Analysis and design of FRP externally

Materials and Structures/Materiaux et Constructions,Vol.34, August-September2001, pp 418-425
Analysis and design of FRP externally-reinforced
concrete beams against debonding-type failures
M. Maalej, W. H. Goh and P. Paramasivam
Department of Civil Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576
Paper received:June22, 2000; Paperaccepted:March 1, 2001
A B S T R A C T
R I~ S U M I~
Epoxy-bonding of FRP plates to the tensile face of
RC beams has been shown to be an effective repair and
strengthening technique. However, local failure by
debonding or ripping of concrete cover has been
reported in experiments to be a likely mode of failure
due to high interfacial shear and normal stress concentrations, Predictive models for finding the interracial
shear stress have been reviewed and evaluated using
experimental data reported in the literature. The most
critical parameters governing the interracial shear
strength and stress as determined by the models were
also examined. Through understanding of the conditions that result in debonding failure, a better approach
towards designing FRP-plated RC beams against this
mode of failure might be achieved.
Le renforcement externe d elements en b~ton arme a l'aide de
plaques synthdtiques ret~rc&s de fibres (FRP), s'est rdvdld &e
une technique efficace de r&abilitation des structures.
Cependant, la rupture localepar d&ollement ou fissure du bdton
a dtd pr&ent& dans des essais comme le mode de rupture le plus
frdquent a cause de la forte concentration des contraintes de
cisaillement et normales aux extrdmit& des plaques. Des
modules th&riques visant 21trouver les contraintes de cisaillement
ont dtd examin& et &atu& en utitisant des donn&s exp&imentales rapport&s clans la litt&ature. Les param~tres les plus critiques gouvernant la contrainte de cisaillement et la rdsistance au
cisaillement de l'interface colle-bdton, comme ddtermind par les
modeles th&riques, ont aussi dtd examin& Pour comprendre les
(frets qui r&ultent de la rupture par d&ollement, une meilleure
mdthode de conception peut ~tre r&lis& afin d'dliminer ou de
retarderce mode de rupture.
1. I N T R O D U C T I O N
ural cracks along the beam, resulting in debonding or
ripping of the concrete cover along the level of conventional internal reinforcement. The recently proposed
methods to predict and prevent premature failure of
FRP-plated RC beams are timely; however, such methods need further testing and evaluations before they can
be relied upon in practice.
For a given strengthening application, the primary
issue is to decide what type of FRP reinforcing system
and how much EB-FRP flexural reinforcement should
be used. The ideal system would be one where the FRP
properties are fully utilized. Published data in the literature indicate that the efficiency of FRP external reinforcement and the ductility of FRP-plated beams
decrease with increasing FRP axial rigidity (area times
elastic modulus) due to premature failure [1]. In this
paper, state-of-the-art methods for the analysis and
design ofFRP-plated RC beams against &bonding type
failures are reviewed and evaluated using experimental
Repair and strengthening of RC members with EBFRP (Externally-Bonded Fibre Reinforced Polymer) has
evolved progressively over the past decade. For beam
members, failure can occur due to flexural compression,
beam shear, FRP rupture, or FRP debonding.
Debonding-type failures are prevalent in beam tests
reported in the literature. The prevalence of &bonding
failures among each of the other modes emphasizes the
need either for reliable means of preventing this type of
failure or for a practical method of predicting it.
Attempts to address this need can be seen in recent publications where approximate analyses were used to compute the shear and normal stress concentrations in the
adhesive layer of FRP-plated RC beams. The recently
published work was motivated by observations that premature failures may occur because of shear and normal
stress concentrations at FRP cut-off points and at flex1359-5997/01 9 RILEM
41 8
Maalej,Goh,Paramasivam
data reported in the literature. An important goal of this
study is then to use the proposed models to derive relationships between FRP efficiency and FRP axial rigidity
that designers can use to predict failure mode and
achieve an opportune balance between strength gain and
deflection capacity.
ad a
(
m20 = M~
A number of published articles dealt with the topic of
predicting the failure mode of concrete beams strengthened in flexure with externally-bonded reinforcement [28]. Among the studies that focused on the debonding
mode of failure, Roberts' study [2] was the first to provide
specific analytical equations, which may be used to predict
&bonding failure or design against it. Specifically, the
above-referenced study led to the development of a model
for predicting the shear and normal stresses at the
FRP/concrete interface. This model is considered in tiffs
paper for the purpose of review and evaluation using
experimental data reported in the literature.
Roberts' model [2] was originally proposed for the
analysis of steel-plated RC beams. The analysis was presented in 3 stages. In the first stage, stresses were determined assuming fully composite action between the RC
beam and the adhesive-bonded steel plate. In the second
and third stages, the analysis was modified to take into
account the actual boundary conditions at the steel plate
curtailment. The complete solution was then obtained
by superposition. In this model, a cracked section transformed into a steel plate equivalent was used in the
analysis. The governing equations for the shear and normal stress distributions are given by:
1
/
z(x) = ba [+~t{_tl0sinh~xx~ tlo c~176 tla coshctx~
sinh~ta
(1)
j]
where
I
]0.5
0t = Ep bp dp
EpIp "~
Ip +Ec Ic )
(9)
( p Ip
Eplp
f20 = F0/E
+ E c I c ]+(.tl0 + ~20)badp/2
(lO)
"1:10 = 1 [Fo
(3)
_[ Kn -]0.25
(4)
tlo=_M~ bpdp(hp-h)
(5)
t l a = ~-~-a bpdp(hp - h)
(6)
bpddhp-h)
1
z2~ = b-~[ct{t 1~c~
sinhcta
aa - t la}]
and
(11)
(12)
a
= Length of steal plate
b c, bp, b a = Width of concrete, steel plate, adhesive
dc, d[, da = Depth of concrete, steel plate, adhesive
Eo ffp, Ea Elastic modulus of concrete, steel plate,
adhesive
F0, Fa
= Global shear force at x = 0, x = a
f20
= Shear force in plate at solution development
stage 2 (x = 0)
= Shear modulus of adhesive
Oa
h
= Depth of neutral axis computed based on
cracked section analysis
Effective
depth of steel plate
hP
=
Second moment of area of the transformed
equivalent steel section about the neutral
axis based on cracked section analysis
Second moment of area about individual
Io Ip
centroid for concrete, steel plate
= Adhesive normal stiffness per unit length
K s
= Adhesive shear stiffness per unit length
M0, Ma = Global bending moment at x -- 0, x = a
m20
= Bending moment in steel plate at solution
development stage 2 (x = 0)
tl0, tla = Axial force in steel plate at solution development stage 1 at x = 0, x =a
X
= Distance along steel plate measured from
plate cut-off
(~
= Coefficient used in ~c (x) and defined by
Equation (3)
y
= Coefficient used in o (x) and defined by
Equation (4)
o (x)
= Normal stress at a distance x from plate cutoff
(x)
= Interfacial shear stress at a distance x from
plate cutoff
"~10,"C20 = Shear stress in adhesive at solution development stage 1, 2 (x = 0)
Roberts [2] compared the shear stress distribution
obtained from Equation (1) with a more rigorous solu=
(2)
K~
(8)
Kn= E ba
2. REVIEW OF PREDICTING MODELS
FF(x)
,
,
____1[-T--bpdp (hp -h )
(7)
b a
K s = O a d--7
419
Materials and Structures/Mat~riaux et Constructions, Vol. 34, August-September 2001
Comparisons were
initially made between
the results predicted by
the above-referenced
models for a RC beam
with reported properties of the concrete,
steel reinforcement,
FRP and adhesive used
[9]. All models predicted that stress concentrations are rapidly
reduced as the distance
from the plate cutoff is
increased. However,
the results from the
Fig. 1 - Reinforced concrete beam with externally-bonded FRP showing important parameters used in
models
differed in the
Roberts' model.
following:
(1) As indicated in
Fig. 2, Roberts' revised model predicted shear stress
concentrations at the plate cutoff that were significantly
higher than those predicted by Roberts' original model.
This is expected as the end moment used in Roberts'
revised model was a corrected moment (M*) at a distance of approximately half-beam depth from the plate
cutoff (see Fig. 1), instead of the global moment at the
plate cutoff itself(M0). The level of significance of using
this corrected moment would depend on the depth of
the beam and plate used. Deep beams and plates would
require a larger correction, thus making the corrected
and uncorrected moments significantly more different.
(2) When an uncracked section is transformed into a
plate equivalent, and a plate end moment M* was used in
Roberts' model, the predicted results were significantly
lower than those predicted by both Roberts' original
Fig. 2 - Results predicted by Roberts for beam C with load P/2 =
model and Roberts' revised model (where a cracked sec100kN.
tion transformed into a plate equivalent was assumed).
tion based on partial interaction theory [8] as well as
with experimental results presented by Jones et al. [4]. It
3. PARAMETERS AFFECTING INTERFACIAL
was c o n c l u d e d that the above solution (given by
Equation (1)) underestimated the magnitude of the stress
SHEAR STRESS
concentration by up to 30%, due primarily to the
Experimental data on thirty FRP-plated RC beams
approximations made during the first stage of the soluwith
reported failure modes and FRP strains at failure
tion. Roberts [2] proposed a correction by replacing M 0
were
gathered from an experimental database compiled
(the value of the global m o m e n t at x = 0 used in
recently
by Bonacci and Maalej [1]. The original data
Equations (5) and (9)) by a modified m o m e n t M*,
for
the
beams
were reported in References [9-18]. The
which is the value of the global moment at x = (dc+dp)/2
beams
were
analyzed
using the Roberts' revised model.
from the end of the steel plate (see Fig. 1). This correcProperties of the adhesives were assumed if they had not
tion resulted in satisfactory correlation between the
been reported. In addition to using the model for premodel prediction and both the more rigorous solution
dicting the interracial shear stress, flexural analysis was
based on partial interaction theory [8] and the available
performed at the same time to determine the FRP strain
test data [4]. The resulting model is referred to in this
at the critical beam section for bending and to monitor
paper as Roberts' revised model.
the strain in the concrete at the extreme compression
W h e n the depth of neutral axis h, the second
fibre. This enabled the determination of whether the
moment of area of the equivalent steel section I, and the
beams would fail by flexural compression of concrete or
second moment of area of the concrete about its individtensile rupture of FRP prior to debonding.
ual centroid I c are c o m p u t e d on the basis of an
Roberts' revised model predicted high interfacial
uncracked concrete section, Equations (1)-(12) lead to
shear stresses (compared to Roberts' original model or
Roberts' uncracked section model, the results of which
Roberts' uncracked section model) due to its adoption of
will briefly be touched upon in this paper.
420
Maalej, Goh, Paramasivam
interfacial shear stresses were not high
enough to cause &bonding-type failures.
Property
ProprietarySystem 1 ProprietarySystem2
As such, the failure loads and modes from
Elasticmodulusof adhesive(MPa)
12800
1470
flexural analysis are expected to be close to
Shearmodulusof adhesive(MPa)
2000
565
those from experimental data.
Using Roberts' revised model, a paraAdhesivelayerthickness(mm)
2
0.636
metric study was conducted to determine
Elasticmodulusof FRP( M P a )
165,210,300
230
the most critical parameters controlling
Tensilerupturestrengthof FRP(MPa) 2800, 2400, 1300
3400
interracial shear stresses within the beam.
The following parameters were found to
Tensilerupturestrainof FRP(mm/mm) 0.017, 0.012, 0.0045
0.014
be the most important: (1) FRP plate
thickness, (2) FRP modulus, (3) adhesive shear modulus
a cracked section and use of a corrected end moment
and
(4) adhesive thickness. Studies were conducted to
M*. This suggests that the mode of failure is unlikely to
find
out how each of these parameters affects the FRP
be flexural compression or FRP rupture as the high
efficiency
(defined as the FRP strain at actual
interfacial shear stress is likely to result in debonding failfailure/FRP
rupture strain) and the mode of failure.
ure. It is noted that when Roberts' revised model preFactors
affecting
the interfacial shear strength were also
diction of debonding failure corresponded well with the
examined
based
on
a model proposed by Chaalal et al.
actual failure mode, the failure loads predicted by the
same model were significantly lower than those
{61
reported. In cases where both predicted failure modes
and actual failure modes were by concrete compression
3.1 Effect of FRP thickness o n FRP e f f i c i e n c y
or FRP rupture, predicted and actual failure loads were
found to be in close agreement. In these cases, predicted
at d e b o n d i n g
Table 1 - Properties of FRP and adhesive provided by manufacturers
1.0
4
~i ,
i~ i
~
x\
~
o Exp. Data (No Anch.)
[] Exp. Data (Anch.)
-*-SM2 (CFRP, Type 1)
~o~.
~ ~.
~
-~- B2 (CFRP, Type 1)
0.8
0.6
One of the most critical parameters affecting the
interfacial shear stress is the FRP plate thickness.
Experimental data had been gathered and compiled
which reflect the FRP strain at the beam critical section
for bending at failure. For progressively increasing loads,
Roberts' revised model was used to predict the interfacial shear stress at the plate cutoff. The corresponding
FRP strain at the critical beam section was also calculated from sectional analysis. In the absence of reported
values of adhesive elastic and shear moduli, adhesive
properties from two proprietary systems (adhesive type 1
and adhesive type 2) were assumed for beams reinforced
with C F R P (Carbon Fibre Reinforced Polymer).
Unless stated otherwise, the adhesive used in proprietary
system 1 was adopted for CFRP-plated beams by
default. The properties of these two proprietarY systems
and their corresponding adhesives are shown in Table 1.
Reported experimental data and results from the
above analysis (solids lines) are shown in Figs. 3-4. Note
that the theoretically-predicted curves have been generated assuming that &bonding failures take place when
the maximum shear stress at the FRP cut-off point
exceeds the interfacial shear strength (to be discussed
later). The experimental data show a general trend of
decreasing FRP efficiency with increasing FRP relative
axial rigidity .(APE/AsEs),
where .AP, A s, E.P and E~ are
P
the cross-sectional areas and elastic moduh of the FRP
and longitudinal steel, respectively. This is expected as
interracial shear stress concentration increases with
increasing thickness of the FRP plate. At the onset of
debonding, the stress in the FRP plate at the critical
beam-section for bending would thus decrease with
increasing FRP thickness. Experimental data reviewed
in this study showed that measured FRP strains at critical beam sections for bending were generally higher for
anchored beams than for those non-anchored. This was
0.4
0.2
0.0
0.0
0.5
i
i
1.0
ApEp/A~Es
1.5
2.0
Fig. 3 - Comparison between experimental data and results predicted by Roberts' revised model. The terms C, P2, SM2 and B2
refer to FRP-strengthened beams tested in studies [9], [10], [11],
and [12], respectively. GFRP refers to glass fibre reinforced polymer, and Type 1 refers to the adhesive of proprietary system 1
(Table 1).
1.0
o Exp. Data (No Anch.)
o Exp. Data (Anch.)
-_. SM2 (CFRP, Type 2)
, - SM2 (Propriety System 2)
- - S M 2 (CFRP, Type 1)
C
o
C
~,
t~
~.4
:
C.2
(.0
F
0.0
q
0.5
1.0
F
1.5
2.0
ApEp/AsE~
Fig. 4 - Effect of adhesive properties on FRP efficiency as predicted by Roberts' revised model.
421
Materials and Structures/Materiaux et Constructions, Vol. 34, August-September2001
because stress concentration was reduced at the points of
anchorage, thereby delaying the onset of debonding.
This allowed the FRP plate to develop a significant part
of its tensile rupture strain prior to debonding, leading to
higher FRP efficiency. From the experimental trend, it
appears that limiting the FRP thickness, and hence the
relative axial rigidity, would increase the FRP efficiency
at debonding. This would, however, reduce the cross
sectional area of the FRP required for flexural strengthening. The width of the FRP plate should, therefore, be
as wide as possible to provide the necessary FRP crosssectional area required for flexural strength.
From Fig. 3, Roberts' revised model appears to predict results that are generally in close agreement with the
actual trend set by the experimental data. At low relative
axial rigidity (A E/AsEs),
FRP &bonding takes place
p
after the FRP ~velops a significant part of its tensile
rupture strain, leading to a high FRP efficiency.
However, the failure load is generally not high enough
to cause the beam to fail by flexural compression first.
The beams reinforced with CFRP adopting the adhesive
properties of proprietary system 1 (adhesive type 1)
resulted in lower FRP efficiencies at &bonding failure
compared to the actual experimental data. This could be
due to the use of inappropriate values for the elastic and
shear moduli of the adhesive, which appeared to be very
stiff(E a = 12800 MPa, G a = 2000 MPa).
A comparison was made for beam SM2 tested by
Arduini and Nanni [11] for which a less-stiff adhesive
(adhesive type 2) used in the proprietary system 2 was
adopted (see Fig. 4). It was found that the interfacial
shear stress in the beam was lowered for the same load.
This allowed the FRP plate at the critical section for
bending to develop higher stresses at debonding, leading
to an increased FRP efficiency. The actual FRP efficiency of 0.40 at a relative axial rigidity of 0.60 for beam
SM2 was still higher than the FRP efficiency computed
when Roberts' revised model was used. This suggests
that the actual adhesive used in SM2 is probably less stiff
than both adhesives used in proprietary systems 1 and 2.
It could thus be seen that the properties of the adhesive
play an important role in determining the interfacial
shear stresses, and ultimately, the FRP efficiency and
failure load. In what follows, Roberts' revised model
was used again to evaluate the effect of other parameters
on the interfacial shear stress and FRP efficiency.
1.0
0.8
.~
0.6
o
0.4
r~
0.2
0.0
240
260
280
300
320
340
A d h e s i v e shear m o d u l u s G a (MPa)
Fig. 5 - Variation of FRP efficiency with adhesive shear modulus.
increased from 240 MPa to 320 MPa. This suggests that a
less-stiff adhesive should be used to reduce the interracial
shear stresses that would lead to debonding. However, it
should be realized that it may not be possible to independently change the shear modulus of the adhesive without
changing other adhesive-related properties such as the
interfacial shear strength. For the purpose of determining
the shear modulus of the adhesive, the "Standard Test
M e t h o d for Shear Strength and Shear Modulus of
Structural Adhesives" documented in ASTM E 229-97
[19], could be performed.
3.3 Effect of adhesive thickness on FRP
efficiency at debonding
The other adhesive parameter that affects the FRP
efficiency at debonding is the thickness. Parameters for
beam C were once again adopted. All parameters
remained unchanged while the adhesive thickness was
varied. The FRP efficiency was found to increase significantly with increasing adhesive thickness (see Fig. 6).
This is due to a significant reduction in interfacial shear
stress combined with a small increase in interfacial shear
strength (as predicted by Chaalal et al. [6]. See next section). In general, the required thickness of adhesive
depends on the thickness of the FRP plate, with a
thicker plate requiring a thicker layer of adhesive to be
1.0
0.8
3.2 Effect of adhesive shear modulus on FRP
efficiency at debonding
es
0.6
ga
Two adhesive parameters, the shear modulus and
thickness, were found to affect the FRP efficiency at
debonding failure significandy. The properties of the FRP
system used in beam C tested by Saadatmanesh and Ehsani
[9] were adopted for analysis in this case. The shear modulus of the adhesive was first varied and its effect on FRP
efficiency at debonding was studied. As can be seen from
Fig. 5, the FRP efficiency was reduced from about 85% to
less than 70% when the shear modulus of the adhesive was
422
0.4
[..r. 0.2
0.0
0
1
2
3
4
5
Adhesive layer thickness d a ( m m )
Fig. 6 - Variation of FRP efficiency with adhesive layer thickness.
Maalej, Goh, Paramasivam
applied for full contact between the FRP plate and the
concrete surface. Experimental data, however, suggest
that the bond strength decreases with increasing glueline thickness [20]. Even though a thicker adhesive layer
appeared to be conducive in reducing interfacial shear
stress concentrations according to Roberts' revised
model, the need to control the adhesive thickness would
still exist due to potentially weaker bond strengths for
thicker adhesive layers.
From the parametric studies, it was observed that the
most critical parameters controlling the interfacial shear
stresses are the FRP plate thickness, FRP modulus, adhesive shear modulus and the adhesive thickness. By comparing the trends set by the experimental data and results
generated by the predictive model, it appears that Roberts'
revised model could indeed be used to predict debonding
type failures. An experimental program, however, should
be conducted to determine the elastic and shear moduli of
the adhesive as these parameters play an important role in
determining the interfacial shear stresses.
5
~
~
~
p
~
~', 4 § Shear strength
"Shear s ~
"~/
/~
2
00kN
/~--"
Ep= !4-gGPa
Ea = 300 MPa
Ga = 120 MPa
d a = l mm
J
1 ill(
0
0
0.5
1.0
1.5
2.0
Flip plate thickness dp (ram)
Fig. 7 - Variation o f interfacial shear strength/stress
plate thickness for b e a m P2.
4. PARAMETERS AFFECTING INTERFACIAL
SHEAR STRENGTH
F_p=40C~
4.5
-
K///-+-
4.0
where is 3' given by Equation (4).
For a given adhesive, factors that influence "~uinclude
the adhesive thickness, the FRP plate thickness and the
FRP elastic modulus. Debonding occurs when the
interfacial shear stress exceeds the interfacial shear
strength. However, when the FRP plate thickness is
small, other modes of failure (such as concrete flexural
compression and FRP rupture) are also possible before
the interfacial shear stress can exceed the interfacial shear
strength. As can be seen from Fig. 7 based on beam P2
tested by Sharif et al. [10], the interfacial shear strength
drops with increasing FRP plate thickness. The inter facial shear stress, however, increases as the FRP plate
thickness is increased. The range of FRP thickness at
which &bonding might occur was found to vary widely
depending on the thickness and the mechanical properties of the FRP and adhesive used.
Figs. 7-8 show the effect of using a stiffer FRP plate
on the FRP thickness at debonding. The FRP plate
thickness at debonding decreased from 1.8 mm to about
0.37 mm when the FRP elastic modulus was increased
from 14.9 GPa to 40 GPa. For an FRP plate of 0.5 mm
thickness, when E_ is increased from 14.9 GPa to 40
GPa, the interracial shear stress increased from 2.0 MPa
to 5.2 MPa, while the interracial shear strength increased
from 4.2 MPa to 4.5 MPa. This suggests that the
increase in interracial shear strength did not outweigh
9
.
P
.
,t
Shearsuvn~
--~- ~
The adhesive interfacial shear strength ('Cu)was computed based on an expression given by Chaalal et al. [6].
The proposed expression took into account the effect of
normal stress concentration at the plate curtailment as
given by Roberts' model:
(13)
with FRP
5.5
5.0
5.4
Zu - 1+'r tan33 ~
2.5
3.5
0.25
stress
0.45
p~te thid~ss ~, ( m )
Fig. 8 - Variation of interracial shear strength/stress
plate thickness for beam P2 (Ep = 40 GPa).
0.65
with FRP
4.4
42
9
3.8
3.6
"~ 3.4
3.2
3.0
2.0
=2mm
--~ Shear strength
Shear stress
2.2
2.4
2.6
2.8
3.0
3.2
FRP plate thickness dp (ram)
Fig. 9 - Variation o f interfacial shear strength/stress
plate thickness for b e a m P2 (d a = 2 m m ) .
with FRP
the increase in interracial shear stress when a stiffer FRP
plate was used. The stiffness of the FRP plate is therefore an important parameter to control when designing
FRP-strengthened RC beams against &bonding failure.
Figs. 7 and 9 show the effect of varying the thickness of
the adhesive layer on the FRP thickness at debondmg (the
adhesive thickness was increased from 1 mm to 2 ram).
The effect of this change was to increase the FRP thickness
at &bonding from about 1.8 mm to about 2.7 ram. This
is due to a significant reduction in inteffacial shear stress as
423
Materials and Structures/Materiaux et Constructions, Vol. 34, August-September 2001
Table 2 - Effect of changing various parameters
on the interracial shear strength and stress
Factor
Interracial shear stress
Roberts' revised model [2]
? Ea
??
?da
~
Interracial shear strength
Chaalal etal. [6]
?
?? Strong dependenceon thefactor, ? Wealedepende,,a'o, thefactor,
predicted by Roberts' revised model and a small increase in
interracial shear strength as predicted by Chaalal et al. [6].
For an FRP plate of 2 mm thickness, the interfacial shear
stress according to Roberts' revised model decreases from
4.5 MPa to 3.4 MPa when da is increased from 1 mm to
2 mm. The corresponding increase in interracial shear
strength according to Chaalal et al. [6] is from 4.0 MPa to
4.1 MPa. As pointed out earlier, the latter result is inconsistent with experimental data showing decreasing bond
strength with increasing glue-line thickness [20].
Whenever possible, ' direct measurements of the interracial
bond strength between the FRP plate and the concrete
surface should therefore be undertaken for the type of
adhesive to be used. From a practical standpoint, however,
most proprietary systems have recommended adhesive
thicknesses that should be used and for which data on
interracial bond strength may be obtained from the manufacturer.
Table 2 shows a summary of the effect of changing
different FRP and adhesive parameters on the interfacial
shear stress and strength. The table shows that the factors that affect the interracial shear stress would also
affect the interfacial shear strength, but to a lesser extent.
The effect of these parameters, particularly on the interfacial shear stress, should therefore be taken into account
when designing an FRP-strengthened RC beam.
Bonacci and Maale] [1] studied the behavioral trends
of RC beams strengthened in flexure with externallybonded FRP by compiling and analyzing an experimental database. The deflection ratio for strengthened
beams (defined as the midspan deflection at peak load of
a strengthened beam divided by the midspan deflection
at peak load of a control beam) was found to increase
with increasing FRP efficiency ratio. Fig. 3 suggests
that the latter decreases with increasing relative axial
rigidity (ApEp/AsEs). Therefore, one would expect the
deflection ratio to decrease with increasinrID A p E /A SE S
ratio. By limiting A pE/AsE,
13
s it would be possible to
prevent or delay debondlng type failures as well as ensure
adequate deflection capacity.
For a given strengthening application, a pre-determined strengthening ratio (defined as the strength of the
beam with e x t e r n a l l y - b o n d e d
FRP divided by the
strength of the conventionally reinforced control beam)
would be targeted. Given that numerous proprietary
FRP strengthening systems are currently available, the
optimum system to use would be one that meets the tar424
geted strengthening ratio while limiting
the A E/AsE
~
9
. P
ratio. In this case, it would be possible to achieve an
opportune balance between strength gain and deflection
capacity. For this purpose, FRP efficiency-relative axial
rigidity trends (such as those shown in Fig. 3) can be
established from experiments and/or analytical models
(such as Roberts' revised model) and used to guide the
optimum design ofFRP-strengthened RC beams.
While the focus of the present paper was on one
aspect of the short-term structural performance of FRP
strengthened beams, the long-term performance is also
very important. Specifically, the durability of an FRP
strengthening system under cyclic freezing and thawing,
aggressive substances, and fatigue needs to be considered
in design. In addition, the designer should be aware that
FRP plates generally do not have sufficient fire resistance for many applications, and therefore often need
additional protection.
5. CONCLUSIONS
In this study, predictive models for determining the
interfacial shear stress distribution in FRP-plated RC
beams have been reviewed and evaluated using experimental data reported in the literature. The most critical
parameters governing the interfacial shear stress (and
strength) as determined by the reviewed predictive models were also examined. Roberts' revised model, derived
on the basis of a cracked beam section and a modified
moment M*, predicted results that were in close agreement with actual trend set by the experimental data.
Experimental as well as model results revealed that the
FRP efficiency increases with decreasing FRP relative
axial rigidity. In addition, data reported in the literature
suggested a direct relationship between beam deflection
capacity and FRP efficiency. With the availability of
numerous proprietary FRP strengthening systems, it
would be possible to select an FRP strengthening system
which offer an opportune balance between strength gain
and deflection capacity for a given application.
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