Proceedings of the International Symposium on Bond Behaviour of FRP in Structures (BBFS 2005) Chen and Teng (eds)

© 2005 International Institute for FRP in Construction

253

EQUILIBRIUM DEBONDING

C. Czaderski 1, M. Aram 1,2 and M. Motavalli 1,2 1 Empa, Swiss Federal Laboratories for Materials Testing and Research, Structural Engineering Research

Laboratory, Überlandstrasse 129, 8600 Dübendorf, Switzerland, Email: christoph.czaderski@empa.ch 2 University of Tehran, Department of Civil Engineering, Tehran, Iran

ABSTRACT A large-scale, 17 m long, internally prestressed RC bridge girder which was taken from a Swiss highway bridge was strengthened for flexure by using CFRP plates and tested to failure. The specialties of the tests are firstly, the size and secondly, the complicated internal stress state due to internal prestressing and the joint at mid-span. At this joint stable equilibrium debonding of the CFRP plates occurred. Measured shear stresses are presented and influences on equilibrium debonding are discussed. The strengthened test beam is compared with an unstrengthened reference beam. Lastly, a nonlinear FE analysis of the tests using the software ATENA is presented. KEYWORDS prestressed concrete, flexural post-strengthening, CFRP plates, equilibrium debonding, stable debonding. INTRODUCTION Today, CFRP (carbon fibre reinforced polymer) plates or fabrics are used worldwide in the construction industry for post-strengthening of concrete structures. A typical strengthening is to apply straight CFRP plates on the underside of beams or plates to increase the flexural capacity. For this strengthening, mostly the failure mode ‘debonding’ occurs. This means that the CFRP plate separates from the concrete surface before the tensile capacity of the CFRP is reached. Many different calculation and design methods can be found in references (e.g. Teng et al. 2002; Täljsten 2004), code (SIA166 2004) and guidelines (e.g. fib 2001; ISIS 2001; JCSE 2001; ACI 2002; TR55 2004). However, the mechanism of debonding is still not fully understood. In addition, only less research on post-strengthening of internally prestressed concrete structures using CFRP plates is available (e.g. Shahawy et al. 1996; El-Hacha et al. 2004). An interesting description of equilibrium and compatibility bond stresses is given in (Neubauer 2000; Neubauer and Rostasy 2001). A fracture mechanic approach for stable or unstable delamination crack growth is presented in Rabinovitch and Frostig 2001. In this paper, two large-scale tests on bridge girders are presented (see also Czaderski and Motavalli 2005). One test beam (called as test beam no. 4) was strengthened for flexure by using CFRP plates and statically tested to failure. Furthermore, a reference beam (called as test beam no. 3) was tested. EXPERIMENTS

Test beams The replacement of the superstructure of the highway bridges “Viadotto delle Cantine a Capolago” (see Figure 2) in the south part of Switzerland gave Empa the possibility to get five large-scale beams for several investigations. The bridge was built in the years 1965/1966. The test beams originate from the north to south traffic-direction bridge with a total length of 340 meters. The structural systems of this bridge were continuous beams with 4 or 5 spans of 20 m length. Prefabricated RC elements (two per span) were connected by using two tendons (parallel wire bundle consisting of 26 wires). The tendon profile corresponded to the bending moment. The tendons were injected after the prestressing. The prefabricated elements consisted of 12 stressing bed wires in the bottom flange. On top of the beams a concrete plate was cast-in-situ as well as a cross girder in the middle of the span. The investigated test beams originate from a middle span of a four span continuous beam. The test beams are 17 m long and have a flange width of 0.8 m, see Figure 1.

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The presented investigation is a part of a test program on five similar test beams. On the first beam an extensive material investigation was performed to determine the material properties of concrete, steel reinforcement and tendons. Furthermore, the remaining tendon force was measured using the test method “cutting wires” (Czaderski and Motavalli 2004). The second test beam (called as test beam no. 4) was strengthened for flexure by using unstressed CFRP plates and statically tested to failure. After this, a reference beam (called as test beam no. 3) was tested. A further beam was strengthened with stressed CFRP plates and a last beam will be first damaged before the strengthening.

15.8

3.4

AA B

B

3.43.5 3.5

0.3

0.2

14 x 0.5 = 7.0

front side

rear side

D25 - D36D37 - D48

12 x 0.1

1.01.0

tendon high

0.6 0.6

17.0

0.15

0.15

F F F FK4/K5

deformeter measurements:

0.6 0.6

~1.33

D131

D130

D129

D132

D133

D134

D135

D136

D137

D138

D139

D140

D141

D142

D145

D144

D143

D146

D147

D148

D149

D150

D151

D152

D153

D154

D155

D1566 CFRP plates Sika CarboDur S512length 15.5 m

tendon low

Figure 1: Test beam no. 4, strengthened with CFRP plates, test set-up

2 x 6 stressing bed wires d = 7 mminitial tensile stress according tooriginal drawing: 1128 MPa (11.5 t/cm2)

Cut A - A Cut B - B

Figure 2: View on the underside of the bridge before the replacement of the

superstructure

Figure 3: Reinforcement of the beams in cuts A-A and B-B at mid-span (cross girder is not shown)

Table 1: Material properties

Material Compressive cube strength fc,cube

Elastic modulus Ec Axial tensile strength fct

MPa MPa MPa Cast-in-situ concrete 52 32’700 2.4 Prefabricated concrete 56 38’100 2.8

Cross-section Yield strength Tensile strength Elastic modulusReinforcement in lower flange As = 385mm2 619 679 Es = 205’000

12 Stressing bed wires Aps = 462mm2 1’374 1’723 Eps = 205’000 2 Tendons Ap = 2001mm2 1’449 1’790 Ep = 205’000 6 CFRP plates (each 50x1.2mm, bf x tf)

Af = 360mm2 - 3’100 Ef = 165’000

Cross-section prestress force 12 Stressing bed wires Asp = 462mm2 771 MPa 356 kN

2 Tendons each Ap = 1001mm2at left quarter span: 652MPa at mid-span: 523MPa at right quarter span: 740MPa

652 kN 523 kN 740 kN

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Material properties The material properties given in Table 1, which are used for the calculations later in this paper, are determined on beam no. 1 or assumed. See also Czaderski and Motavalli 2004. Furthermore, the values for the CFRP plates are taken from the Sika® product data sheet. Test results

Behaviour during loading The debonding started at mid-span. It was a stable debonding what means that the debonding region kept constant during constant load (deformation controlled “load” steps), but increased with load increase. In Figure 4 and Figure 5, the measured strains along the right side of the beam (see Figure 1) on two load steps and for the strengthened and unstrengthened test beam using a so-called deformeter can be seen. The strengthened beam show lower strains at beam under- and topside than the reference beam. At beam length of about 9 to 12 m, the strain in the CFRP plate increased due to the increasing tendon profile. After 12 m the tendon profile still increases at little but the externally applied bending moment decreases what is the reason that the strain in the plates decreases. In the joint, a clear strain peak is visible. The next chapter discusses the possible influences on this strain peak. Figure 7 shows the measured strain peak for the load step 250 kN in more detail. The deformeter measurements are mean values over a length of 100mm. Two lines are drawn to give the idea of possible effective strains, which depend on local shear stresses. However, the high strain change from 3.5 to 1.54‰ presented in Figure 7 results in a high global shear stress between CFRP plate and concrete and might govern the debonding mechanism. The global mean shear stress can be calculated, if simplified, by dividing the force change trough the area in which it is transferred, equation (1).

f

fff

bLAE

⋅∆

⋅⋅∆=

ετ (1)

∆ε = measured strain changes in CFRP plate ∆L = deformeter length In Table 2, calculated shear stresses from the deformeter measurements are presented. In general, it can be noticed, that the shear stresses increased with increasing load and decreased probably after debonding. A mean value of the maximum measured shear stresses before the debonding of 3.3 MPa was determined. This value is lower as the shear stress resistance given in the Swiss code SIA166 2004 (τc from SIA262 2003):

MPa0.5f3.05.25.2 cclim,l =⋅⋅=⋅= ττ (without safety factors) (2)

Behaviour during failure The failure occurred as a debonding failure. The debonding zone increased during loading. At the point where the stable debonding changed in an unstable debonding, the CFRP plates (maximum measured strain: 9.8‰) separated from the right side of the beam and moved to the left side. The beam itself showed a large crack between the lower flange and the web, a web failure and a concrete crushing at beam topside. Apart from the debonding failure, the failure mode of reference beam no. 3 was similar as beam no. 4. Firstly, a large crack between the underside flange and the web occurred. At failure, the web crushed. Furthermore, at topside of the beam a compression failure occurred.

-2

-1

0

1

2

3

4

5

7 8 9 10 11 12 13 14 15 16Beam length [m]

Stra

in [‰

]

beam no. 4: F= 250 kN, CFRP strain (mean value)beam no. 3: F= 250 kN, beam underside (mean value)beam no. 4: F= 250 kN, Concrete strainbeam no. 3: F= 250 kN, Concrete strain top sidejoint at mid-span

joint at mid-span

reference beam no. 3

beam no. 4

-2

-1

0

1

2

3

4

5

7 8 9 10 11 12 13 14 15 16Beam length [m]

Stra

in [‰

]

beam no. 4: F= 300 kN, CFRP strain (mean value)beam no. 3: F= 300 kN, beam underside (mean value)beam no. 4: F= 300 kN, Concrete strainbeam no. 3: F= 300 kN, Concrete strain top sidejoint at mid-spanreference beam no. 3

beam no. 4

joint at mid-span

Figure 4: Strain measurements on the beams no. 3 and 4 along the right side for load F=250 kN

Figure 5: Strain measurements on the beams no. 3 and 4 along the right side for load F=300 kN

256

1.56 1.69 1.64

Deformetermeasurementson CFRP plate front sidefor F = 250 kN:

possible effective strains↓

↓eq. (1)

τ=3.9MPa

∆εf=1.96‰

1.78 2.31 3.25 3.50 1.54 0.93 1.04 0.75 1.01‰ Figure 6: Stable debonding at mid-span Figure 7: Strain at mid-span for load step 250 kN

Table 2: Calculated shear stresses for the measured CFRP plate strains

Shear stresses [MPa] from CFRP plate strain front side Shear stresses [MPa] from CFRP plate strain rear side

∆D28/29 ∆D29/30 ∆D30/31 ∆D31/32 ∆D32/33 ∆D39/40 ∆D40/41 ∆D41/42 ∆D42/43 ∆D43/44 ∆D44/45Load F measurement length: [mm] Load F measurement length: [mm]

kN 100 100 100 100 100 kN 100 100 100 100 100 100

100 -0.1 0.4 -0.1 -0.3 -0.1 100 0.0 0.0 0.2 -0.1 -0.2 0.0200 0.2 1.9 -0.2 -2.8 -0.1 200 0.1 0.1 1.4 -0.1 -2.4 -0.1250 1.0 1.9 0.5 -3.9 -1.2 250 0.1 0.7 2.0 0.1 -3.3 -1.3300 2.6 2.6 -2.9 -0.3 -3.1 300 2.6 2.2 -2.1 0.1 -0.4 -4.0

0 0.1 -0.3 -0.3 0.8 -0.7 0 -0.4 1.3 -1.2 -0.8 1.6 -0.90 0.1 -0.3 -0.3 0.8 -0.6 0 -0.5 1.2 -1.0 -0.8 1.6 -0.7

300 3.3 0.0 -1.0 1.1 -5.0 300 1.0 3.2 -1.5 -0.8 0.5 -3.8367 0.9 0.4 -1.0 0.3 -1.7 367 -0.5 1.3 -0.4 -2.4 3.0 -1.1

0 1.8 -0.6 -1.0 1.3 -1.8 0 -0.1 2.0 -1.4 -1.3 1.8 -1.10 1.6 -0.4 -1.1 1.4 -1.8 0 -0.1 2.0 -1.3 -1.3 1.8 -1.1

300 1.1 0.5 -1.3 0.2 -1.3 300 -0.5 1.3 -0.1 -2.5 2.3 -0.5353 1.1 0.5 -1.1 0.0 -1.2 353 -0.7 1.4 -0.3 -2.2 2.1 -0.3

mean absolut value of maximum: 3.5 mean absolut value of maximum: 3.0

total mean absolut value of maximum: 3.3 ANALYTICAL INVESTIGATION OF EQUILIBRIUM DEBONDING

Strain in CFRP plates due to different tendon forces 4 single loads F = 250 kN

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2 4 6 8 10 12 14 16

Test beam length [m]

Stra

in [‰

]

Tendon 736kN, Stressing Bed Wires 356kN

Tendon 523kN, Stressing Bed Wires 356kN

Tendon 150kN, Stressing Bed Wires 356kN

Measurement

Figure 8: Strain in CFRP plates along test beam no. 4, measurement and cross-section analysis

With conventional cross-section analysis by using equilibrium and compatibility, the strains in the CFRP plates for the load F = 250 kN were calculated for different tendon forces, see Figure 8. With the software (Cubus 2005) cross-section analysis every 0.1 m along the beam was done. The influence of the tendon force on the strain in the CFRP plate is clearly noticeably. For comparison, the measured strain is also given. From this comparison, it seems that the tendon forces at mid-span are 150 kN and along the beam between 736 kN and

257

523 kN. The investigation in (Czaderski and Motavalli 2004) on beam no. 1 already showed that the tendon force at mid-span is lower than at the quarter of beam length (Table 1), even though not so low as it seems here. Equilibrium at mid-span To show the influence parameters on the strain peak at mid-span and therefore also on the shear stresses between the CFRP plate and the concrete, the force in the lower flange at mid-span for the cracked cross-section is formulated for section A-A beside the joint and section B-B in the joint, see Figure 1 and Figure 3. Section A-A:

fffApspspsApspsA0pssssApppAppA0pA AEAEAEAEAEAEF εεεεεε +++++= (3) εp0A = prestrain in tendon in section A-A εpA = additional strain in tendon due to load in section A-A εsA = strain in reinforcement due to load in section A-A εps0A = prestrain in stressing bed wires in section A-A εpsA = strain in stressing bed wires due to load in section A-A εfA = strain in CFRP plate due to load in section A-A Approximately, for simplification purposes εpA = εsA = εpsA = εfA:

fffApspsfApspsApsssfAppfAppApA AEAEAEAEAEAEF εεεεεε +++++= 00 (4) The force FA can be calculated with (4), the properties given in Table 1 and a tendon force of 523 kN, for εfA = 0.69‰ as FA = 1846kN, what is a similar value as determined with the cross-section analysis (Figure 9).

0.6918

-0.1305-0.1305

-0.2987

Strain [ Stress [N/mm ]2

=1=1=1

c

s

p

γγγ

-11.44-56.63

114.15

0.73

1832.502

0.36

-1.83E+3

F [kN], z [m]

Figure 9: Cross-section analysis in section A-A for load F = 250 kN (tendon force 523 kN)

The force in the lower flange in section B-B can be formulated similarly as follows:

fffBppfBppBpB AEAEAEF εεε ++= 0 (5) εp0B = prestrain in tendon in section B-B εfB = strain in CFRP plate due to load in section B-B Because of equilibrium, FA is equal to FB. Using B0pA0p0p εεε∆ −= and fAfBf εεε∆ −= the strain increase in the joint can be formulated as follows:

ffpp

pspsfApspsApsssfApppf AEAE

AEAEAEAE+

+++∆=∆

εεεεε 00 (6)

Using the material properties given in Table 1 for equation (6), the strain increase in the joint (∆εf) can be formulated as follows:

87.020.037.0 00 ⋅∆+⋅+⋅=∆ pApsfAf εεεε (7)

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Using εfA = 0.69‰, εps0A = 3.763‰ and ∆εp0 = 0‰ for (7), a strain increase of ∆εf = 1.01‰ can be calculated. This corresponds well with the cross-section analysis presented in Figure 9 and Figure 10. Consequently, the CFRP plate strain increase in the joint at mid-span depends on the load, on the stiffness EA of the interrupted reinforcement and on the prestress differences.

-0.0663

-0.4321

1.7221

-0.0663

Strain [ Stress [N/mm ]2

=1=1=1

c

s

p

γγγ

-15.98-78.59

284.15

0.71

1806.463

0.40

-1.81E+3

F [kN], z [m]

Figure 10: Cross-section analysis in section B-B for load F = 250 kN (tendon force 523 kN)

Shear stress due to the strain increase at mid-span From strain change in CFRP plate, the shear stress can also be calculated using equation (1). Table 3 presents a parameter variation to show the influence of different loads and internal prestressing on the shear stress. It can be concluded that the shear stresses depends on the loading, on discontinuities in the reinforcement but also in changes in the internal stress state due to prestressing.

Table 3: Calculations of strain increases and shear stresses Tendonforce εp0 Load F εfA εps ∆εp0 ∆εf εfB τ τ

eq. (7) =εfA+∆εf eq. (1) eq. (1)MPa MPa

kN ‰ kN ‰ ‰ ‰ ‰ ‰ ∆L=200mm ∆L=100mm

150 0.73 200 1.21 3.763 0 1.20 2.41 1.19 2.38150 0.73 250 1.77 3.763 0 1.41 3.18 1.39 2.79150 0.73 300 2.33 3.763 0 1.61 3.94 1.60 3.20

523 2.55 200 0.15 3.763 0 0.81 0.96 0.80 1.60523 2.55 250 0.69 3.763 0 1.01 1.70 1.00 2.00523 2.55 300 1.24 3.763 0 1.21 2.45 1.20 2.40

523 2.55 200 0.15 3.763 1.82 2.39 2.54 2.37 4.73523 2.55 250 0.69 3.763 1.82 2.59 3.28 2.56 5.13523 2.55 300 1.24 3.763 1.82 2.79 4.03 2.77 5.53

736 3.59 250 0.12 3.763 1.04 1.70 1.82 1.68 3.37736 3.59 275 0.37 3.763 1.04 1.79 2.16 1.77 3.55736 3.59 300 0.64 3.763 1.04 1.89 2.53 1.87 3.75

736 3.59 250 0.12 3.763 2.86 3.28 3.40 3.25 6.50736 3.59 275 0.37 3.763 2.86 3.37 3.74 3.34 6.68736 3.59 300 0.64 3.763 2.86 3.47 4.11 3.44 6.88

NONLINEAR FE ANALYSIS

Model The finite element analysis (FEA) of the experimentally tested beams was conducted using the ATENA commercial package (ATENA2D 2004). A two-dimensional nonlinear finite element model was used. It is based on a smeared crack model for concrete, in which cracked concrete is represented as an orthotropic material. The nonlinear concrete model includes compression and tension softening. Steel reinforcement and prestressed wires are assumed to behave in an elastic-plastic manner with strain hardening effects, while FRP reinforcement is assumed to be linear elastic up to brittle fracture in tension. The concrete of the test beams were modelled with four-node quadrilateral isoparametric elements. The internal bars, tendons and external FRP plates were modelled with two-node bar elements. The material properties given in Table 1 were used for the calculations. The presented results of the calculations in Figure 12 and Figure 13

259

are for two different tendon forces which were taken constant along the beam. Figure 11 illustrates the general FE mesh and crack pattern of beam no. 4 at F=250 kN. A finer mesh was used near the mid-span joint.

Figure 11: General FE mesh and crack pattern at F=250 kN

Results

-1

0

1

2

3

4

7 8 9 10 11 12 13 14 15 16

Beam length [m]

Stra

in [‰

]

beam no. 4: F= 250 kN, CFRP strain (mean value)ATENA calculation, beam no. 4, F=250kN, tendon force 523kNATENA calculation, beam no. 4, F=250kN, tendon force 736kNjoint at mid-span

joint at mid-span0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250

deflection at mid-span [mm]

load

F [k

N]

beam no. 3 (reference beam)beam no. 3, phase 1beam no. 3, phase 3beam no. 3, phase 4beam no. 4, CFRP strengthenedbeam no. 4, phase 1beam no. 4, phase 2beam no. 4, phase 3beam no. 4, phase 4ATENA: beam no. 3 (p=523)ATENA: beam no. 3 (p=736)ATENA: beam no. 4 (p=523)ATENA: beam no. 4 (p=736)

Fmax = 435 kN (100%)

Fmax = 352 kN (81%)

reference beam no. 3

beam no. 4

Figure 12: Comparison of strain measurements at beam underside with FEA

Figure 13: Comparison of beam deformation measurements with FEA

The comparison in Figure 12 of the strain measurements along the right side of the beam no. 4 with the two FEA presents once more that the tendon force has a strong influence on the strain in the CFRP (see Figure 8). The results are similar as the analytical calculations. The strain in the joint is also too low what shows again, that the tendon force in the test beam at mid-span is probably lower than in the rest of the beam. The load-deformation curves of the reference beam no. 3 and the strengthened beam no. 4 is displayed in Figure 13. It can be seen that due to strengthening the maximal load increased about 20% and the deformation at maximum load was also larger. The FEA shows for the beam no. 4 that at lower loads the calculations with the higher tendons force have a better agreement with the measurements and vice versa at higher loads. The FEA of the reference beam no. 3 with the lower tendon force demonstrate a good correspondence with the measurements. DISCUSSIONS AND CONCLUSIONS The large-scale tests showed that the strengthening for flexure using CFRP plates is feasible also on real large-scale structures. The strengthened beam reached about 20% more maximum load than the reference beam. Also the strain at top and underside of the beam are lower in the case of the strengthened beam if compared to the reference beam. Equilibrium debonding The debonding at mid-span is called ‘equilibrium debonding’ because it was caused from the strain peak in the CFRP plates. This strain peak is the result of the different forces in the CFRP plates in the cross-section in the joint at mid-span (cut B-B, Figure 1) and in the cross-section beside the joint (cut A-A). This force gradient activates global shear stresses between CFRP plates and concrete surface which causes debonding. The reason for the force (and strain) gradient in the CFRP plates and consequently for ‘equilibrium debonding’ are discontinuities in the reinforcement and changes in the internal stress state due to prestressing. Maximum global shear stresses of 3.3 MPa (mean value) before debonding were measured at mid-span during the test. This value is lower as the shear stress resistance which can be determined from the Swisscode. It can be concluded that potential debonding points at structures which are strengthened for flexure are locations where internal reinforcements or tendons start to yield and discontinuities along the beam due to changes of reinforcement or internal stress state. This has to be considered for the design.

260

Stable debonding As described above, due to equilibrium reasons, the strain in the CFRP plate at mid-span had a peak and thus a high shear stress between CFRP plate and concrete occurred. Consequently, debonding started at this location. This debonding was ‘stable’. That means that after debonding the load could further be increased. It is assumed that the following reasons are responsible for debonding being stable:

• distinctive peak in CFRP strain • after debonding a relieve of the CFRP plate takes place because a longer length of the plate is used to

carry the load and the strain is distributed From this, it can be assumed that the phenomenon ‘stable debonding’ occurs e.g. for the following cases:

• for three point tests at the region under the loading where the internal reinforcement yields • strengthening of the negative moment for continuous beams over the supports and yielding of the

internal reinforcement • discontinuities of the reinforcement and the internal stress state due to internal prestressing

ACKNOWLEDGMENTS The financial support of ASTRA, the Swiss Federal Roads Authority, is acknowledged. Furthermore, thanks go to the canton Ticino who provided the test beams. REFERENCES ACI (2002). ACI440.2R-02, Guide for the design and construction of externally bonded FRP systems for

strengthening concrete structures., American Concrete Institute. ATENA2D (2004). nonlinear FE calculation software, version 2.1.11. Prague, Czech Republic, Cervenka

Consulting. Cubus (2005). STATIK5 (structural analysis of frames) and FAGUS5 (cross-section analysis). Zurich, Cubus

Engineering Software. Czaderski, C. and M. Motavalli (2004). "Remaining Tendon Force of a Large-Scale 38-Years-Old Prestressed

RC Bridge Girder." PCI Journal, submitted for consideration for publication. Czaderski, C. and M. Motavalli (2005). Strengthening of a large-scale prestressed RC bridge girder. COBRAE

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El-Hacha, R., R. G. Wight and M. F. Green (2004). "Prestressed carbon fiber reinforced polymer sheets for strengthening concrete beams at room and low temperatures." Journal Of Composites For Construction 8(1): 3-13.

fib (2001). Externally bonded FRP reinforcement for RC structures - Bulletin 14, International Federation for Structural Concrete (fib), Switzerland.

ISIS (2001). Strengthening Reinforced Concrete Structures with Externally-Bonded Fibre Reinforced Polymers, Design Manual No. 4, ISIS Canada.

JCSE (2001). Recommendations for upgrading of concrete structures with use of continuous fiber sheets, Japan Society of Civil Engineers.

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Neubauer, U. and F. S. Rostasy (2001). Debonding mechanism and model for CFRP-plates as external reinforcement for concrete members. International Conference Composites in Construction, Oct. 2001, Porto.

Rabinovitch, O. and K. Frostig (2001). "Delamination failure of RC beams strengthened with FRP strips a closed-form high-order and fracture mechanics approach." Journal Of Engineering Mechanics-Asce 127(8): 852-861.

Shahawy, M. A., T. Beitelman, M. Arockiasamy and R. Sowrirajan (1996). "Experimental investigation on structural repair and strengthening of damaged prestressed concrete slabs utilizing externally bonded carbon laminates." Composites Part B-Engineering 27(3-4): 217-224.

SIA166 (2004). Klebebewehrungen (Externally bonded reinforcement), Schweizerischer Ingenieur- und Architektenverein SIA.

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Teng, J. G., J. F. Chen, S. T. Smith and L. Lam (2002). FRP Strengthened RC Structures. Chichester, John Wiley & Sons, Ltd., England.

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