Delivered by ICEVirtualLibrary.com to: IP: 128.178.25.28 On: Fri, 16 Jul 2010 12:27:31 Shear strengthening of reinforced concrete beams with CFRP I. A. Bukhari*, R. L. Vollum†, S. Ahmad* and J. Sagaseta† Engineering University, Taxila; Imperial College London The current paper reviews existing design guidelines for strengthening beams in shear with carbon fibre reinforced polymer (CFRP) sheets and proposes a modification to Concrete Society Technical Report TR55. It goes on to present the results of an experimental programme which evaluated the contribution of CFRP sheets towards the shear strength of continuous reinforced concrete (RC) beams. A total of seven, two-span concrete continuous beams with rectangular cross-sections were tested. The control beam was not strengthened, and the remaining six were strengthened with different arrangements of CFRP sheets. The experimental results show that the shear strength of the beams was significantly increased by the CFRP sheet and that it is beneficial to orientate the FRP at 458 to the axis of the beam. The shear strength of FRP strengthened beams is usually calculated by adding individual components of shear resistance from the concrete, steel stirrups and FRP. The superposition method of design is replaced in Eurocode 2 by the variable angle truss model in which all the shear is assumed to be resisted by the truss mechanism. The current paper proposes a methodology for strengthening beams with FRP that is consistent with Eurocode 2. Introduction Fibre reinforced polymer (FRP) composites are widely used for strengthening concrete structures be- cause they have many advantages over conventional strengthening methods. Much research has been carried out over the past decade into the performance of con- crete beams strengthened in shear with externally bonded FRP composites. Previous experimental studies have shown FRP composites are effective in increasing the shear capacity of reinforced concrete (RC) beams. Despite numerous interesting studies, the shear behav- iour of RC beams strengthened with FRP is not well understood. The majority of tests have been carried out on simply supported beams without steel stirrups strengthened with complete side wrap, U-wrap or full wrapping of the section with carbon fibre reinforced polymer (CFRP) sheet. More tests are required to deter- mine whether the increment in shear strength due to CFRP is sensibly independent of the presence of conventional shear reinforcement as commonly assumed. Review of current design methods for FRP strengthening in shear Current American Concrete Institute (ACI 2002 and International Federation for Concrete 2001) design guidelines for strengthening RC beams in shear with CFRP are based on empirical design equations derived by Khalifa et al. (1998) and Triantafillou and Antono- poulos (2000) respectively. The nominal shear strength ‘V n ’ is calculated by adding individual contributions calculated for the concrete ‘V c ’, internal steel stirrups ‘V s ’, and external FRP composites ‘V f ’ resulting in the general equation V n ¼ V c þ V s þ V f (1) where V c is the shear strength of a beam without stir- rups and V s is calculated with a 458 truss. The shear contribution of externally bonded FRP re- inforcement is calculated analogously to that of internal steel stirrups. Triantafillou (1998) proposed that the contribution of the FRP sheet to shear strength of a RC beam V f is given by V f ¼ r f E f å fe b w z f 1 þ cot â ð Þ sin â (2) where b w is the beam width and E f is the elastic * Engineering University, Taxila, Pakistan † Department of Civil and Environmental Engineering, Imperial Col- lege London, London, UK (MACR 800164) Paper received 17 November 2008; last revised 22 January 2009; accepted 11 March 2009 Magazine of Concrete Research, 2010, 62, No. 1, January, 65–77 doi: 10.1680/macr.2008.62.1.65 65 www.concrete-research.com 1751-763X (Online) 0024-9831 (Print) # 2010 Thomas Telford Ltd
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Shear strengthening of reinforced concrete
beams with CFRP
I. A. Bukhari*, R. L. Vollum†, S. Ahmad* and J. Sagaseta†
Engineering University, Taxila; Imperial College London
The current paper reviews existing design guidelines for strengthening beams in shear with carbon fibre reinforced
polymer (CFRP) sheets and proposes a modification to Concrete Society Technical Report TR55. It goes on to
present the results of an experimental programme which evaluated the contribution of CFRP sheets towards the
shear strength of continuous reinforced concrete (RC) beams. A total of seven, two-span concrete continuous beams
with rectangular cross-sections were tested. The control beam was not strengthened, and the remaining six were
strengthened with different arrangements of CFRP sheets. The experimental results show that the shear strength of
the beams was significantly increased by the CFRP sheet and that it is beneficial to orientate the FRP at 458 to the
axis of the beam. The shear strength of FRP strengthened beams is usually calculated by adding individual
components of shear resistance from the concrete, steel stirrups and FRP. The superposition method of design is
replaced in Eurocode 2 by the variable angle truss model in which all the shear is assumed to be resisted by the
truss mechanism. The current paper proposes a methodology for strengthening beams with FRP that is consistent
with Eurocode 2.
Introduction
Fibre reinforced polymer (FRP) composites are
widely used for strengthening concrete structures be-
cause they have many advantages over conventional
strengthening methods. Much research has been carried
out over the past decade into the performance of con-
Figure 8. Load–vertical strain in CFRP sheet (mid-depth)
Bukhari et al.
74 Magazine of Concrete Research, 2010, 62, No. 1
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The variable angle truss model is an idealisation
based on the lower bound theorem of plasticity in
which all the shear force is assumed to be resisted by
the stirrups. In reality, the angle of the compression
field in the truss is steeper than assumed in Eurocode 2
and part of the shear force is resisted by Vc, which is
not constant as assumed in Equation 1. The following
issues are relevant to the application of the variable
angle truss model to beams strengthened in shear with
CFRP.
(a) Figure 9 shows that Eurocode 2 (British Standards
Institution, 2004) gives greater shear strengths than
Equation 1 if the reinforcement index exceeds a
critical value of around twice the minimum value
specified in Eurocode 2.
(b) The area of steel shear reinforcement contributing
to the shear strength is assumed to be constant in
the ‘standard method’ but varies with cotŁ in
Equation 13. The contribution of steel shear rein-
forcement to shear strength is reduced when the
beam is strengthened with FRP if the design shear
force is sufficiently high to govern the maximum
permissible value of cotŁ.(c) Tests show that internal steel stirrups and external
CFRP shear reinforcement are most efficient when
oriented at 458. This can be seen by comparing the
shear strengths of the authors’ beams C2, C5, C6
and D6 or Chaallal et al.’s (1998) beams RS90 and
RS135. The increased efficiency of inclined stir-
rups is not reflected in Equation 13 which predicts
that changing the orientation of the shear reinforce-
ment FRP from 908 to 458 reduces the shear
strength by 1% if cotŁ¼2.5.
(d) The procedure of deriving the effective stress
(E�fe) in CFRP from test data with Equations 1
and 2 is dubious since Vc is not constant as as-
sumed and the truss angle is not 458. The proce-
dure would give very different stresses to the yield
stress if used for beams with steel stirrups.
Equation 13 can be modified as follows to give the
shear strength of beams without internal stirrups
strengthened with CFRP
VRd,FRP ¼ Czf bwEf cot Łþ cot �ð Þ sin � (15)
where C is the least of either r�feEquation12 or r*�feTR55where r is the FRP ratio defined below Equation 2, r*is defined in Equation 9 and �fe is calculated in accor-
dance using Equation 12 or TR55 (Concrete Society,
2003) as noted. The following methods were investi-
gated for calculating the shear strength (V ¼ Vc + Vs +
Vf ) of beams strengthened with CFRP with Eurocode 2.
(a) Method 1: Vc + Vs was taken as the greatest of Vcor VRd,s from Equation 13 with the maximum
permissible value of cotŁ corresponding to the
shear capacity of the strengthened beam. Vf was
calculated using Equation 15 with cotŁ ¼ 1.
(b) Method 2: Vc + Vs was taken as Vc + VRd,s where
VRd,s was calculated using Equation 13 with
cotŁ ¼ 1. Vf was calculated as in (a) above.
(c) Method 3: As (a) above but Vf was calculated with
Equation 15 using the value of cotŁ used for VRd,s
in Equation 13. V ¼ Vc + Vs + Vf was not taken as
less than Vc.
The methods were assessed for beams within the
authors’ database with U or side wrapping where suffi-
cient data were available. The database consisted of 30
beams reinforced in shear with only CFRP (six beams
from this study, five beams from Adhikary and Mut-
suyoshi (2004) (B-4 to B-8 inclusive), eight beams
from Khalifa and Nanni (2002, 2000) (BT2 to BT5
inclusive and SO3-2 to SO3-4 and SO4-2), nine beams
from Triantafillou (1998) (S1a, S1b, S2a, S2b, S3a,
S36b, S1-45 to S3-45) and two beams from Zhang and
Hsu (2005) (Z4 45, Z4 90)) and 20 beams with CFRP
and steel shear reinforcement (four beams from
Chaallal et al. (1998), all 11 beams from Pelligrino and
Modena (2002) and five beams from Monti and Liotta
(2007) (UF90, UF45+A, UF45+D, WS45+, UF90)).
The beams of Monti and Liotta (2007) and Pelligrino
and Modena (2002) are not included in Table 1. The
CFRP was oriented at 908 in all the beams except those
with 45 in their label where the orientation was 458.
The beams of Monti and Liotta (2007) had unusually
low concrete cube strengths of 13.3 MPa. The top of
the CFRP was stopped 150 mm below the top of these
beams, which had an effective depth of 410 mm, to
simulate the presence of a flange. The top of the sheet
was mechanically anchored in all the beams except
UF90, which had a comparatively low strength.
The strengths of the beams are compared in Figure 9
with the strengths calculated with method 3. Figure 9
shows that method 3 overestimates the strength of a
significant number of beams with stirrups and is there-
fore not recommended. Method 2 is illustrated in Fig-
ure 9 (with ªc ¼ 1.5 and � ¼ 908) for Chaalal et al.’s
beams in which f 9c was 35 MPa. Figures 10(a) and
10(b), in which the material factors of safety were
Pelligrino
Monti UF90
Chaallal
0
0·1
0·2
0·3
0·4
0·5
0
Stirrup index [ /( ) CE ]/( )A f b s fs y w f ck� ν
M2 Chaalal 35 MPafc �
M3 c 1γ �
M3 c 1·5�γPelligrino no internal stirrupsNo CFRPPelligrino CFRP internal stirrups�Internal stirrups CFRP�No internal stirrups
Chaallal
Vf
hd
/(0·
9)
ckv
0·300·250·200·150·100·05
Figure 9. Comparison between measured and predicted shear
strengths
Shear strengthening of reinforced concrete beams with CFRP
Magazine of Concrete Research, 2010, 62, No. 1 75
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taken as 1.5 for concrete and 1.0 for steel and CFRP,
show that methods 1 and 2 give similar results for the
beams in the database. Figures 9 and 10 show all three
methods are less conservative for beams with internal
steel shear reinforcement, which suggests that the prin-
ciple of superposition assumed in Equation 1 is not
strictly valid due to strain incompatibility. The reduced
efficiency of CFRP in beams with internal stirrups is
related to two fundamental issues. First, the presence of
internal stirrups changes the crack pattern. A single
dominant shear crack tends to form in beams without
internal stirrups strengthened with CFRP whereas mul-
tiple parallel shear cracks form in beams with internal
stirrups. The influence of stirrups on the crack pattern,
and consequently the anchorage of the CFRP, which
determines its effective area, is not included in the
design methods discussed in this paper or that of Monti
and Liotta (2007).
Second, methods 1 to 3 which utilise the lower
bound theorem of plasticity, assume
(a) that the internal stirrups yield at failure; and
(b) that the effective strain in the CFRP at failure is
independent of the area of internal shear reinforce-
ment.
Assumption (a) is only credible if the strain in the
CFRP at failure is sufficient for the internal stirrups to
yield. Strain measurements such as those in Figure 8
suggest this is likely to be the case unless the axial
rigidity of the CFRP is very high. In methods 1 to 3,
Equation 13 is used to calculate Vc + Vs (with cotŁcalculated in terms of the shear capacity of the
strengthened beam) whereas in method 2, Vc + Vs is
taken as the design shear strength of the un-strength-
ened beam. Providing the stirrups yield, both ap-
proaches imply Vc + Vs is independent of the strain in
the stirrups, which is not generally the case since shear
failure is relatively brittle. In reality, loss of aggregate
interlock is likely to reduce Vc + Vs if the crack widths
in the strengthened beam are greater than in the un-
strengthened beam at failure. Vc + Vs is also likely to
reduce if the strain in the internal stirrups at failure is
less in the strengthened than un-strengthened beam.
Figure 9 shows that the variable angle truss model in
Eurocode 2 can give significantly higher shear
strengths than the ‘standard method’ for beams with
internal steel stirrups. It follows that method 1 can give
significantly higher strengths for strengthened beams
with CFRP than method 2 which calculates Vs + Vcusing the ‘standard method’. The current authors con-
sider it unwise to take advantage of this increase in
strength for reasons discussed above. Therefore, it is
suggested in the absence of further test data to the
contrary that method 2 is used to assess the shear
strength of beams strengthened with CFRP.
Conclusions
This paper describes a series of six tests on contin-
uous beams strengthened in shear with CFRP. The tests
showed that it is beneficial to orientate the fibres in the
CFRP sheets at 458 so that they are approximately
perpendicular to the shear cracks. The tests also sup-
port the hypothesis that the efficiency of CFRP reduces
with its axial rigidity. TR55 (Concrete Society, 2003) is
unique among the design methods considered in this
paper in not relating the effective strain in CFRP to its
axial rigidity. Consequently, TR55 (see Figure 1(c))
was found significantly to overestimate Vf in some
beams including ones tested by the current authors and
Pelligrino and Modena (2002). Therefore, it is sug-
gested that TR55 should be modified to include Equa-
tions 12a and 12b, which relate the effective strain in
CFRP to its axial rigidity in side and U-wrapped sec-
tions respectively.
It is shown that the variable angle truss model in
Eurocode 2 can overestimate the shear strength of
beams with internal stirrups that are strengthened with
CFRP. This implies CFRP strengthened beams can have
0
0·5
1·0
1·5
2·0
2·5
0
Normalised axial rigidity /
(a)
�f f(2/3)cE f
M1 no stirrups 90 M1 stirrups 90M1 no stirrups 45 M1 stirrups Chaalal 45M1 stirrups Monti 45
VV
test
pred
/
20015010050
0
Normalised axial rigidity /
(b)
�f f(2/3)cE f
VV
test
pred
/
200150100500
0·5
1·0
1·5
2·0
2·5
M2 no stirrups 90 M2 stirrups 90M2 no stirrups 45 M2 stirrups Chaalal 45M2 stirrups Monti 45
Figures 10. Comparison between measured and predicted