theoretical modelling of frp strengthened concrete...

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







• Conclusions

4

TESTS ON CFRP STRENGTHENED BEAMS

BEAM 3

Not strengthened beam

BEAM 2

CFRP passive beam

BEAM 1

CFRP pre-stressed beam

5


ANALYSIS OF BEAM 3

No strengthening

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


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


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

9


ANALYSIS OF BEAM 2

Strengthening with passive CFRP

10



Material Type

Design

strength

(MPa)

Elastic

modulus

(MPa)

Steel B500B 500 210000

Concrete C30/37 49 36889

CFRP IM80C 2369 230000

Adhesive SK41 - 7100


200

300

2Φ16

2Φ16


Note: the CFRP design strength has been evaluated

from the ultimate strain observed during the

laboratory test

11


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


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

)




13


ANALYSIS OF BEAM 1

Strengthening with pre-stressed CFRP

14




Material Type

Design

strength

(MPa)

Elastic

modulus

(MPa)

Steel B500B 500 210000

Concrete C30/37 49 36889

CFRP IM80C 2369 230000

Adhesive SK41 - 7100


200

300

2Φ16

2Φ16

15


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



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

)



17

COMPARISONS

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90

LO

AD

(kN

)


FEM ANALYSIS

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90

LO

AD

(kN

)


CTH EXPERIMENTAL RESULTS

BEAM 3 – No strengthening

BEAM 2 – Strengthening with

passive CFRP


pre-stressed CFRP

BEAM 3 – No strengthening


passive CFRP


pre-stressed CFRP

FEM vs EXPERIMENTAL RESULTS

18

Outline







• Conclusions

19

CFRP + GFRP STRENGTHENED BEAMS

SPECIMEN 2

(CFRP pre-stressed laminates +

GFRP longitudinal panels)

SPECIMEN 1

(Not strengthened)

20

TESTS ON CFRP + GFRP STRENGTHENED BEAMS

FOUR-POINT BENDING TEST

Test configuration

21

TESTS ON CFRP + GFRP STRENGTHENED BEAMS

FOUR-POINT BENDING TEST

Specimen 1 Specimen 2

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


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


STRESS-STRAIN CURVES FOR CONCRETE AND STEEL


25

Stress-strain curve for CFRP laminates


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


26


Load F = 25 kN

SUPPORT

MIDSPAN

Model of half specimen


27


SUPPORT

MIDSPAN



Load F = 100 kN

28


SUPPORT

MIDSPAN



Load F = 135 kN

29


Load F = 50 kN

SUPPORT

MIDSPAN



30


Load F = 100 kN

SUPPORT

MIDSPAN



31


Load F = 300 kN

SUPPORT

MIDSPAN



32


Load F = 380 kN

SUPPORT

MIDSPAN



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)


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

)


Tensile failure of concrete

Yielding of steel

Tensile failure of concrete

Tensile failure of CFRP

34

EXPERIMENTAL TEST RESULTS (August 2017)


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


0

50

100

150

200

250

300

350

400

450

0 20 40 60 80 100 120 140 160 180

LO

AD

(k

N)


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)


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

theoretical modelling of frp strengthened concrete...

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