strengthened Specimen 2 – Strengthened with CFRP+GFRP
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140
LO
AD
(K
N)
DEFLECTION AT MIDSPAN (MM)
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200
LO
AD
(K
N)
DEFLECTION AT MIDSPAN (MM)
35
FEM PREDICTIONS vs EXPERIMENTAL RESULTS
Specimen 1 – Not Strengthened Specimen 2 – Strengthened with CFRP+GFRP
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180
LO
AD
(k
N)
DEFLECTION AT MIDSPAN (mm)
Analysis Results Experimental Results
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140
LO
AD
(k
N)
DEFLECTION AT MIDSPAN (mm)
Analysis Results Experimental Results
36
Conclusions
• Non-linear finite element analysis of experimental tests
• Very good theoretical predictions of experimental results
• Requires high specialisation to be implemented in a commercial software
• Not suitable for design Need for a simplified model and calculation tool
Workpackage:
Author(s):
Date:
WP4
PSV
2017-09-22
Theoretical modelling of FRP strengthened
beams
Copyright © 2015-2018. All rights reserved.
This publication is produced by SUREBRIDGE work group. Any duplication or use of objects such as diagrams in other electronic or printed
publications is not permitted without the author's agreement.
2017-09-22
This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and
demonstration under grant agreement No. 31109806.0009
SUREBRIDGE is co-funded by Funding Partners of The ERA-NET Plus Infravation and the European Commission. The Funding Partners of the
Infravation 2014 Call are:
MINISTERIE VAN INFRASTRUCTUUR EN MILIEU, RIJKSWATERSTAAT
BUNDESMINISTERIUM FÜR VERKEHR, BAU UND STADTENTWICKLUNG,
DANISH ROAD DIRECTORATE,
STATENS VEGVESEN VEGDIREKTORATET,
TRAFIKVERKET – TRV,
VEGAGERÐIN,
MINISTERE DE L'ECOLOGIE, DU DEVELOPPEMENT DURABLE ET DE L'ENERGIE,
CENTRO PARA EL DESARROLLO TECNOLOGICO INDUSTRIAL,
ANAS S.p.A.,
NETIVEI, ISRAEL - NATIONAL TRANSPORT INFRASTRUCTURE COMPANY LTD,
FEDERAL HIGHWAY ADMINISTRATION USDOT
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