103

Interfacial debonding failure for reinforced

concrete beams strengthened with carbon-fibre-
reinforced polymer strips
Ryan Bakay, Ezzeldin Yazeed Sayed-Ahmed, and Nigel Graham Shrive

Abstract: Rehabilitation of structures using fibre-reinforced polymers (FRPs) has become a preferred strengthening techni-
que. Crack-induced debonding failure has been repeatedly recorded when using fibre-reinforced polymer (FRP) laminates
to strengthen reinforced concrete (RC) beams and (or) slabs in flexure. A testing programme has been performed to deter-
mine the effect of the concrete compressive strength and the amount of shear reinforcement on the interfacial debonding.
The ultimate strain at failure in the bonded laminates (usage efficiency) and the strain compatibility between the laminates
and the concrete sections have been investigated. The current design methods for reinforced concrete members strength-
ened with FRP do not explicitly consider the interfacial debonding failure; using the results of the experimental pro-
gramme, the applicability and limitations of these design methods are identified. New design procedures are proposed and
compared with the experimental programme results and the currently adopted procedures.
Key words: bond strength, debonding, fibre-reinforced polymer, strengthening.
Résumé : La restauration des structures par l’utilisation de polymères renforcés de fibres (PRF) est devenue la méthode
préférée de renforcement. Le décollement causé par des fissures a été enregistré à plusieurs reprises lors de l’utilisation de
laminés aux PRF pour renforcer en flexion les poutres–dalles en béton armé. Un programme d’essai a été réalisé afin de
déterminer l’effet de la résistance en compression du béton et la quantité de renforcement en cisaillement sur le décolle-
ment à l’interface. La résistance à la rupture des laminés liés (rendement à l’usage) et la compatibilité des contraintes entre
les laminés et les sections de béton ont été examinées. Les méthodes de calcul normalement utilisées pour concevoir les
éléments en béton armés renforcés de PRF ne tiennent pas compte explicitement du décollement à l’interface; les résultats
du programme expérimental ont permis de déterminer l’applicabilité et les limites de ces méthodes de conception. De nou-
velles procédures de conception sont proposées et comparées aux résultats du programme expérimental ainsi qu’aux procé-
dures utilisées actuellement.
Mots-clés : résistance du lien, décollement, polymère renforcé de fibres, renforcement.
[Traduit par la Rédaction]

Introduction
However, when composite action is not maintained to ul-
Failure modes of reinforced concrete (RC) beams–slabs timate load, interfacial debonding of the laminates occurs in
strengthened by soffit-bonded fibre-reinforced polymer a premature failure mode. Interfacial debonding (as the most
(FRP) laminates can be separated into two categories based common mode of failure) may occur due to one of the fol-
on the duration of the composite action between the two ma- lowing:
terials. When composite action is maintained until the ulti-
concrete cover separation along the end of the bonded la-
mate load is reached, failure occurs by one of the following minates (Teng et al. 2002)
(Teng et al. 2002):

plate-end interfacial debonding (Teng et al. 2002)

concrete crushing
intermediate (flexure or flexure shear) crack-induced in-

FRP tensile rupture terfacial debonding – IC (Smith and Teng 2002a, 2002b)

shear failure of the concrete beam.
critical diagonal crack-induced interfacial debonding

Received 30 June 2007. Revision accepted 22 August 2008. Published on the NRC Research Press Web site at cjce.nrc.ca on 24 January
2009.
R. Bakay. Read Jones Christofferson, 1816 Crowchild Trail NW, Calgary, AB T2M 3Y7, Canada.
E.Y. Sayed-Ahmed.1 Structural Engineering Department, Ain Shams University, Cairo 11517, Egypt.
N.G. Shrive. Civil Engineering Department, University of Calgary, Calgary, AB T2N 1N4, Canada.
Written discussion of this article is welcomed and will be received by the Editor until 31 May 2009.
1Corresponding author (e-mail: eysahmed@gmail.com).

Can. J. Civ. Eng. 36: 103–121 (2009) doi:10.1139/L08-096 Published by NRC Research Press
104 Can. J. Civ. Eng. Vol. 36, 2009

(CDC) (Teng et al. 2004). Several parameters affect the the behaviour reasonably well. A simple model (Chen and
premature debonding failure mode (Teng et al. 2002). Teng 2001; Teng et al. 2002) defines the maximum stress
Among these, the authors argue that the shear strength of in the bonded FRP laminates, sup, by
the concrete cover below the flexural reinforcement in vffiffiffiffiffiffiffiffiffiffiffiffiffi
the beam–slab plays a decisive role. Other parameters u pffiffiffi0ffi
uEp fc
pertain to the beam’s geometry, concrete compressive s up ¼ abp bL t
tp
strength, amount of shear reinforcement, amount of the
steel and FRP reinforcement, etc. 2 31=2
It was believed from previous work that higher concrete 2  ðbp =b c Þ
½1 bp ¼ 4 5
strengths lead to this sudden brittle failure mode given the 1 þ ðbp =bc Þ
higher fracture energy that is released when high-strength 8
> L  Le : 1 0 1
concrete cracks. A contrary prediction would be that higher <
concrete strength would lead to an increased shear capacity, bL ¼ pL
according to conventional design methods, which should de- > L < Le : sin@ A
: 2Le
lay, if not prevent, the failure mode in question. The contrary
arguments reflect that the effect of concrete strength was un-
clear and worthy of study (Bakay 2003). Thus, an experimen- sffiffiffiffiffiffiffiffiffi
tal study to investigate the effects of the concrete strength Ep tp
was performed. As failure almost resembles shear cracking, Le ¼ pffiffiffiffi
fc0
the effect of shear reinforcement was also investigated.
where a is an empirical factor calibrated against experimen-
Bond between fibre-reinforced polymer and tal data for beams and slabs; bp and bc are the FRP laminate
concrete and the concrete beam widths, respectively; L is the length
Strain compatibility through the depth of a reinforced of the FRP laminates beyond the maximum moment loca-
concrete section with externally bonded FRP relies on a per- tion; EP is the elastic modulus of the FRP; f ’c is the concrete
fect bond and has been assumed for analysis and design: compressive strength (MPa); tp and Le are FRP laminates’
some experimental investigations support this assumption thickness and effective bond length (mm), respectively.
(Triantafillou and Plevris 1992; Spadea et al. 1998). How- Teng et al. (2002) recommended design values for a ran-
ever, a perfect bond does not always occur. Based on exper- ging between 0.38 and 0.43, which corresponded to the
imental investigations performed by Chen and Teng (2001) lower limit with only a 5% exceedence generated in their
and Yuan et al. (2004), it was argued by Lu et al. (2005) beams–slabs experimental programme; Hosny et al. (2006)
that the major factors affecting the bond-slip behaviour (and showed that the factor a still needs further calibration.
thus composite action) between the concrete surface and the The second scenario for intermediate crack-induced inter-
FRP laminates are facial debonding is attributed to the formation of one or
more significant cracks between the crack where debonding

concrete compressive strength initiates and the free end of the bonded laminates. In this sit-

bond length up to a certain effective length uation, the stress state is totally different from that of the

axial stiffness of the FRP simple pull-off tests. Simple bond models cannot simulate

FRP-to-concrete width ratio this behaviour. Chen et al. (2007) proposed the following

adhesive axial stiffness and adhesive compressive equation for the ultimate load, Pu, of such cases:
strength.
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
> bb 2Gf Ep tp arccosb
>
> pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for L 
Many models have been proposed for the bond strength >
< 1b2 l
between the FRP laminates and the concrete; these were ½2 Pu ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
summarized elsewhere (Bakay et al. 2008). In most models, >
> bb 2Gf Ep tp sinðlLÞ arccosb
>
> for L <
the assumed stress state simulates a pull-off test specimen : 1  b cosðlLÞ l
where the FRP laminates are bonded to the concrete and
subjected to tension.
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 1ffi
The FRP plate-end debonding has been investigated ex- u
u 2
tensively and various models have been proposed (Teng et ut 1 bb A
al. 2002; Bakay et al. 2008), with some being assessed by l ¼ t f @ þ
2Gf Ep tp bc Ec tc
Smith and Teng (2002a, 2002b). Fewer models are available
for intermediate crack-induced debonding, which has been
quite a common failure mode. Chen et al. (2007) indicate 0 1
that intermediate crack-induced interfacial debonding can tf @ E b t
p p pA
¼ 1þ
occur in two scenarios. In the first, there are no significant df Ep tp Ec bc tc
cracks between the free end of the bonded laminates and
the crack where debonding initiates, typical for beams or
slabs with low reinforcement ratios. The stress state in this where Gf is the fracture energy, which is defined by the area
scenario has similarity to that in the simple pull-off tests. under the bond-slip model adopted in the calculations for
Thus, for this case, the bond strength models can simulate this joint; b is the ratio between the forces in the bonded la-

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Bakay et al. 105

Fig. 1. Schematic of the test setup: (a) loading and internal forces, (b) elevation of the test setup, (c) side-view of the test setup, (d ) cross
section of the tested beams and stress–strain distributions (not to scale). All dimensions in millimetres. a, depth of the concrete compression
blocks; Af, cross-sectional area of the FRP laminate; As, area of the steel reinforcement; b, width of the concrete element; BMD, bending
moment diagram; c, depth to the N.A.; Cc, compression force acting on the concrete; CFRP, carbon-fibre-reinforced polymer; ds, depth to
the steel reinforcement; Ff, equivalent compression block depth coefficient; Fs, tensile stress in the steel reinforcement; h, beam depth; L,
unsupported length; M, bending moment; P, load; SFD, shear force diagram; Tf, tensile force in the FRP laminate; Ts, tensile force in the
steel reinforcement; RC, reinforced concrete; a1, equivalent compression block depth coefficient; b1, equivalent compression block centroid
location coefficient; 3cu, concrete crushing strain; 3f, strain in the FRP laminate; 3s, strain in the steel reinforcement.

minates at the two crack locations; l is a factor determined Experimental investigation

as in eq. [2]; tf is the local bond strength between the two
cracks; Ec is the elastic modulus of concrete; and tc is the Twelve reinforced concrete beams with bonded CFRP
thickness of the concrete element; and df is the maximum strips were tested monotonically in flexure to scrutinize the
slip of the bonded laminates between the two cracks, re- effect of concrete compressive strength and shear reinforce-
spectively. Despite the attempts of Chen et al. (2007) to ment on the crack-induced interfacial debonding failure
simplify this proposed equation, it still contains implicit mode. The beams were tested in a simply supported, four-
parameters that are difficult to evaluate practically. point loading test arrangement. To assess repeatability in

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106 Can. J. Civ. Eng. Vol. 36, 2009

Fig. 2. Instrumentation of the tested beams: (a) schematic and dimensions, (b) instrumentation setup, (c) concrete gauges, and carbon-fibre-
reinforced polymer strip gauges looking at the beam from both its (d ) side and (e) bottom. RC, reinforced concrete. All dimensions in
millimetres.

the experiment, two beams of each type were constructed. Based on the design values of the concrete strengths, the
The test setup and the beams cross section are shown in amount of required shear reinforcement that facilitated flexural
Fig. 1. Gauges configuration adopted to record the response or shear failure was determined: stirrups spacing of 100, 160,
of the beam during testing is shown in Fig. 2. and 320 mm were selected. Stirrups were constructed from
All beams were 150 mm wide, 300 mm deep, and 2000 mm No. 10 (yield strength fy = 500 MPa) deformed high-strength
long. Concrete was batched using the mix design summarized steel bars. Two No. 20 deformed bars were used as the flexural
inTable 1 and the results are detailed in Table 2. Three reinforcement (fy = 500 MPa; elastic modulus of the steel Es =
100 mm diameter, 200 mm high test cylinders were cast from 200 GPa).
each batch to test for compressive strength. The beams and For all beams, CFRP strips with a total area of 180 mm2
test cylinders were cured under wet burlap for 18 d. were bonded to the beam soffits as externally applied

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Bakay et al. 107

Table 1. Mix design for concrete batches.

Mix Cement 20 mm dacite 10 mm river River sand Beach sand Water Slump Target f ’c
No. (kg/m3) (kg/m3) gravel (kg/m3) (kg/m3) (kg/m3) (L/m3) (mm/m3) (MPa/m3)
1 500 680 250 410 410 160 50 65
2 440 720 260 400 400 168 80–90 50
3 320 750 230 450 450 179 80–95 35

Table 2. Test results for the 12 beams.

FRP strain (%) at:

Mix Beam Actual strength, Stirrup Cracking Failure Max. deflection Failure West East
No. No. f ’c (MPa) spacing (mm) load (kN) load (kN) (mm) mode load load
1 1 69.9±2.3 160 *50 449 13 IC 0.83 0.38
1 4 64.1±2.2 160 *50 426 11 IC 0.43 0.59
2 2 65.1±0.7 160 *50 433 12.6 IC 0.62 0.54
2 3 57.2±2.0 160 *48 408 11.8 IC 0.47 0.59
3 9 46.1±1.9 160 *50 406 11.8 CC+IC 0.66 0.56
3 10 48.8±2.0 160 50–60 389 11.6 CC+IC 0.58 0.56
3 11 41.6±0.4 160 *50 395 13.1 CC+IC 0.59 0.57
3 12 40.3±1.3 160 *50 371 11.3 CC+IC 0.57 0.49
3 5 45.4±2.9 100 *40 425 11.9 CC+IC 0.62 0.53
3 6 43.7±1.5 100 *50 410 11.9 CC+IC 0.59 0.52
3 7 43.7±3.5 320 50–60 343 10 SF+CDC 0.49 0.49
3 8 41.8±0.4 320 40–50 347 10.8 SF+CDC 0.48 0.65
Note: FRP, fibre-reinforced polymer; IC, intermediate flexure or flexure shear crack-induced debonding; CC, concrete crushing in compression; SF,
shear failure; CDC, critical diagonal crack-induced debonding.

strengthening. Four beams (beams 1 to 4) were strengthened Beams 1 to 4

with three CFRP strips, each with a cross-sectional area of The concrete strength of beams 1 to 4 ranged between
60 mm2. The remainder of the beams used one CFRP strip 57.2 and 69.9 MPa, with ‘‘adequate’’ shear reinforcement
having a cross-sectional area of 180 mm2. (No. 10 spaced at 160 mm) with three CFRP strips
Material specifications for the CFRP strips and the epoxy (180 mm2) bonded to their soffits. During loading, hairline
adhesive (Sikadur 30) were provided by the manufacturer flexural cracks appeared in the constant moment region
(Sika Canada Inc., Pointe-Claire, Que.). The elastic modulus, with shear cracks forming within the shear span. Simultane-
tensile strength, and breaking strain of the CFRP strips are ously, the CFRP strips began to debond from the beam be-
listed as 165 GPa, 2800 MPa, and 1.7%, respectively. The yond the support at one end. The reaction force provided by
same properties for the epoxy adhesive are listed as 4.5 GPa, the support prevented this debonding from leading to total
24.8 MPa, and 1%, respectively. The CFRP strips were exter- separation of the laminates from the beams. The load–de-
nally anchored as they covered the full length of the beam, and flection curves (Fig. 3) indicate cracking loads of approxi-
were trapped between the beam and its supports. mately 50 kN with no regions of plastic deformation. For
beam 1, there was almost a complete absence of post-peak
displacement, but there was some post-peak ductility in the
Results of the experimental investigation other beams because of the less destructive nature of the
The main results for all the tested beams are summarized failures.
in Tables 1 and 2 with the load–deflection curves presented Failure occurred at loads ranging between 408 and
in Fig. 3. For ease of comparison, beams are arranged as fol- 449 kN at a maximum mid-span deflection ranging between
lows: 11 and 13 mm. Failure happened when an intermediate in-
clined crack progressed from the level of the conventional

1 and 4: ‘‘high’’ concrete strength and ‘‘adequate’’ shear
steel reinforcement down to the external CFRP laminates
reinforcement.
and back toward the support (Fig. 4). Additional cracking in

2 and 3: ‘‘moderate’’ concrete strength and ‘‘adequate’’ beam 1 (thought to have resulted from the dynamic effects
shear reinforcement. of the rapid failure) progressed along the line of the steel re-

9 to 12: ‘‘low’’ concrete strength and ‘‘adequate’’ shear inforcement into the constant-moment region with crack
reinforcement. widths being quite large at failure. Beams 2 to 4 failed in a

5 and 6: ‘‘low’’ concrete strength and ‘‘high’’ shear rein- similar manner to beam 1, but with significantly less dam-
forcement. age. For beams 2 and 4, the CFRP strips separated with a

7 and 8: ‘‘low’’ concrete strength and ‘‘low’’ shear rein- chunk of concrete torn from the end of the beam.
forcement. After failure, some concrete remained bonded to the lami-

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108 Can. J. Civ. Eng. Vol. 36, 2009

Fig. 3. Load–deflection curves: (a) effect of concrete compressive strength with stirrup spacing of 160 mm; (b) effect of shear reinforce-
ment with concrete strength for the beams ranging between 41.8 and 48.8 MPa. sv, spacing between the stirrups.

nate, indicating that failure progressed through the concrete ibility between the CFRP strip and the concrete is lost at a
cover and not through the adhesive layer. As the concrete in very early stage of loading: the support reaction, acting as
the constant-moment region did not crush, failure appeared an external anchor, held the CFRP in place. This loss of
tohave resulted from the intermediate flexure crack-induced strain compatibility was encountered in all beams and agrees
debonding. No visual evidence was present that may suggest with the findings and arguments of Sayed-Ahmed et al.
that the three individual CFRP strips behaved any differently (2004) and Breña et al. (2003).
than a single strip would have. The strain in the CFRP strips recorded at the ultimate
The strain distribution along the concrete section and in load varied between 0.38% and 0.82% under each load point
the CFRP strips was recorded during the test at the locations for beams 1 to 4, a value that is well beneath the ultimate
shown in Fig. 2. A sample of the strain distributions corre- breaking strain of 1.7%. This would indicate a CFRP mate-
sponding to 20%, 40%, 60%, 80%, and 100% for beam 7 rial effectiveness, with respect to strain, of only 48%.
are plotted in Fig. 5. A very similar scheme were recorded
for all beams. Beams 5 and 6
The recorded strain distributions show that strain compat- The concrete strength of beams 5 and 6 were 45.4 and

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Bakay et al. 109

Fig. 4. Failure of beam 1 in an intermediate flexure or flexure shear crack-induced debonding (IC) mode, beam 5 in concrete crushing
acting interactively with an IC mode, and beam 7 in interactively acting shear critical diagonal crack-induced debonding (CDC) mode: (a)
front view of beam 1, (b) back view of the beam 1, (c ) front view of beam 5, (d) front view of beam 7, (e) back view of beam 7, (f ) end
peeling of the strip for beam 1, and (g) end peeling of the strip with a chunk of concrete for beam 5.

43.7 MPa, respectively. Both beams were over-reinforced for spalling of the concrete near one of the ends was noticed.
shear (shear reinforcement: No. 10 at a spacing of 100 mm). The region was approximately 30 mm  30 mm with a depth
One CFRP strip (180 mm2) was bonded to the soffit of each varying between 5.0 and 10.0 mm. This region was filled with
beam. Prior to application of the laminates to beam 5, some adhesive prior to application of the laminate; note that in this

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110 Can. J. Civ. Eng. Vol. 36, 2009

Fig. 5. Strain profiles for beam 7 at sections: (a) under the east (right) point load P2 and (b) under west (left) point load P1.

region, the adhesive thickness would have exceeded that rec- moment region was also apparent. Video recording of this
ommended by the manufacturer. test revealed that the compressive failure of the concrete
Cracking progressed similar to the previous beams and in was the limiting factor for this beam and the debonding
this instance the tendency of the laminates to peel away occurred interactively with the concrete crushing.
from the beam beyond the support tore a chunk of concrete The ultimate load reached for beam 5 was 425.4 kN,
from the beam and it remained bonded to the laminates whereas for beam 6 the maximum load was 410 kN: both
(Fig. 4g). Some peeling, but to a much lesser extent, was of these peak loads occurred with a centre-span deflection
noticed at the opposite end of the beam. of 11.9 mm. Despite the significantly reduced concrete
Two distinct failures were observed for these beams. Sim- strength compared with beams 1 to 4, the ultimate load ca-
ilar to the previous cases, a crack propagated from the steel pacity was only marginally less than, and in some cases
reinforcement level to the CFRP strips and back to the sup- slightly higher than, those beams. Shifting of the primary
port, separating the CFRP strip from the beam with some failure mode from the premature debonding to concrete
concrete remaining bonded to the strip: distinct intermediate crushing has allowed more efficient use of the concrete
crack-induced interfacial debonding. However, unlike the compression region.
previous cases, crushing of the concrete in the constant- A change in slope of the load–deflection plot at approxi-

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Bakay et al. 111

mately 40 kN corresponds to the cracking load of beam 5, compressive failure of the concrete occurred prior to sepa-
which agrees with the experimental observations; whereas, for ration of the CFRP laminates from the beam. Crushing oc-
beam 6 the cracking load appears to be about 50 kN (Fig. 3) and curred away from the external load points similar to beams
it was experimentally observed to be about 60 kN. The slope 5 and 6, in contrast to beams 7 and 8. Cracking resulting
remains linear thereafter until the ultimate loads are almost from the strip separation extending into the constant mo-
reached. There was very little post-peak deformation. ment region along the line of the steel reinforcement. The
The strain incompatibility between the CFRP and the con- peak loads obtained ranged between 389 and 406 kN at
crete was also recorded for these beams, but it was less se- deflections ranging between 11.3 and 11.8 mm. The crack-
vere compared with beams 1 to 4 where failure was solely ing loads were approximately 50 kN (Fig. 3) as observed
from crack-induced interfacial debonding. The CFRP strain during testing. In beam 10, there is a slight shift in the
gauges provided strains at the ultimate loads ranging be- load-displacement plot at approximately 240 kN, which re-
tween 0.52% and 0.62%, implying that only 36% use was sulted from stopping the test to trace cracks. Beams 9, 10,
made of the CFRP capacity. Thus, altering the failure mode and 11 had more post-peak ductility than beam 12.
did not increase the usage efficiency of the CFRP strip. The lack of strain compatibility between the CFRP strips
and the concrete section is again confirmed from the early
Beams 7 and 8 stages of loading for this group. The maximum values of
Beams 7 and 8 were designed to fail in shear rather than flex- the measured CFRP strain ranged between 0.48% and
ure. The concrete strength of beam 7 was 43.7 MPa, and that of 0.66%, which is only a 39% use of the CFRP capacity.
beam 8 was 41.8 MPa. The beams were under-reinforced
for shear (No. 10 at a spacing of 320 mm). One CFRP Discussion
strip (180 mm2) was bonded to the soffit of each beam.
The experimental investigation reveals that the failure
Flexural cracks first become evident around 50–60 kN in mode of RC beams strengthened with CFRP laminates is de-
the constant-moment region, which is supported by the pendent on the duration of composite action between the
load–deflection plot (Fig. 3). The ultimate loads reached two materials. Three modes of failure were observed: con-
were 343 kN at a corresponding deflection of 10.0 mm crete crushing, shear failure, and crack-induced interfacial
(beam 7), and 347 kN at a maximum centre-span deflection debonding. Depending on the concrete compressive strength
of 10.8 mm (beam 8). A distinctive mode of failure was evi- and the shear strength of the beam, interactive failure modes
dent for these beams (Fig. 4d): shear failure as the primary between concrete crushing or shear failure and interfacial
mode acting interactively with critical diagonal crack- debonding were also recorded.
induced interfacial debonding of the CFRP strip.
Another main outcome of the testing programme is the
During loading, a shear crack developed and traversed the
confirmation of the loss of strain compatibility between the
entire depth of the beam, extending from the location of the
CFRP strips and the concrete section at a relatively early
external load point to the CFRP laminates (Fig. 4d). In beam
stage of loading in all 12 beams. Increasing the concrete
7, the crack was steeper in the middle region of the beam
strength or the shear resistance of the beam had no effect
than in the upper and lower portions; whereas for beam 8,
on this behaviour. The strain measurements also revealed
the slope was more uniform. Once the crack reached the
that the efficiency of use of the bonded CFRP strip was re-
CFRP strip, propagation back to the support proceeded
duced because of the interfacial debonding.
slower than in previous tests, separating the CFRP strip
from the beam. This was distinct critical diagonal crack- Effect of concrete compressive strength
induced interfacial debonding. In conjunction with failure,
some crushing of the concrete occurred under a load point, Failure mode
which may be a localized effect as it only occurred in the Higher strength beams (beams 1–4) failed due to crack-
vicinity of a point load, but it also suggests that the flexu- induced interfacial debonding with no evidence of concrete
ral and shear capacities of the beams were nearly equal. crushing. For lower strength beams (beams 9–12), concrete
Again, there was a lack of strain compatibility between the crushing occurred interactively with interfacial debonding:
CFRP strip and the concrete section from the very early stages concrete crushing was the primary cause of failure.
of loading (Fig. 5). The maximum recorded CFRP strain was The degree of peeling of the laminates from the beam be-
0.49% and 0.65%, implying only 38% of the CFRP capacity yond the support locations as cracking progressed dynamically
was used. Thus, altering the failure mode neither increased could not be quantified with respect to concrete compressive
the efficiency of CFRP usage nor changed the incompatibility strength or mode of failure. Three varieties of peeling of the
of strain between the CFRP strip and the concrete section. laminates were observed: peeling with no cracking in the con-
crete, peeling with a chunk of concrete remaining bonded to
Beams 9 to 12 the laminates, and peeling that resulted in separation of a piece
The concrete strength of beams 9–12 ranged between 40.3 of concrete from the beam. Separation of a chunk of concrete
and 48.8 MPa, respectively. The beams had ‘‘adequate’’ from the remainder of the beam occurred in the two beams
shear reinforcement (No. 10 spaced at 160 mm). One CFRP with a compressive strength of approximately 65 MPa.
strip (180 mm2) was bonded to the soffit of the beam. The extent of damage resulting from the dynamic effects
Failure was similar to that of beams 5 and 6 in which two dis- of failure is also interesting. In instances where crack-in-
tinct failure modes could be observed: concrete crushing in the duced interfacial debonding appeared to occur as either a
constant-moment region and intermediate crack-induced primary or secondary failure, the extent of crack propagation
interfacial debonding. During testing, it was observed that into the constant-moment region was not always equal.

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112 Can. J. Civ. Eng. Vol. 36, 2009

Fig. 6. Concrete compressive (comp.) strengths of the tested beam specimens versus the ultimate loads and the maximum deflections for the
analyzed beams with a stirrup spacing of 160 mm. R2, correlation coefficient.

However, there appeared to be no relation between concrete stant-moment region cracking significantly reduced any ca-
strength and the dynamic cracking effects during failure. pacity for post-peak deflection.
When dynamic cracking was extensive and progressed into The ‘‘low’’ shear reinforcement specimens exhibited the
the constant-moment region, there appeared to be a reduc- lowest deflections of all tests, but the number of tests does
tion in post-peak deflection (beams 1, 5, 6, and 9). not allow for a firm conclusion to be drawn.
Ultimate load Carbon-fibre-reinforced polymer usage efficiency and
The authors emphasize that conclusions must be drawn in strain compatibility
light of the small sample size, containing in some instances The CFRP strip usage efficiency is based here on the ulti-
only small variations in concrete strengths. Generally, higher mate recorded strain, compared with the nominal rupture
strength beams failed at higher loads. The linear regression strain. No definitive trends are obvious when the maximum
(Fig. 6) confirms this trend with a correlation coefficient, CFRP strains are compared with the compressive strength of
R2, higher than 86%. However, there is some variability the concrete. However, concrete compressive strength could
about the trend. be expected to affect the usage efficiency of the CFRP strips
For the ‘‘high’’ and ‘‘low’’ shear reinforced tests, there is in that the maximum strain was dependent on the failure
insufficient information to draw conclusions regarding the mode, which was in turn dependent on the concrete strength.
compressive strength and ultimate load. Strain compatibility between the strip and the concrete was
lacking for all beams regardless of the concrete compressive
Ductility strength.
Little variation in the mid-span deflection at ultimate load
was observed: deflections ranged from 10 to 13 mm. Con- Effect of shear strength of beams
crete strength has no obvious effect on the deflection at ulti-
mate load (Fig. 6). The beams with the two highest Failure mode
compressive strengths had the two highest deflections. In Altering the amount of shear reinforcement changed the
terms of post-peak behaviour, the lowest amount of post- mode of failure from flexural toward shear. Here, beams
peak deflection was exhibited by beam 1, the strongest with ‘‘adequate’’ or ‘‘high’’ shear reinforcement displayed
beam and the one with the most destructive failure. As no difference in failure mode for similar concrete strengths.
lower strength beams exhibited similar damage during the Both sets of beams failed as a result of the concrete failing
formation of crack-induced debonding cracking, concrete in compression with secondary interfacial debonding. In
strength cannot be the only factor in the lack of post-peak these instances, the location of the shear reinforcement
displacement. The extensive cracking resulted in a substan- should not have influenced failure as crushing occurred in a
tial reduction of capacity, with the other beams that cracked region without shear stirrups and interfacial debonding
extensively (beams 5, 6, and 9) showing the same effect. cracking occured in the concrete cover layer, where there
The deflection observed at peak load was nearly the same were no stirrups. The crack formation resulting from secon-
for all the lower strength beams (beams 9–12). Examination dary interfacial debonding was much larger and destructive
of these tests supports the conclusion that the extensive con- for beams 5 and 6 (over-reinforced for shear) than most of

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Bakay et al. 113

Fig. 7. Shear strength (stirrup spacing) versus ultimate load or maximum deflection for: (a) beams 6, 8, and 12; (b) beams 5, 7, and 11.
Comp., compressive; R2, correlation coefficient.

the beams with similar concrete strengths and ‘‘adequate’’ peak failure loads than beams with ‘‘adequate’’ or ‘‘low’’
shear reinforcement, with the exception of beam 9. ones (Tables 1 and 2 and Fig. 7). The failure modes of com-
Beams 7 and 8 with ‘‘low’’ shear reinforcement failed parable beams appear similar with no indication that the dif-
interactively between shear and critical diagonal crack- ference in shear reinforcement led to failure. The difference
induced debonding: a major critical diagonal (shear) crack in maximum load for beams 6 (lowest of the ‘‘high’’ shear
extended throughout the entire depth of the beam and pro- reinforcement beams) and 9 (highest of the ‘‘adequate’’
gressed to separation of the laminate. Given the inclination of shear reinforced beams) is only 5 kN. However, the peak
the crack, it is not likely that any stirrups intersected the crack load of beam 5 (‘‘high’’ shear reinforcement), 424 kN, is
plane. Some crushing was apparent in the constant-moment considerably higher than any of beams 9 to 12 (‘‘adequate’’
region, with the inclined crack connecting to this crushed shear reinforcement), with the greatest disparity being 53 kN
region. Thus, it may be expected that the externally ap- (beam 12). The difference is suggestive of something more
plied load was near the flexural capacity of the beam, but than random cracking, experimental error or other uncon-
analysis of the beams indicated that this was not the case. trolled events. Further tests may shed light on this issue.
It is clear that beams that failed in shear (beams 7 and 8)
Ultimate load had lower peak loads than those that failed in flexure
Beams with ‘‘high’’ shear reinforcement reached higher (beams 5, 6, and 9 to 12). Shear is an undesirable failure

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114 Can. J. Civ. Eng. Vol. 36, 2009

mode that underutilizes both the concrete compression block veloping the full laminates’ capacity should be provided so
and the FRP reinforcement. that this mode of failure is avoided. It is also stated that if de-
bonding governs design, analysis may proceed by limiting the
Ductility stresses and strains in the FRP to predefined values. However,
There is no noticeable difference in the deflection at peak no appropriate limits are established for determining whether
load between the ‘‘high’’ and ‘‘adequate’’ shear reinforce- or not debonding of the composite laminates will govern the
ment beams (Figs. 3, 7). Figure 7 shows the marginal varia- design. An expression for development bond length, lfrpd, a
tion in deflection with shear strength. ‘‘Low’’ shear- concept similar to that for steel reinforcement, is given by
reinforced beams reached lower deflections at peak load
compared with all other specimens: probably because of 3f
½3 lfrpd ¼ kd Ef tf kd ¼ pffiffiffi0ffi
similar stiffness but lower applied load. k fc
Following the achievement of peak loads, beams 5, 6, and
9 displayed virtually no additional deflection. This is attrib- where Ef, and tf are the elastic modulus and the thickness of
uted to the larger cracks and greater extent of damage, espe- the FRP laminates, respectively; 3f is the strain in the lami-
cially in the constant-moment region. The ‘‘low’’ shear nates; k is a constant; and f ’c is the concrete compressive
reinforcement beams displayed steady reduction in strength strength.
at the peak load: failure occurred more slowly, which is im- In contrast to the implications of the ISIS guidelines via
portant from a practical safety standpoint. eq. [3], it has been argued that the failure load increases with
bonded length up to a critical length beyond which the load
Carbon-fibre-reinforced polymer usage efficiency and
remains constant (Chen and Teng 2001; Teng et al. 2002;
strain compatibility
Udea et al. 2003; Yuan et al. 2004; Lu et al. 2005). Different
For low concrete strength, the degree of efficiency reached
equations defining the critical (effective) bond length have
in the FRP appears constant. The maximum strains in the two
been given by many researchers (Bakay et al. 2008).
‘‘high’’ shear reinforcement beams (beams 5 and 6) were
0.52% to 0.62%, almost the same as those recorded for beams The ISIS design calculations were undertaken with the as-
with ‘‘adequate’’ shear reinforcement (beams 9–12: 0.49% to sumption that concrete crushing would be the limiting crite-
0.66%) or for beams with ‘‘low’’ shear reinforcement (beams ria for flexural failure. For all specimens, the estimated
7 and 8: 0.49% to 0.65%). Shear reinforcement, therefore, CFRP strains at concrete crushing were well below the
does not appear to affect CFRP efficiency. breaking value, validating this assumption. Using strain
The strain profiles for all beams show that strain incom- compatibility, the steel reinforcement was determined to
patibility between the CFRP strip and the concrete section have yielded in all beams when concrete crushed. Thus, con-
does not change with increasing shear strength. sidering flexure, the beams were all in the second failure
category of the ISIS design guidelines. Sample calculations
performed using MathCad version 13 (Parametric Technol-
Analytical models ogy Corporation, Needham, Mass.) are shown here:
Some of the current models for predicting the behaviour
of members strengthened with FRP are outlined and applied ISIS guidelines  beam 1 Pf ¼ 449 kN
to the specimens of the experimental programme. fc0 ¼ 69:9 MPa Af ¼ 180 mm2 Ef ¼ 165 GPa
As ¼ 600 mm2 fy ¼ 500 MPa
ISIS Canada design guidelines a1 ¼ 0:85  0:0015 fc0 ¼ 0:745
Intelligent Sensing for Innovative Structures (ISIS) Canada b1 ¼ 0:97  0:0025fc0 ¼ 0:795
has published manuals to facilitate design of structural mem- b ¼ 150 mm h ¼ 300 mm ds ¼ 265 mm
bers using FRP technology. One of these manuals is con- 3cu ¼ 0:0035
cerned with strengthening RC structures with externally 3cu
bonded fibre-reinforced polymers (Neale 2001). These guide- a1 fc0 bb1 c ¼ As fy þ hEf Af ! Solve; c
c
lines follow the current Canadian standard (CSA 2002), with ½4 c ¼ 98:98 mm
consideration of the following possible modes of failure:

concrete crushing. 3cu d
3s ¼ ¼ 0:00937

steel yielding followed by either concrete crushing or c
FRP rupture. 3cu

debonding of the FRP reinforcement near or at the con- Mr ¼ a1 fc0 bb1 c½ds  b1 ðc=2Þ þ hEf Af ðh  ds Þ
c
crete–FRP interface
Mr ¼ 149:79 kN  m
Pf
A design is initiated with the assumption of a particular Mexp ¼ ð0:6Þ ¼ 134:7 kN  m
2
failure mode from the previously defined three modes. If this
initial mode is determined not to be the cause of failure, then
the process is repeated with the assumption of another failure where Pf is the failure load recorded experimentally for
mode. This method does not incorporate guidelines for design beam 1, Af is the cross sectional area of the laminates, Ef is
with the assumption that interfacial debonding may be the the elastic modulus of the laminates, As is the area of ten-
main cause of failure. Rather, it recommends that appropriate sion steel, fy is the yield strength, a1 is the equivalent com-
anchorage should be supplied or an adequate bond length de- pression block depth coefficient, b1 is the equivalent

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Bakay et al. 115

compression block centroid location coefficient, b is the where b is the beam depth, Av is the area of shear reinforce-
beam width, h is the beam depth, ds is the depth to the steel ment, sv is the spacing between the stirrups, vc is the shear
reinforcement, 3cu is the concrete crushing strain, c is the strength of the concrete, vs is the shear strength provided by
depth to the neutral axis, 3s is the strain in the steel reinfor- the stirrups, and vr is the shear strength of the beam.
cement, Mr is the moment resistance of the beam, and Mexp The results obtained for all the beams are listed in Ta-
is the failure moment experimentally recorded. ble 3. This method underpredicts the capacities of beams
The failure loads predicted for all beams are listed in Ta- failing as a result of interfacial debonding (beams 1–4),
ble 3 and are compared with the experimental failure loads. with the predicted capacities being 82% to 86% of the ex-
The accuracy of this method can be seen to be quite variable. perimental values. When shear was obviously the cause of
This is due in part to the fact that the original design assump- failure (beams 7 and 8), the simplified shear calculations
tion of concrete crushing was not the cause of failure of all underpredicted the capacity significantly, giving only about
the beams. The ISIS method overpredicted the capacity of 65% of the experimental load. The predicted capacity would
the higher strength concrete beams and those contained low be even less if the suggested safety factors were employed.
levels of shear reinforcement — the beams that failed from This simplified shear method could possibly be modified to
debonding without any concrete crushing. In all beams where generate more accurate predictions and simple design guide-
crushing of the concrete was noticed (lower concrete lines for beams failing as a result of interfacial debonding, if
strengths and ‘‘adequate’’ shear reinforcement), ISIS guide- the effect to the CFRP strips were somehow incorporated
lines provided reasonable agreement with the experimental into the method. However, the contribution of the laminates
results; the guidelines were particularly good for the beams to the shear capacity of such RC beams has not yet been
with ‘‘high’’ shear reinforcement. In all cases, the predicted fully ascertained.
strength was higher than the actual strength, particularly for
beams wthat failed due to FRP interfacial debonding. In Shear friction
these latter beams, even using the support reaction to anchor The general form of the shear friction concept incorpo-
the CFRP did not prevent debonding of the laminates, con- rates the effects of concrete, steel stirrups, and pre-stressing
firming the existence of an effective bond length. (Loov 2000). When applied to the beams tested, loads be-
With the inclusion of the appropriate safety factors, the low the experimental values were predicted in all cases ex-
strengths predicted by the ISIS guidelines would fall below cept for the highly shear-reinforced beams. As shown in
the actual strengths and in some cases, be overly conserva- Table 3, the predicted capacities for beams 5 and 6 were
tive. In the case of beam 5, where the closest agreement is nearly identical to the experimentally obtained failure loads,
found, incorporation of safety factors would drop the pre- being only slightly higher. Although the shear friction con-
dicted capacity to about 70% of the actual capacity. cept includes the effect of the stirrups, it does not account
for the bonded FRP laminates. Nevertheless, the results ob-
More definitive guidelines regarding anchorage details
tained seem to model the behaviour of the beams quite well.
and strain limitations need to be established. Along with
Sample calculations performed using MathCad are shown
such guidelines, the purpose of the anchoring should be
here:
made clear. Whether the anchorage is to prevent interfacial
debonding failure or to prevent complete separation of the Shear friction  beam 1 Pf ¼ 449 kN
laminates is open to question. fc0 ¼ 69:9 MPa
The ISIS guidelines do not provide guidance on how to pre- bw ¼ 150 mm h ¼ 300 mm d ¼ 265 mm
dict the shear capacity of beams with only soffit-bonded fy ¼ 500 MPa Av ¼ 144 mm2 sv ¼ 160 mm
CFRP laminates. Hence, the shear capacity of the beams was ½6 0 0:25 0:25
bv ¼ 0:35 ð30=f
pffiffiffiffi c Þ ð500=hÞ
investigated according to the simplified shear method [CSA v45 ¼ bv fc0 bh
A23.3–94 2000 (CSA 2000)] and the method of shear friction.
vs1 ¼ A fy
pv ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
vr ¼ 2 v45 vs1 ðds =sv Þ  vs1 ¼ 214:7 kN
Simplified shear method
The simplified shear method (CSA 2000) determines the bv is a coefficient related to the concrete compressive
capacity of a beam to resist shear as a sum of the resistances strength and the beam depth, v45 is the shear resistance of
provided by both the concrete and the steel stirrups. Sample concrete in the 458 crack, and vs1 is the ultimate resistance
calculations performed using MathCad are shown here: of the shear reinforcement.
CSA A23:3  94 Simplified shear method  beam 1
Pf ¼ 449 kN
fc0 ¼ 69:9 MPa b ¼ 150 mm d ¼ 265 mm Blaschko et al. method
fy ¼ 500 MPa Av ¼ 144 mm2 sv ¼ 160 mm The proposed method by Blaschko et al. (1998) is based
on the Eurocode 2 approach. Unlike the previous methods
½5 l¼1 pffiffiffiffi for shear design, this one specifically incorporates the
vc ¼ 0:2l fc0 bds amount of externally applied FRP laminates into the calcula-
Av fy d tions. Sample calculations performed using MathCad are
vs ¼
sv shown here:
vr ¼ vc þ vs ¼ 185:72 kN

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116 Can. J. Civ. Eng. Vol. 36, 2009

Blaschko et al: ð1998Þ method  beam 1 Hosny et al. (2006) method was developed for nonanchored
Pf ¼ 449 kN externally bonded laminates. A second reason is the factor a
fc0 ¼ 69:9 MPa Af ¼ 180 mm2 Ef ¼ 165 GPa defined in eq. [1]: it needs further calibration, particularly
As ¼ 600 mm 2
Es ¼ 200 GPa s cp ¼ 0 for end-anchored laminates. Sample calculations performed
b ¼ 150 mm h ¼ 300 mm ds ¼ 265 mm using MathCad are shown here:
½7 k ¼ 1:6  ðds =1000Þ Hosny et al: ð2006Þ method  beam 1
t R ¼ 0:18ðfc0 Þ1=3 r1 ¼ ð1=bds Þ½As þ Af ðEf =Es Þ Pf ¼ 449 kN
VR ¼ ½t R kð1:2 þ 40r1 Þ þ 0:15s cp  bds ¼ 76:85 kN fc0 ¼ 69:9 MPa b ¼ 150 mm
h ¼ 300 mm d ¼ 265 mm
Modified Blaschko et al: method  beam 1 Af ¼ 180 mm2 Ef ¼ 165 GPa
t R ¼ 0:5ðfc0 Þ1=3 ! VR ¼ 213:48 kN fuf ¼ 2800 GPa 3uf ¼ 0:017
where Es is the steel reinforcement ratio, scp is the axial tf ¼ 1:2 mm Lf ¼ 1800 mm
compression (if any) acting on the beam, k is the coefficient bf ¼ 150 mm df ¼ 300 mm
related to the depth of the steel reinforcement, tR is the As ¼ 600 mm2 Ef ¼ 200 GPa
shear strength paramater, r1 is the steel reinforcement ratio, fy ¼ 500 MPa 3y ¼ 0:0022
and VR is the steel resistance to the beam. a1 ¼ 0:85  0:0015fc0 ¼ 0:745
The results of the application of this method to all the b1 ¼ s 0:97 ffi 0:0025fc0 ¼ 0:795 3cu ¼ 0:0035
beams are presented in Table 3, which reveals that the esti- ffiffiffiffiffiffiffiffi
E f tf
mated capacity is below the actual capacity of all beams. Le ¼ pffiffiffi0ffi ¼ 153:9 mm
Modifying this method by altering the shear strength para- fc
2 3
meter to tR = 0.5( f ’c)1/3 significantly improves its outcomes. 1:00 1 Lf  Le
6 7
Plevris et al. method bL ¼ 6 pL
4 sin@ f A Lf < Le 5 ¼ 1:0
7
The Plevris et al. method (Triantafillou and Plevris 1992; 2Le
Plevris et al. 1995) postulates that the load at which failure sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2  ðbf =bc Þ
will occur is directly proportional to the shear modulus and ½8 bp ¼ ¼ 0:707
the areas of the steel and FRP reinforcement. A factor is in- 1 þ ðbf =bc Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffi
corporated that accounts for the influence of the depth to u pffiffiffi0ffi
width ratio of the crack, which is likely related to the shear uEf fc
fdb ¼ abL bp t ¼ 758 MPa
deformation of the beam. This factor was determined based tf
on test results from a small number of specimens. The re-
fdb
sults of applying this method to the tested beams (Table 3) 3db ¼ ¼ 0:0046
shows that all beam capacities were overestimated. Ef
3cu
a1 ffc0 bb1 c ¼ As fy þ hEf Af ! solve; c
Hosny et al. method c
Hosny et al. (2006) adopted Chen and Teng’s model c ¼ 70:2 mm
(Chen and Teng 2001) to explicitly account for interfacial 3cu h
debonding. They adopted procedures similar to those de- 3f ¼
c
fined by the CSA S806–02 (CSA 2002). These specifica-
tions base the nominal moment of concrete elements with 3cu d
3s ¼ ¼ 0:00937 > 3y ðsteel yieldedÞ
surface-bonded CFRP strips on the assumptions of strain c
compatibility and equilibrium of forces, provided that 0 1
c 3cu

plane sections remain plane Mr ¼ a1 fc0 bb1 c@d  b1 A þ hEf Af ðh  dÞ

a perfect bond exists between the CFRP strips and the 2 c
concrete Pf

the maximum compressive concrete strain is 0.0035 Mr ¼ 108 kN  m Mexp ¼ 0:6 ¼ 134:7 kN  m
2

the maximum tensile CFRP strain is 0.007.
where fuf is the ultimate strength of the laminate, 3uf is the
Hosny et al. (2006) replaced the constraint placed on the ultimate strain of the laminate at rupture, Lf is the laminate
CFRP strain with eq. [1] and applied this technique to pre- bonded length, df is the depth of the FRP laminate, 3y is the
cast–prestressed concrete hollow core slabs strengthened yield strength of the steel reinforcement, bf is the width of
with externally bonded CFRP strips. They obtained reason- the FRP laminate, fdb is the debonding strength of the FRP
able agreement with their test results. laminate, and 3db is the strain of the laminate at debonding.
The method, programmed using MathCad, was applied to
all beams of the current experimental investigation (Table 3). Proposed design technique
The results show that this method underestimates the capaci-
ties of the beams with the exception of those that failed in The previous discussion reveals that any design technique
shear. The main reason for this discrepancy is the end an- for flexural members with bonded FRP laminates that does
chor provided by the support for the FRP laminates: the not explicitly consider interfacial debonding cannot accu-

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 Bakay et al.
Table 3. Comparison between ultimate loads obtained analytically and those obtained experimentally (kN).

Ultimate load (kN)

Simplified Shear fric- Blaschko et al. (1998) Blaschko et al. (1998) Hosny et al. Experimental result{
Beam ISIS shear tion 0.18(f ’c )1/3 0.5(f ’c )1/3 Plevris et al.* (2006) P1 = P2 = P/2
1 249.7 185.7 168.3 76.8 213.4 516.9 180.4 224.5
2 243.5 183.3 166.2 75.0 208.4 516.9 178.2 216.5
4 242.3 182.9 165.8 74.6 207.3 516.9 177.7 213.0
3 232.5 179.4 162.4 71.9 199.6 516.9 173.9 204.0
9 213.2 173.2 156.1 66.8 185.6 516.9 166.4 203.0
10 218.5 174.8 157.8 68.2 189.3 516.9 168.4 194.5
11 204.3 170.5 153.2 64.6 179.5 516.9 162.5 197.5
12 201.5 169.7 152.4 63.9 177.5 516.9 161.3 185.6
5 212.2 244.4 216.0 66.5 184.8 516.9 165.8 212.7
6 208.7 243.3 214.7 65.6 182.4 516.9 164.4 205.0
7 208.7 112.2 88.3 65.6 182.4 516.9 164.4 171.5
8 204.7 111.0 87.4 64.7 179.7 516.9 162.7 173.5
*Triantafillou and Plevris (1992) and Plevris et al. (1995).
{
Experimental load defined in the table is the point load acting on the beam, which is half the value of the total failure load.

Table 4. Results of applying the proposed procedures to the tested beams.

Interfacial debonding load Concrete cover resistance

CSA-A23.3
f ’c Failure Failure load, Point load, P1 = Point load CFRP strain Concrete cover (CSA 2000)
Beam (MPa) mode Pult (kN) P2 = Pult /2 (kN) (kN) Pdb/Pult (%) stress (MPa) (MPa) CEB-fib (1999) (MPa)
195 0.87 0.587 5.4 5.02 5.35
2 64.1 IC 433 216.5 182 0.84 0.492 5.05 4.8 5.04
4 65.1 IC 426 213 185 0.87 0.515 5.14 4.84 5.09
3 57.2 IC 408 204 169 0.83 0.401 4.74 4.54 4.66
9 46.1 CC+IC 406 203 144 0.71 0.221 4.1 4.07 4.01
10 48.8 CC+IC 389 194.5 148 0.76 0.247 4.18 4.19 4.17
11 41.6 CC+IC 395 197.5 135 0.68 0.159 3.89 3.88 3.74
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12 40.3 CC+IC 371 185.6 132 0.71 0.138 3.82 3.81 3.66
5 45.4 CC+IC 425 212.7 142 0.67 0.206 4.05 4.04 3.97
6 43.7 CC+IC 410 205 139 0.68 0.186 3.98 3.97 3.87
7 43.7 SF+CDC 343 171.5 139 0.81 0.186 3.98 3.97 3.87
8 41.8 SF+CDC 347 173.5 135 0.78 0.158 3.888 3.88 3.75
Note: Pdb, debonding load; CFRP, carbon-fibre-reinforced polymer; IC, intermediate flexure or flexure shear crack-induced debonding; CC, concrete crushing in compression; SF, shear failure; CDC,
critical diagonal crack-induced debonding.

117
118 Can. J. Civ. Eng. Vol. 36, 2009

rately predict the failure load. The authors suggest that the a1 fc0 bb1 c þ As0 Fy ¼ As Fy þ Af Ef 3f
main cause of interfacial debonding of soffit-bonded FRP
laminates is the inability of the concrete cover, between the ½9 a1 fc0 bb1 c þ As0 Fy  As Fy
3f ¼
steel shear reinforcement and the FRP, to transfer force to Af Ef
the laminates through shear. With this being the case, there
are two requirements for any debonding design technique to where A’s is the area of compressive (if any) steel, Fy is the
be efficient: (i) shear stress determination in the concrete for steel yield strength; and 3f is the strain in the laminates.
any given externally applied load and (ii) assessment of the The compatibility condition is adopted despite the fact
concrete ability to resist to this applied stress. Ideally, the that in all tests a lack of compatibility developed at early
means of determining the load and resistance will be accom- loading stages. However, as shown in the previous strain
plished using conventional design methods and practices. profiles, severe incompatibility did not occur until interfacial
debonding took place, and the procedure herein is seeking
Determination of shear stresses in the the point of interfacial debonding.
concrete cover The second step is to relate the external moment acting on
the beam due to the external load to the internal moment. As
Referring to Figs. 1a and 1d, equilibrium and compatibil- all the beams were loaded in four-point loading, the external
ity conditions are first adopted to relate the CFRP bonded and internal moments, Mext and Mint, respectively, are given
laminates’ strain 3f to the depth of the concrete in compres- by
sion:

8
> 1 L
>
> Px þ ðwo:wt Lx  wo:wt x2 Þ for 0  x 
< 2 3
½10 Mext ¼ L 1 L L
>
> 2
: P 3 þ 2 ðwo:wt Lx  wo:wt x Þ
> for
3
x
2

0 1
b c
Mint ¼ a1 fc0 bb1 c@h  1 A þ A0 Fy ðh  d 0 Þ  As Fy ðh  ds Þ
s s
2

where P is the externally applied point load, x is the dis- be obtained as a function of distance along the beam. It is
tance along the beam’s span measured from the support; important to note that this expression is only valid in the vi-
wo.wt is the self-weight of the beam, and ds and d ’s are the cinity of the maximum moment, as the derivation has been
depths to the tension and compression steel reinforcement, simplified using the equivalent stress block for the concrete.
respectively. Differentiation of the strain expression will yield an equa-
Equating the internal and external moments to get the tion for the rate of change of force in the external laminates:
depth to the neutral axis of the compression block, c, in the rate of change of force in the CFRP laminates is ob-
terms of the external moment as a function of the distance x tained as a function of the known beam geometry, design
along the beam span results in load, and distance along the span. Again, this equation is
Mint ¼ Mext only valid near the region of maximum moment. Physically,
this rate of change of force is accomplished via shear in the
a1 fc0 bðb21 =2Þc2  a1 fc0 bb1 hc concrete cover and is thus, the applied load on the concrete
cover. The computer package MathCad was used to evaluate
þ½As Fy ðh  ds Þ  As0 Fy ðh  ds0 Þ þ Mext  ¼ 0
the previous differentiation and solve the above system of
equations. The procedure is described analytically as follows
b1 2
½11 A ¼ a1 fc0 b B ¼ a1 fc0 bb1 h
2 3f f ðxÞ
C ¼ As Fy ðh  ds Þ  As0 Fy ðh  ds0 Þ þ Mext
Tf ¼ Ef Af 3f Ef Af f ðxÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
B  B2  4AC ½12 0 1
c¼ f ðxÞ 1 @dTf A
2A t conc ¼
bc dx
Substituting for c in eq. [9], an expression for the devel-
opment of strain in the externally bonded FRP laminates can

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Bakay et al. 119

Fig. 8. Sample calculations for the proposed method adopted to calculate the shear stress in the concrete cover applied to beam 1. fc, con-
crete compressive strength; Af, cross-sectional area of the FRP laminate; Ac, cross-sectional area of the concrete beam; dsc, depth to the
compression steel reinforcement; Lshear, shear span; CSA, CSA 2000; CEB-fib 1999.

where Tf is the tension in the laminates and tconc is the shear should be considered as a shear stress only, with negligible
stress in the concrete. tensile stresses in the concrete cover layer. Plotting these
The procedures are simplified if the steel reinforcement is values on Mohr’s circle would show that the principle
assumed to have yielded, but this assumption must be veri- stresses occur at 458 to the beam axis. This corresponds
fied. If the steel does not yield, the steel stress is calculated well with the observed angle of cracking noticed in both
using the strain compatibility equation and the Young’s this and other experimental tests. At this point, the concrete
modulus of the steel (Fs = Es3s). resistance to these applied stresses should be determined. A
For beam 1, failure occurred at a point load of 224.5 kN number of characteristics including tensile strength and
(total load of 449 kN) shortly after the interfacial debonding modulus of rupture have been considered, each taking many
was initiated at a point load approximately equal to 195 kN. forms in various design codes worldwide. For example, the
For this beam, at the vicinity of the point load and at a value CSA-A23.3 (CSA 2002) and the CEB-fib (CEB) defined
of 195 kN, the proposed method yields a force in the CFRP these values by:
strips equal to 174 kN with a corresponding strain of 0.0059. pffiffiffiffi
CSA : fr ¼ 0:6 fc0 0 1
Likewise, at this location the rate of change of the force in
the laminates, equal to the shear stress transferred through ½13 d
the concrete cover, is 5.4 MPa. This method is applied to CEB : fr ¼ 0:214ðfc0 Þ0:69 @1:6  A
1000
all beams in the experimental programme (Table 4) with
sample calculations shown in Fig. 8.
where fr is the concrete rupture strength.
Using the concrete strengths defined via eq. [13], the
Shear resistance of the concrete cover loads at which the interfacial debonding initiated in all the
The value of the stress determined in the previous section beams tested were predicted using the proposed procedures.

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120 Can. J. Civ. Eng. Vol. 36, 2009

Fig. 9. Comparison between the CSA-A23.3 (CSA 2002) and CEB-fib (1999)) stress limits and the predicted strain in the concrete cover
for: (a) beam 1 at applied point load = 195 kN (total applied load = 390 kN), (b) beam 12 at applied point load = 132 kN (total applied
load = 264 kN). CFRP, carbon-fibre-reinforced polymer.

These values along with the strain developed in the CFRP 12, 5, and 6). For the beams under-reinforced for shear
laminates at the initiation of debonding are listed in Table 4. (beams 7 and 8), the mode of failure was not confined to
Figure 9 also shows these values along with the forces de- the concrete cover region, but shear cracking progressed
veloped in the CFRP strips for beams 1 and 12. through the entire depth of the beam. Thus, the interfacial
Table 4 shows that debonding initiated at 83% ~ 87% of debonding occurred at almost the same load as in beams 5
the failure load (higher strength concrete beams 1 to 4) and and 6 (which have almost the same concrete strength), cor-
at 67% ~ 71% of the failure load (weaker concrete beams 9– responding to 78%.~ 81% of the failure load.

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Bakay et al. 121

Summary Chen, J.F., Yuan, H., and Teng, J.G. 2007. Debonding failure along a
softening FRP-to-concrete interface between two adjacent cracks
An experimental investigation has been performed in in concrete members. Engineering Structures, 29(1): 257–270.
which the effects of the concrete compressive strength and CSA. 2000. Design of concrete structures. CSA standard A23.3–94
the amount of shear reinforcement were investigated to de- (R2000). Canadian Standards Association, Mississauga, Ont.
termine their relation to crack-induced debonding failure. CSA. 2002. Design and construction of building components with
Three modes of failure were observed: concrete crushing, fibre-reinforced polymers. CSA standard S806–02 (2002). Cana-
shear failure, and crack-induced interfacial debonding. De- dian Standards Association, Mississauga, Ont.
pending on the concrete strength and the beam’s shear Hosny, A.A., Sayed-Ahmed, E.Y., Abdelrahamn, A.A., and Alh-
strength, interactive failure modes were also observed: con- laby, N.A. 2006. Strengthening precast-prestressed hollow core
crete crushing or shear failure and interfacial debonding. slabs to resist negative moments using CFRP strips: an experi-
Strain compatibility between the CFRP laminates and the mental investigation and a critical review of CSA 806–02. Cana-
concrete section was lost from the early stages of loading in dian Journal of Civil Engineering, 33(8): 955–967. doi:10.1139/
all beams. Increasing the concrete compressive strength or L06-040.
the beam’s shear resistance had no effect on this behaviour. Loov, R.E. 2000. Shear design of concrete – A simpler way. In
The strain measurements also revealed that the usage effi- Proceedings of the 3rd Structural Specialty Conference, Cana-
ciency of the bonded CFRP strip was reduced because of dian Society for Civil Engineering, London, Ont., 7–10 June
2000. Canadian Society for Civil Engineering, Montréal, Que.
the interfacial debonding.
pp.49–56.
The published literature and the experimental programme Lu, X.Z., Teng, J.G., Ye, L.P., and Jiang, J.J. 2005. Bond-slip mod-
revealed that the main cause of FRP laminate interfacial de- els for FRP sheets/plates bonded to concrete. Engineering Struc-
bonding is the inability of the concrete cover to transfer tures, 27(6): 920–937.
force to the laminates through shear, leading to laminate de- Neale, K. 2001. Strengthening reinforced concrete structures with
bonding: not explicitly considered by the currently available externally-bonded fibre reinforced polymers. Design Manual
design techniques. Thus, proposed design procedures were No. 4. ISIS Canada, Winnipeg, Man.
developed where the concrete cover shear stress correspond- Plevris, N., Triantafillou, T.C., and Veneziano, D. 1995. Reliability
ing to any given externally applied load was determined and of RC members strengthened with CFRP laminates. Journal of
compared with the concrete resistance. The method was ap- Structural Engineering, 121(7): 1037–1044. doi:10.1061/(ASCE)
plied to the tested beams and yielded good agreement with 0733-9445(1995)121:7(1037).
the experimental results. Sayed-Ahmed, E.Y., Riad, A.H., and Shrive, N.G. 2004. Flexural
strengthening of precast reinforced concrete bridge girders using
Acknowledgements bonded CFRP strips or external post-tensioning. Canadian Jour-
nal of Civil Engineering, 31(3): 499–512. doi:10.1139/l04-005.
ISIS Canada and Centre for Transportation Engineering Smith, S.T., and Teng, J.G. 2002a. FRP strengthened RC beams –
and Planning (C-TEP) are gratefully acknowledged for their I: Review of debonding strength models. Engineering Structures,
financial contributions. Material donations made by Sika 24(4): 385–395. doi:10.1016/S0141-0296(01)00105-5.
Canada are greatly appreciated. The experimental pro- Smith, S.T., and Teng, J.G. 2002b. FRP strengthened RC beams –
gramme was performed at the Civil Engineering Depart- II: assessment of debonding strength models. Engineering Struc-
ment, University of Newcastle, Australia. The aid of the tures, 24(4): 397–417. doi:10.1016/S0141-0296(01)00106-7.
technical staff is much appreciated. Spadea, G., Bencardino, F., and Swamy, R.N. 1998. Structural be-
havior of composite RC beams with externally bonded CFRP.
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