1.1 Introduction 1.2 FRP Composite

1.1 Introduction
The use of FRP composites in reinforced concrete members has emerged as one of the most
promising technologies to address the rehabilitation of infrastructures. There is a wide range
of applications for FRP reinforcement that covers new construction as well as the
rehabilitation of existing structures. Externally bonded FRP reinforcement has been shown to
be applicable for the strengthening of many types of RC structures such as columns, beams,
slabs, walls, tunnels, chimneys, and silos, and can be used to improve flexural and shear
capacities, and also provide confinement and ductility to compression members (A. Khallifa
et al 2000).
Common methods of shear strengthening include side bonding, U-jacketing and full
wrapping Figure. 2.1. Both FRP strips and continuous sheets have been used, and the fibres
in the CFRP may also be oriented at different angles. In this chapter, information is provided
on FRP materials and their applications in structural engineering with an emphasis on
strengthening for shear. In addition, a description on basic theories of shear and the analytical
tools available to model the shear behaviour of reinforced Concrete beams is discussed.
Side bonding
U-jacket
Fully wrapped
Figure 2.1 FRP shear strengthening configurations.
1.2 FRP Composite
The mechanical properties of any solid form can be modified by adding another material. In
other words, composites consist of two or more distinctly different materials which are
combined in a controlled way to achieve a mixture having more useful properties than any of
the constituents on their own. These composite materials can be classified into macroscopic
composites, where the constituent materials or phases can be distinguished with the naked
8
eye, and microscopic composites, where optical or electron microscopes are needed to see the
constituent phases (N. J. Mills 1993).
The materials can be basically classified as gases, liquids, and solids, as shown in Figure 2.2
(A. Strong 2006). Most materials can be converted from one state to another through heating
or cooling. If only materials that are structural solids at normal temperatures are examined,
three major types of materials are encountered, metals, polymers and ceramics. The polymer
materials can be further divided into synthetic polymers and natural polymers. Most synthetic
polymers are represented by materials such as nylon, polyethylene, and polyester. Some
synthetic polymers could be manufactured copies of naturally occurring materials (such as
synthetic rubber) or even natural polymers that have been so radically modified that they no
longer have the general properties of the original natural polymer, such as celluloid or
cellophane, which are derived from cellulose.
Figure 2.2 Diagram illustrating the definition of polymers (A. Strong 2006).
FRP materials are composites consisting of high strength fibre embedded in a polymeric resin
Figure 2.3. Epoxy resins are widely used because of their versatility, high mechanical
properties, and high corrosion resistance. Epoxies shrink less than other materials. However
they cost more than other resins. (Dasarath Rao 2007).
9
Figure 2.3 Representation of FRP material (Dasarath Rao 2007).
1.3 Polymers
Polymer materials are composed of very large molecules and the name polymer is derived
from poly, meaning many, and mer, meaning unit (V.B. John
2003). The simple
understanding of polymers can be gained by imagining the molecular nature of materials to
be like a chain, or perhaps, a string of pearls, where the individual pearls represent small
molecules that are chemically bonded together. Therefore, a polymer is a molecule made up
of smaller molecules that are joined together by chemical bonds. In other words, polymer
means many parts or units which are the small molecules. As shown in Figure 2.4 (A. Strong
2006).
Polymers are large molecules consisting of repeated chemical units (`mers') joined together.
To make the chain, many links or "-mers" are hooked or polymerized together. The units are
called monomers, two of the units bonded together are called dimer, bonding of three units
are called trimer and so on, the bonding of many units leads to a polymer. Polymers are
typically classified into two categories depending upon the reaction to heating and cooling.
They are called thermosets and thermoplastics. The important difference between these two
categories is their behaviour under pressure and heat. A thermoplastic polymer is one which
melts or flows when heated, and then capable of being shaped or reshaped while in its heated
semifluid state. Thermosets are usually malleable prior to curing, and designed to be moulded
into their final form, or used as adhesives. In general thermoset polymers are termed a resin
system during processing and matrix after the curing. Thermoset materials are generally
stronger than thermoplastic materials, and are also better suited to high-temperature
applications (Dasarath Rao 2007). In the case when the reinforcement is a fibre it yields
composites known as the fibre composites.
10
Figure 2.4 Illustration of small molecules combined in a polymer chain (A. Strong 2006).
Most polymer materials have some characteristics that are similar to viscous liquids and some
that are similar to elastic solids. These are therefore known as viscoelastic. Viscoelastic
materials can be either liquid or solid, although the distinction between liquids and solids in
these materials is not clear one, as shown in Figure 2.5. (A. Brent Strong 2006).
Figure 2.5 Continuum of viscoelasic properties and representation using simple mechanical devices
(A. Strong 2006).
11
The plot of the applied force (stress) is shown in Figure 2.6a. the plot of response of the
solidlike material Figure 2.6b indicates a direct and linear response to the applied force. The
solidlike material moves (strains) instantaneously at the application of the constant force and
continues at this position as long as the force is applied. At the moment the force is relieved,
the solidlike material returns to its original position. This behaviour is like that of a spring.
The plot of response of liquidlike material possessing viscous flow is shown in Figure 2.6c.
In this material the imposition of the steady force begins to deform the material, but the
movement increases linearly as time proceeds, this movement will continue so long as the
steady force is applied. When the force is relieved, the liquidlike material will stop moving
but will not return to the original position (A. Strong 2006).
Figure 2.6 The mechanical response of solidlike, liquidlike, and viscoelastic materials to an imposed
constant force (A. Strong 2006).
The response of a viscoelastic material to an applied constant force is illustrated in Figure
2.6d. Viscoelastic materials begin to move immediately upon application of the force, but not
as much as the elastic material, although more than the viscous material. The response is,
therefore, intermediate between the two other materials. The viscoelastic materials will
12
continue to move so long as the force is applied. When the force is stopped the viscoelastic
material will attempt to recover to the original position but will be slowed in this recovery.
1.4 Carbon fibre reinforced polymer (CFRP)
CFRP material has proved to be more efficient than other composites when applied to
concrete as an external reinforcement. Because of its enhanced durability characteristics
compared to glass or aramid, and its relatively high elastic modulus, carbon FRP shows a
higher confining performance. In the days when carbon fibre was first being produced, some
distinction was made between standard carbon fibres and those that were subjected to a
higher-temperature final-processing step and were therefore more purely graphite fibres. That
distinction has now largely disappeared and so the terms carbon fibres and graphite now refer
to the same material. The major advantage of carbon fibres over all other fibres is their very
high elastic modulus. Carbon fibres are among the stiffest of all known materials, especially
when compared on an equal-weight basis (A. Strong 2006). Table 2.1 illustrates the typical
properties of carbon fibres.
Table 2.1 Typical properties of dry carbon fibres (C. Peter Et al, 1983).
Property
High-modulus Carbon fibres
High-strength Carbon fibres
Density (kg/m3)
1950
1750
Diameter (µm)
8
8
Tensile modulus(GN/m2)
390
250
Tensile strength (MN/m2)
2200
2700
Strain at break (in tension)(%)
0.5
1
Linear expansion coefficient(/K)
-0.5 to -1.2 x 10-6
-0.1 to -0.5 x 10-6
Figure 2.7 shows the material properties of the four types of reinforcement used in this
program, including Glass Fibre Reinforced Polymers, GFRP (Isorod) produced by Pultrall
Inc., Canada; GFRP (C-Bar) produced by Marshall Industries Composites, Inc., USA; Carbon
Fibre Reinforced Polymers, CFRP (Leadline) produced by Mitsubishi Kasei, Japan; and
conventional steel. (F. Wegia 2005, H.A. Abdalla 2002).
13
Figure 2.7 Material characteristics of the FRP and steel reinforcements. (F. Wegia 2005).
It can be seen from Figure 2.8 that the balanced reinforcement ratios for FRP reinforced
concrete sections are much lower than those for steel reinforced concrete sections. This is due
to the higher tensile strength and the lower modulus of elasticity of the FRP reinforcements
relative to conventional steel. For practical ratios of FRP reinforcements and in order to
control deflection and cracking, most of the FRP reinforced concrete sections will be overreinforced. It has to be noted that whether the FRP reinforced concrete section is underreinforced or over-reinforced, the flexural failure will be a brittle failure. This is due to the
fact that the FRP reinforcements do not yield as in the case of steel reinforcement (H.A.
Abdalla 2002).
Figure 2.8 Balanced reinforcement ratios for sections reinforced with GFRP, CFRP, and steel (H.A.
Abdalla 2002).
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1.5 Applications of CFRP
There are three broad divisions into which applications of CFRP in civil engineering can be
classified:

Applications for new construction.

Repair and rehabilitation applications.

Architectural applications.
CFRP’s have been used widely by civil engineers in the design of new construction.
Structures such as bridges and columns built completely out of CFRP composites have
demonstrated exceptional durability, and effective resistance to effects of environmental
exposure. One of the most common uses for CFRP involves the repair and rehabilitation of
damaged or deteriorating structures. In this case, the CFRP composite is used to retrofit an
existing and deteriorated structure to bring its load carrying capacity back to the level for
which it was designed. Architects have also discovered many applications for which FRP can
be used (Dasarath Rao 2007).
1.6 Strengthening techniques
There are two strengthening techniques which have been used for the structural rehabilitation
of concrete structures (Barros et al 2004 and 2007). :
1.6.1 Near surface mounted (NSM)
The NSM technique comprises following steps: (1) using a diamond blade cutter, slits of 4–5
mm width and 12–15 mm depth are cut on the concrete surface of the elements to strengthen;
(2) slits are cleaned by compressed air; (3) CFRP laminates are cleaned by acetone; (4) epoxy
adhesive is produced according to supplier recommendations; (5) slits are filled with the
epoxy adhesive; (6) epoxy adhesive is applied on the faces of the laminates; and (7) laminates
are introduced into the slits and epoxy adhesive in excess was removed(Barros et al 2007), as
shown in Photograph 2.1.
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Photograph 2.1 Strengthening with the NSM reinforcement technique (Rizkalla et al, 2004).
1.6.2 Externally bonded reinforcement (EBR)
It is possible to choose between several systems of reinforcement in EBR technique that
differ for the type of fibre, and for the resins, as shown in Photograph 2-2. The systems
available are the following (Cerretini 2004):

Wet Lay-Up systems composed of dry multidirectional or unidirectional fibre sheets,
cured in-situ.

Pre-preg Systems composed of unidirectional or multidirectional fibre sheets preimpregnated with a “Saturating Resin” but not still cured. In the future will be
possible to use fabrics designed for specific applications.

Pre-cured Systems composed of cured strips, shells, jackets or angles, installed
through the use of adhesives.
16
Photograph 2.2 externally bonded FRP sheets/strips (Rizkalla et al, 2004)
Vacuum infusion is one method which is used for application of CFRP to concrete structures.
The basic FRP strengthening technique, which is most widely applied involves the manual
application of Wet Lay-Up systems, as shown in Photograph 2.2 (Cerretini 2004). To apply
the wet lay-up strips of CFRP sheet by the EBR technique, the following procedures were
executed: (1) on the zones of the beams surfaces where the strips of sheet would be glued, an
emery was applied to remove the superficial cement paste (in the shear strengthening
experimental program the beam’s edges were also rounded); (2) the residues were removed
by compressed air; (3) a layer of primer was applied to regularize the concrete surface and to
enhance the adherence capacity of the concrete substrate; and (4) using epoxy resin, the strips
of sheet were glued on the faces of the beam. In cases that laminates were applied according
to the EBR technique, identical procedures to the ones adopted in the EBR sheets were
followed, but instead of epoxy resin it was used adhesive epoxy was used to bond the
laminates to concrete (Barros et al 2007), as shown in Photograph 2.3. The Wet Lay-Up
system will be used for shear strengthening in this study.
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Photograph 2.3 strengthening with the EBR reinforcement technique (Rizkalla et al, 2004).
1.7 The bond between CFRP and the concrete
External bonding of CFRP plates or sheets has emerged as a popular method for the
strengthening of RC structures. In this strengthening method, the performance of the CFRPto-concrete interface in providing an effective stress transfer is of crucial importance. Indeed,
a number of failure modes in CFRP-strengthened RC members are directly caused by debonding of the CFRP from the concrete. Therefore, for the safe and economic design of
externally bonded CFRP systems, the behaviour of CFRP-to-concrete interfaces needs to be
understood. The bond of CFRP reinforcement to the concrete substrate is a critical problem
influencing the effectiveness of the technique of retrofitting and repairing existing structures.
For a beam system, concrete de-bonding, which is often brittle, can occur with little or no
visible warning at load levels significantly lower than the expected flexural or shear strength
of the retrofit system (Ching et al , Aiello et al 2007, X.Z. Lu et al 2005, Shang et al 2005
X.Z. Lu et al 2006, X.Z. Lu et al 2009).
An important step toward understanding bond behaviour is to have an assumption for local
bond stress versus slip relationship. Tensile strength in the case of bond failure, strain
distribution of FRP, and bond stress distributions can be obtained using bond stress versus
slip relationship modelled by mathematical or numerical analysis. Experiments on bond that
18
analyze specimens have been carried out, and the procedures applied to those experiments are
divided into three types, as follows. Figure 2.9 shows typical models for these three types.

Cut off type.

Bilinear type.

Tensile softening type.
Figure 2.9 Bond stress – slip model (K. Nakaba et al 2001).
Figure 2.10 shows several test methods which are used to understand the bond behaviour
between CFRP laminates and concrete. Experiments using a tile or similar methods (Figure
2.10 (a)) to directly obtain the bond strength have been performed. But in terms of bending
and shearing in this method, it is difficult to directly estimate the bond characteristics of the
concrete-fibre system. One alternative that has been widely used to solve this problem, and
was adopted in researches, consists of a prism with a notch at the centre, reinforced with
CFRP laminates on both faces (Figure 2.10 (b)). Similarly, another alternative consisting of
two prisms reinforced at the centre with CFRP laminates (Figure 2.10 (c)) is proposed to
estimate the bending. To remove the acting force's eccentricity in experiments using
laminates in both faces, experiments using laminate in one face (Figure 2.10 (d)) and
laminate inserted in two concrete prisms (Figure 2.10 (e)) have been performed. In this
arrangement, when the anchorage length is shorter, bond failure with de-lamination of
laminates usually occurs. When the anchorage length is longer, failure occurs with CFRP
rupture. Also, it is reported that when the anchorage length increases, the failure force tends
to be higher, and the apparent average bond stress decreases.(K. Nakaba et al 2001)
19
Figure 2.10 Bond test specimens (K. Nakaba et al 2001).
2.7.1 Proposed bond–slip models
Many theoretical models have been developed in recent years to predict the bond–slip model
of FRP-to concrete bonded joints, generally on the basis of pull test results. X.Z. Lu et al
2005 examined some of them. In addition, X.Z. Lu et al 2005 proposed three bond–slip
models with different levels of sophistication for FRP-to-concrete interfaces.
2.7.1.1 Precise model
By using the meso-scale finite element model of J.G.Teng et al 2005, X.Z. Lu et al 2005
proposed an accurate model to predict the bond–slip model of FRP-to concrete bonded joints
as follows:
Where
20
in which
(MPa) is the concrete tensile strength,
stress (i.e. local bond strength),
ratio factor, and
strips,
(mm) and
(MPa) is the peak value of the bond
(mm) is the slip corresponding to
,
is the width
(mm) are the individual width of and spacing between FRP
is the elastic component of
.
where
(GPa) is the elastic shear modulus of concrete and
(mm) is the effective thickness of the
concrete whose deformation forms part of the interfacial slip
thickness and
(mm) is the adhesive layer
(GPa) is the elastic shear modulus of the adhesive. The bond–slip curve from
the precise model for one of the bonded joints analysed by the finite element method is
shown in Figure 2.11. It is clear that there is a close agreement between this precise model
and the finite element curve.
2.7.1.2 Simplified model
The precise model is accurate but somewhat complicated. A simplified model without a
significant loss of accuracy, was adopted by X.Z. Lu et al 2009 because the simplified model
provides accurate predictions of bond–slip behaviour for FRP-to-concrete interfaces as long
as the elastic modulus of the adhesive used does not fall below a realistic lower bound. This
model (Figure 2.11) defines the interfacial shear stress (or the bond stress) at any point along
the bond length in terms of the relative slip at that point as
21
where
and
can be calculated with Eq. (2.5) and (2.7),
(MPa mm) is the interfacial
fracture energy (equal to the area under the bond–slip curve). The bond–slip curve predicted
by the simplified model is also shown in Figure 2.11, where it can be seen that there is little
difference between this model and the precise model.
2.7.1.3 Bilinear model
Further simplification can be made to the simplified model by adopting a bilinear bond–slip
curve which can be used to derive a simple explicit design equation for the bond strength.
This bilinear model has the same local bond strength and total interfacial fracture energy, so
the bond strength is unaffected by this simplification if the bond length is longer than the
effective bond length. This bilinear model is described by the following equations:
where
In the above equations,
,
and
can be found using Eqs.(5-2), (7-2) and (15-2),
respectively. The prediction of the bilinear model is also shown in Figure 2.11.
22
Figure 2.11 Bond–slip model of (X.Z. Lu et al 2005).
2.7.2 Existing bond strength models
This section provides a summary of five bond strength models

Yuan H et al 2004 model based on a simplified bond-slip model.

Izumo 2003 model, Sato 2003 model, and Iso 2003 model, described in a recent JCI
report.

Yang 2001 model, developed in China.
The following units are used: N for forces, MPa for stresses and elastic modulus, and mm
for lengths.
2.7.2.1 Yuan H et al 2004 model
where
of FRP,
is the ultimate load or bond strength,
is thickness of FRP sheet,
is width of FRP sheet,
is elastic modulus
is the tensile strength of concrete, and
is the width
of the concrete prism.
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2.7.2.2 Izumo 2003 model
The bond strength model proposed by Izumo 2003 is given by
for CFRP sheets
and
for Aramid fibre sheets. where L is bond length.
2.7.2.3 Sato 2003 model
The bond strength model given by Sato 2003 is described by the following equations:
If
, then
is the working width of concrete,
is the effective bond length,
average
bond stress.
2.7.2.4 Iso 2003 model
The bond strength model proposed by M. Iso 2003 is given by
where If
, then
2.7.2.5 Yang 2003 model
The bond strength model proposed by Yang et al. 2003 is
where
,
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1.8 Shear Strengthening with CFRP
Inclined cracks cause the shear strength of beams to drop below the flexural capacity, as
shown in Figure 2.12(b) and (c). The purpose of the web steel reinforcement and the shear
strengthening with CFRP is to ensure that the full flexural capacity can be developed. In
normal situations a concrete structure is designed to reveal large deformations before failure,
which means that the failure is designed as a bending failure. A traditional shear failure often
starts with combined bending and shear that develops an inclined shear crack. The failure is a
shear failure in the highest tensile region where a principal tensile stress crack occurs. The
highest shear stress is present in the mid-depth of the cross-section of the beam, if the beam is
rectangular and has uniform web reinforcement. In normal cases, vertical steel stirrups aid in
resisting the build-up of these stresses, Taljsten 2003.
Figure 2.24 Different failure modes for a rectangular concrete beam (Taljsten 2003).
However, if the structure is strengthened in shear, other possible failure modes can arise, as in
Figure 2.24(b). Shown here is a concrete beam strengthened with composite materials.
Tensile failure in the FRP, compressive failure in the flange or web, and an anchorage failure
for the composite plate or strip can all arise here. With regard to bond-slip behaviour X.Z. Lu
et al 2009 concluded that the variation in width of the critical shear crack controls the stress
25
distribution in the FRP along the length of the crack. This present study will build upon these
findings to produce a new conceptual model incorporating a shear plane.
2.9.1 Design proposals
The design approach for computing the shear capacity of RC beams strengthened with
externally bonded CFRP reinforcement, expressed in ACI design code 2005 format, was
proposed and published in 1998. The design model described two possible failure
mechanisms of CFRP reinforcement namely: CFRP fracture; and CFRP de-bonding.
Furthermore, two limits on the contribution of CFRP shear were proposed. The first limit was
set to control the shear crack width and loss of aggregate interlock, and the second was to
preclude web crushing. Also, the concrete strength and CFRP wrapping schemes were
incorporated as design parameters, A. Khallifa et al 2000.
In traditional shear design (Triantrafilou 1998, A. Khallifa et al 2002, ACI committee 440
(2002), Eurocode (EC2 1992), and Chen 2003), the nominal shear strength of an RC section,
is the sum of the nominal shear strengths of concrete,
(for a cracked section this depends
on the dowel action of the longitudinal reinforcement, the diagonal tensile strength of the
uncracked part of the concrete and the aggregate interlocking effect) and steel shear
reinforcement,
. For beams strengthened with externally bonded FRP reinforcement, the
shear strength may be computed by the addition of a third term to take account for the FRP
contribution,
. This is expressed as follows:
The design shear strength,
, is obtained by multiplying the nominal shear strength by a
strength reduction factor for shear, . The
ACI is 0.85, and the
factor for steel and concrete contribution from
factor for CFRP contribution is suggested to be 0.70. Eq. 2.34 presents
the design shear strength.
To use externally bonded FRP reinforcement in design or retrofit, it is necessary to be able to
predict its contribution to the ultimate shear strength. Therefore, this study attempts to isolate
26
the contribution from the composite,
. The problem is thus to find an expression for
. This
is, however, not so easy. The expression to compute CFRP contribution which based on
rupture is quite similar to that for steel shear reinforcement. However, the rupture point of
CFRP sheet must depend instead on the ultimate condition governed by a yield point (as with
steel) A. Khallifa et al 2002, and Assaf 2007
Triantrafilou 1998, proposed a formula for
which is given in Eq. 2.35. In addition, he
concluded that the strain in the FRP is limited to an effective strain which was obtained from
regression of experimental data.
where
is the ratio of CFRP sheets
,
is the total thickness of the sheets (usually
for the sheets in both sides of the beam),
effective depth of the RC beam,
is the width of the RC beam,
is the modulus of elasticity of CFRP sheets,
effective strain of CFRP sheets at rupture, and
is the
is the
is angle of first fibre orientation measured
clockwise from the horizontal direction for the left side of a shear strengthened beam
The expression Eq.(2.32) used to compute shear contribution of externally bonded CFRP
reinforcement may be rewritten in ACI format (see 11.5.6.4 ACI 318M-2005 ) as Eq. 2.36.
where
is the bonded area of CFRP sheets
at rupture,
and
and
,
is the effective stress of CFRP sheets
is the depth of CFRP reinforcement (usually equal to
for T-sections),
for rectangular section
the spacing and the effective depth of CFRP (see Figure 2.25),
is nominal concrete compressive strength (MPa). Note that for continuous vertical
shear reinforcement, the spacing of the strip,
, and the width of the strip,
, are equal.
The proposed design equation Eq. 2.35 for computing the contribution of externally bonded
CFRP reinforcement may be rewritten in Eurocode (EC2 1992) format as Eq. 2.37.
27
Where
the design shear capacity of concrete
that can be carried without web failure,
reinforcement, and
is the maximum design shear force
is design contribution of steel shear
is partial safety factor for CFRP materials, suggested to be equal to 1.3
A. Khallifa et al 2002.
Figure 2.25.Dimensions used to define the area of FRP. (a) Vertical oriented FRP strips. (b) Inclined
strips.
In Eq. 2.36, a reasonable limit on the maximum amount of additional shear strength that may
be achieved is suggested in terms of the shear strength of concrete and steel shear
reinforcement. The limit was set to provide adequate safety against web crushing caused by
the diagonal compression stress. This limit is like the limit that was set by ACI 318M-2005
11.5.7.8 and 11.5.7.9 on the total shear strength that may be provided by more than one type
of reinforcement to preclude the web crushing. Besides that, there is the spacing of CFRP
strips limit which will be discussed in section (2.9.2)
To apply equations 2.35, 2.36, and 2.37, the effective strain should be determined.
Triantrafilou 1998, concluded that the effective strain depends on the development length
necessary to reach CFRP tensile fracture before de-bonding. As the development length is a
function of the axial rigidity
, the effective strain is also a function of the axial rigidity
and it would be expected that it is roughly inversely proportional to the axial rigidity. The
effective strain was determined by equating the experimental shear strength for several
rigidities to the equations 2.35, 2.36, and 2.37, and back calculating for
1998 illustrated that the relationship between
and
. Triantrafilou
is obtained from the best-fit
28
second order equation up to
and by the equation of straight line for
, given as follows:
0.014
0.012
0.01
fe
0.008
Without wrapping
0.006
Wrapping
0.004
0.002
0
0
0.5
1
1.5
2
2.5
3
f Ef (Gpa)
Figure 2.26 Effective CFRP strain in terms of
.
Some of the experimental data, which was obtained from the study of Triantrafilou 1998, is
compared with results of Eq. 2.38, as shown in Figure 2.26. This figure shows the difference
between experimental data which were obtained from test beams strengthened with wrapping
and beams strengthened without wrapping.
In addition, an effective average CFRP stress
, smaller than its ultimate strength,
, was
used to replace the yield stress of steel. At the ultimate limit state for the member in shear, it
is not possible to attain the full strength of the FRP Triantrafilou 1998. Failure is governed by
either fracture of the FRP sheet at average stress levels well below FRP ultimate capacity due
to stress concentrations, de-bonding of the FRP sheet from the concrete surface, or a
significant decrease in the post cracking concrete shear strength from a loss of aggregate
29
interlock. Thus, the effective average CFRP stress is computed by applying a reduction
coefficient, R, to the CFRP ultimate strength as expressed in Eq. 2.39.
The reduction coefficient depends on the possible failure modes (either CFRP fracture or
CFRP de-bonding). In either case, an upper limit for the reduction coefficient is established in
order to control shear crack width and loss of aggregate interlock.

Reduction coefficient based on CFRP sheet fracture failure
The reduction coefficient was established as a function of
of CFRP) and expressed in Eq. 2.40 for

(where
is the area fraction
.
Reduction coefficient based on CFRP de-bonding failure
The shear capacity governed by CFRP de-bonding from the concrete surface was presented
A. Khallifa et al 2000, as a function of CFRP axial rigidity, concrete strength, effective depth
of CFRP reinforcement, and bonded surface configurations. In determining the reduction
coefficient for bond, the effective bond length,
, has to be determined first. Based on
analytical and experimental data from bond tests, A. Khallifa et al 2000, showed that the
effective bond length slightly increases as CFRP axial rigidity,
, increases. However, he
suggested a constant conservative value for Le equal to 75 mm. The value may be modified
when more bond test data becomes available. After a shear crack develops, only that portion
of the width of CFRP extending past the crack by the effective bonded length is assumed to
be capable of carrying shear, A. Khallifa et al 2000 and 2002.The effective width,
on the shear crack angle of
, based
, and the wrapping scheme is expressed in Eq. 2.41.
The final expression for the reduction coefficient, R, for the mode of failure controlled by
CFRP de-bonding is expressed in Eq. 2.42
30
Eq. 2.42 is applicable for CFRP axial rigidity
, ranging from 20 to 90 mm-GPa (kN/mm).
Research into quantifying the bond characteristics for axial rigidities above 90 mm-GPa is
being conducted at the University of Missouri, Rolla (UMR) (A. Khallifa et al 2002).
The three predicated equations 2.35, 2.36, and 2.37 approximately depend on same
methodology to calculate the yield stress for CFRP reinforcement. Especially equations 2.35
and 2.36 are similar, they are just different in calculation of effective depth of CFRP
sheet/strips. Therefore this study will select the proposal of A. Khallifa et al 2002 to compare
it with the proposal of Chen and Teng 2003, which has a unique approach for calculating of
CFRP’s depth and yield stress. The contribution of FRP strips to the shear capacity by Chen
and Teng 2003 can be expressed as:
Where
is angle of critical shear crack to the longitudinal axis of a beam (see Figure
2.27).For practical design, it can be assumed that
. The contribution of FRP to the
shear strength is thus
in which
is the partial safety factor in a limit state design approach.
here, the effective height of the CFRP
where
and
is suggested
is expressed as:
are the co-ordinates of the top and bottom ends of the effective FRP, which
may be expressed as:
31
in which
is the distance from the compression face to the top edge of the FRP, h is the
height of the beam, and
is the distance from the compression face to the lower edge of
the FRP (Fig. 2.27) (thus,
for U jackets).
Figure 2.27 Notation for a general shear strengthening scheme (Chen and Teng 2001).
The design effective FRP stress
in which
is defined as
is the maximum stress in the FRP and
is termed here the stress
distribution factor which is defined as (X.Z. Lu et al 2009):
where
(
reflects the effect of bond length and
the effect of FRP-to-concrete width ratio
) of the shear test specimen. The FRP plate width
and concrete prism width bc
defined in the Chen and Teng 2001 bond strength model for simple shear lap tests may be
replaced here with the FRP strip width
the fibres) between them
and the centre-to-centre spacing (perpendicular to
. The strip width coefficient
Chen and Teng 2001 can
thus be expressed by Eq.2.7
the bond length coefficient
can be expressed as Chen and Teng 2001
32
in which the normalised maximum bond length l is defined as
where the maximum bond length
where
is given by
is the effective bond length
The stress distribution factor
can be calculated from:
In 2002 ACI committee 440 published a guide for the design and construction of externally
bonded FRP systems for strengthening concrete structures. This guide comprises a design
method for shear strengthening. The shear contribution of the FRP shear reinforcement is
then given by:
The tensile stress in the FRP shear reinforcement at ultimate limit is directly proportional to
the level of strain that can be developed in the FRP shear reinforcement at ultimate state.
33
ACI 440 illustrated that the effective strain in FRP laminates is the maximum strain that can
be achieved in the FRP system at the ultimate load stage and is governed by the failure mode
of the FRP system and of the strengthened reinforced concrete member. The engineer should
consider all possible failure modes and use an effective strain representative of the critical
failure mode. The following subsections give guidance on determining this effective strain
for different configurations of FRP laminates used for shear strengthening of reinforced
concrete members.
Completely wrapped members—For reinforced concrete column and beam members
completely wrapped by the FRP system, loss of aggregate interlock of the concrete has been
observed to occur at fibre strains less than the ultimate fibre strain. To preclude this mode of
failure, the maximum strain used for design should be limited to 0.4% for applications that
can be completely wrapped with the FRP system
This strain limitation is based on testing (Priestley et al. 1996) and experience. Higher strains
should not be used for FRP shear-strengthening applications.
Bonded U-wraps or bonded face plies—FRP systems that do not enclose the entire section
(two- and three-sided wraps) have been observed to delaminate from the concrete before the
loss of aggregate interlock of the section. For this reason, bond stresses should be analyzed to
determine the usefulness of these systems and the effective strain level that can be achieved
(Triantafillou 1998a). The effective strain is calculated using a bond-reduction coefficient
applicable to shear.
(for U-wraps or bonding to two sides)
The bond-reduction coefficient is a function of the concrete strength, the type of wrapping
scheme used, and the stiffness of the laminate. The bond-reduction coefficient can be
computed from Eq. 2.59 (Khalifa et al 1998).
34
The active bond length Le is the length over which the majority of the bond stress is
maintained. This length is given by
The bond-reduction coefficient also relies on two modification factors,
and
, that
account for the concrete strength and the type of wrapping scheme used, respectively.
Expressions for these modification factors are given
2.9.2 Strip spacing limit
The strength model was derived by treating strips as equivalent continuous sheets/plates. For
this treatment to be accurate, the number of strips intersected by the shear crack should be
sufficient. Otherwise, the treatment can lead to either conservative or un-conservative
predictions, depending on the locations of the strips. Consider diagonal shear failure as an
example. The most effective position is the middle of the shear crack for side bonding (Chen
and Teng 2003) (Figure 2.28(a)), but at the lower end for U jacketing (Figure 2.28(b)),
because the bond length is largest in both cases. By contrast, a strip located at either end of
the shear crack for side bonding Figure 2.28(c) and at the upper end for U-jacketing Figure
2.28(d) is completely ineffective due to the lack of any bond length. Therefore, a
strengthening scheme may be completely ineffective if only one strip is intersected by the
shear crack.
35
Figure 2.28 Effect of FRP strip location on effectiveness of shear strengthening (Chen and Teng
2003).
For a shear strengthening scheme to be effective, the spacing between the strips must be
limited. ACI 318M-2005 explained by 11.5.5 that the longitudinal spacing of internal
perpendicular steel shear reinforcement shall not exceed
, nor 600 mm. Beside this, BS
8110 requires that the spacing does not exceed the lesser of 0.75d and 300 mm. However, this
cannot be directly used here because an internal steel link can be assumed to be effective as
long as it intercepts the shear crack but an FRP strip can be completely ineffective even if it
does intercept the shear crack as discussed above.
The studies of A. Khallifa et al 2000 and 2002 proposed a spacing limit should not be so
wide to allow the full formation of a diagonal crack without intercepting a strip. For this
reason, the strips should not be spaced more than the maximum given in Eq. 2.63. this
equation means that the gap between two strips shall not exceed
in all cases and it
requires approximately four strips to intersect the shear crack. Chen and Teng 2003 shows the
spacing limit which is controlled by
for very narrow strips bonded to the full
height of the beam. Therefore this limit may be too restrictive. In addition, the use of
in the
limit leads to inconsistent results for different CFRP bonding heights on the beam sides.
Furthermore, the orientation of the fibres has not been properly considered.
36
For these reasons, Chen and Teng 2003 suggested that the clear strip spacing
(Figure 2.29) should not exceed half the horizontal distance at the lower end of the effective
CFRP covered by the projection of the shear crack in the direction of fibres, which is given
by Eq. 2.64. In Eq. 2.64 an upper limit of 300 mm for internal steel links is used in BS 8110.
Figure 2.29 Strip spacing.
The Concrete Society report TR55 also deals with UK recommendations and practice.
2.9.3 Existing experimental studies (full scale beams with shear strengthening)
The data shown in Table A.1 has been collected from existing literature based on an
extensive literature survey. Table 1 includes 66 beams which present the experimental results
of seven studies. These beams were strengthened with externally bonded CFRPs for shear
tested under three and four-point bending. The geometric and material properties required to
determine the contribution of FRP to the shear capacity by the strength model presented in
the previous section are shown. Further details can be found from the original sources. Tests
that were not sufficiently well documented have been excluded.
The experimental program of A. Khallifa et al 2000 consisted of six full-scale, simply
supported beams. One beam was used as a bench mark and five beams were strengthened
using different configurations of CFRP. The parameters investigated in their study included
wrapping schemes, CFRP amount, 90°/ 0° ply combination, and CFRP end anchorage as
shown in Table A.2. They concluded that externally bonded CFRP can increase the shear
capacity of the beam significantly. In addition, the results indicated that the most effective
configuration was the U-wrap with end anchorage.
37
A. Khallifa et al 2002 examined the shear performance and modes of failure of rectangular
simply supported RC beams designed with shear deficiencies. Their experimental program
consisted of twelve full-scale RC beams tested to fail in shear. The variables investigated
within this program included steel stirrups, and the shear span-to-effective depth ratio, as well
as amount and distribution of CFRP. As in the previous study, the experimental results
indicated that the contribution of externally bonded CFRP to the shear capacity was
significant.
J.A.O. Barros et al 2006. used a Near Surface Mounted (NSM) strengthening technique,
which was developed to increase the shear resistance of concrete beams. The NSM technique
is based on fixing, by epoxy adhesive, Carbon Fibre Reinforced Polymer (CFRP) laminates
into pre-cut slits opened in the concrete cover of lateral surfaces of the beams. To assess the
efficacy of this technique, an experimental program of four-point bending tests was carried
out with reinforced concrete beams failing in shear. Each of the four tested series was
composed of five beams: without any shear reinforcement; reinforced with steel stirrups;
strengthened with strips of wet lay-up CFRP sheets, applied according to the externally
bonded reinforcement (EBR) technique; and two beams strengthened with NSM pre-cured
laminates of CFRP, one of them with laminates positioned at
laminates positioned at
and the other with
in relation to the beam axis. Table A-1 (see Appendix A)
contains all specimens of J.A.O. Barros et al 2006. except beams which was strengthened
with NSM, because this study deals with EBR sheets only. The study of J.A.O. Barros et al
2006 Shown significantly the influence of the CFRP shear reinforcement ratio
depth
, the beam
and longitudinal tensile steel reinforcement on the beam load carrying capacity
provided by the considered CFRP shear reinforcing systems.
Triantrafilou 1998 aimed to increase the experimental database on shear strengthening of RC
beams using FRP. A series of tests was carried out, eleven deficient in shear identical
concrete beams were fabricated, of which nine were strengthened in shear with epoxy-bonded
CFRP fabrics attached on the two sides, and two were used as control specimens, that is,
without external reinforcement. He concluded that the strengthening of RC beams in shear
using epoxy-bonded composite materials in the form of laminate or fabrics appears to be a
highly effective technique. Within the framework of modern code formats, based on limit
states, the design of FRP strengthened members can be treated in analogy with the design of
internal shear reinforcement, provided that an effective FRP strain is used in the formulation.
38
Therefore he recommended that future studies should focus on the experimental database of
concrete beams strengthened in shear with FRPs through full-scale experimental testing and
on long-term performance.
G. Kim et al 2008 prepared eleven RC beams for an experiment to assess the strengthening
effect of the strengthening materials, and define the shear failure characteristic. They
concluded that the strengthening effect varied according to the shear span-to-depth ratio
of the beams. The ultimate strength of strengthened beams in shear was assessed using
various methods depending on the failure mode. They proposed an equation to predict shear
strength and failure patterns of FRP-strengthened beams in shear by using the plastic model
and the truss model to consider the contribution of FRP in shear. Also they explain that the
composite shear strength of strengthened beams is governed by the bonding characteristics as
well as the strength of FRP. In addition, to determine the amount of strengthening needed to
improve the load carrying capacity of beams. This theory is more effective than either
traditional theory or FE analysis.
Four different configurations of externally bonded carbon fibre fabric strips were used by
C.Diagana et al 2003 to strengthen the reinforced concrete beams in shear. The carbon fibre
fabric, was a dry bi-directional impregnated (epoxy resin) on site. The experimental
programme comprised of two control beams and eight strengthened RC beams. The
reinforced concrete beams were strengthened with carbon fibre fabric vertical strips and 45°
inclined strips in the form of U-wrap or in the form of a ring. The objectives of this study
were to investigate the influence of parameters like carbon fibre fabric span and wrapping
manners on the shear capacity of strengthened RC beams. A mechanical formula was used to
predict the contribution of carbon fibre fabric to shear capacity of strengthened RC beams.
The results obtained by using the mechanical formula have been compared with these
obtained by test.
In study of G. Monti et al 2006 twenty-four beam specimens, purposely designed as underreinforced in shear, were tested with a three-point bending scheme. To develop a mechanicsbased (as opposed to regression-based) model of the shear capacity of reinforced concrete
beams, strengthened with externally bonded fibre reinforced polymers, they followed three
steps: (a) the generalised constitutive law of an FRP layer bonded to concrete was defined
first, then, (b) the compatibility imposed by the shear crack opening and the appropriate
boundary conditions which depend on the strengthening configuration (either side bonding,
39
U-jacketing or wrapping) were included in the formulation, and, finally, (c) analytical
expressions of the stress field in the FRP strip/sheet crossing a shear crack are obtained.
Through these expressions, closed-form equations for the effective de-bonding strength of
FRP strips/sheets were defined as function of, both, the adopted strengthening configuration,
and of some basic geometric and mechanical parameters.
The study of C. Deniaud et al 2001 reviewed the different shear design methods found in the
literature for reinforced concrete beams strengthened externally with fibre reinforced polymer
(FRP) sheets and compares the adequacy of each method by using the test results from the
University of Alberta. The FRP shear design methods presented include the effective FRP
strain and the bond mechanism criteria, the strut-and-tie model, the modified compression
field theory, and a mechanical model based on the strip method with shear friction approach.
Sixteen full-scale T-beam test results were used in the evaluation. Two web heights of 250
and 450 mm and two ready mix concrete batches of 29 and 44 MPa were used in the test
specimens. Closed stirrups were used with three spacing’s: 200 mm, 400 mm, and no stirrups.
Three types of FRP were used to strengthen externally the web of the T-beams: (i) uniaxial
glass fibre, (ii) triaxial (0/60/–60) glass fibre, and (iii) uniaxial carbon fibre. The results of
C.Deniaud et al 2001 showed that the mechanical model using the strip method with shear
friction approach evaluates better the FRP shear contribution.
In 1998, O. Chaallal et al made an experimental investigation on the response RC beams
strengthened in shear using externally applied epoxy-bonded unidirectional carbon-fibre
plastic side strips. Three series of 1300 mm RC beams are considered: (1) a series of beams
having full strength in shear; (2) a series of beams under reinforced in shear; and a (3) series
of beams strengthened in shear. Side strips places either perpendicularly or diagonally to
beam’s longitudinal axis provided the external shear reinforcement. The beams were
instrumented and tested under four-point load conditions. O. Chaallal et al 1998 concluded
that the use of epoxy-bonded strips to restore or increase the load-carrying capacity in shear
of RC beams, substantially reduces shear cracking. RC beams strengthened by diagonal side
strips outperformed those strengthened with vertical side strips.
B.B. Adhikary et al 2004 tested shear strengthening characteristics of continuous
unidirectional flexible carbon-fibre polymer sheets bonded to RC beams. A total of tested
samples (150 mm X 200 mm X 2.600 mm) were eight concrete beams. Various sheet
configurations and layouts were studied to determine their effects on ultimate shear strength
40
of the beams. From the tests of B.B. Adhikary et al 2004, it was found that the externally
adhesive bonded flexible carbon-fibre sheets are effective in strengthening RC beams in
shear. Further, it was observed that the strength increases with the number of sheet layers and
the depth of sheets across the beam section. Among the various schemes of wrapping studied,
vertical U-wrap of sheet provided the most effective strengthening for concrete beam. Beam
strengthened using this scheme showed 119% increase in shear capacity as compared to the
control beam without any strengthening.
To investigate the shear behaviour of RC beams with externally bonded CFRP shear
reinforcement, 16 deep beams without steel shear reinforcement and 11 RC beams without
steel shear reinforcement were cast by Z. Zhang et al 2004 and 2005 respectively at the
concrete laboratory of the New Jersey Institute of Technology. After the beams were kept in
the curing room for 28 days, carbon-fibre strips and fabrics made by Sika Corp. were applied
on both sides of the beams at various orientations with respect to the axis of the beam. All
beams were tested on a 979 kN MTS testing machine. Results of Z. Zhang et al 2004 and
2005 demonstrate the feasibility of using an externally applied, epoxy-bonded CFRP system
to restore or increase the shear capacity of RC beams. The CFRP system can significantly
increase the serviceability, ductility, and ultimate shear strength of a concrete beam; thus,
restoring beam shear strength by using CFRP is a highly effective technique. An analysis and
design method for shear strengthening of externally bonded CFRP has been proposed by
Z.Zhang et al 2004 and 2005.
The study of C. Pellegrino et al 2002 is based on an experimental program carried out on 11
beams with and without transverse steel reinforcement, and with different amounts of FRP
shear strengthening. The test results provided some new insights into the complex failure
mechanisms that characterize the ultimate shear capacity of RC members with transverse
steel reinforcement and FRP sheets.
1.9 Numerical analysis
The Finite Element method is a numerical method which can approximate and solve complex
structural problems
to within acceptable boundaries. Finite element analysis was first
developed by the aircraft industry to predict the behaviour of metals forming for wings. The
ANSYS finite element program has been comprehensively developed to the extent that it
has applications across the whole engineering spectrum (Lawrance, 2002). In particular, civil
41
engineers are frequently interested in modelling materials such as steel and concrete, the
latter requiring complex methodology in its representation. As concrete is an orthotropic
material that exhibits nonlinear behaviour during loading, this behaviour is numerically
implemented in ANSYS (Barbosa and Riberio, 2004). A number of previous researchers have
used the finite element method to provide insight into the behaviour of the FRP- concrete
bonded joints, and CFRP strengthened RC beams.
Hemmaty et al 1993 considered a nonlinear adherence-shear law based on the experimental
studies between concrete and reinforcement in the modelling of reinforced concrete elements.
While modelling the adherence-shear relationship, they used a nonlinear spring/damper
element COMBIN39 (element in ANSYS) for their main modelling. Also, X.Z. Lu et al 2009
used COMBIN39 to model the interface between the FRP elements and the supports. The
study of X.Z.Lu et al 2009 presented a numerical study of the FRP stress distribution at debonding failure in U-jacketed or side-bonded beams using a rigorous FRP-to-concrete bond–
slip model and assuming several different crack width distributions. This element type
COMBIN39 was used in the present study.
Huyse et al 1994 presented a paper concerning analysis of reinforced concrete structures
using the ANSYS nonlinear concrete model. This paper considers the practical application of
nonlinear models in the analysis of reinforced concrete structures. The results of some
analyses performed using the reinforced concrete model of
ANSYS are presented and
discussed. The differences observed in the response of the same reinforced concrete beam, ,
caused by variations in a material model that is always basically the same, are emphasized.
The consequences of small changes in modelling are discussed and it is shown that
satisfactory results may be obtained from relatively simple and limited models.
Santhakumar et al 2004 presented a numerical study to simulate the behaviour of retrofitted
reinforced concrete beams strengthened with CFRP laminates using ANSYS. The effect of
retrofitting on un-cracked and pre-cracked reinforced concrete beams was studied, and the
behaviour of beams obtained from the numerical study showed good agreement with the
experimental data. There was no significant difference in behaviour between the un-cracked
and pre-cracked retrofitted beams
Al-Mahaidi et al 2001 studied the behaviour of three shear deficient T-beams strengthened
using web-bonded CFRP plate. The experimental results have shown that repairing the beams
42
with CFRP strips enhances their shear capacity. The increase in strength ranged between 68%
and 87%. Nonlinear finite element modelling and analysis with DIANA was used to
investigate the behaviour of these beams assuming plane stress conditions and perfect bond
between the concrete surface and the web bonded CFRP strips. Finite element analysis was
shown to be capable of predicting the ultimate strength, stiffness of the beams and strain
levels in CFRP plates with reasonable accuracy. The cracking patterns and crack inclinations
produced by the finite element model were also comparable to the patterns observed from
testing.
Fanning in 2001 presented nonlinear models for reinforced and post-tensioned concrete
beams. The finite element software used (ANSYS) included dedicated numerical models for
the nonlinear response of concrete under loading. These models usually included a smeared
crack analogy to account for the relatively poor tensile strength of concrete, a plasticity
algorithm to facilitate concrete crushing in compression regions and a method of specifying
the amount, the distribution and the orientation of any internal reinforcement. The numerical
model adopted by ANSYS was discussed in this paper. Appropriate numerical modelling
strategies were recommended and comparisons with experimental load-deflection responses
are discussed for ordinary reinforced concrete beams and for post-tensioned concrete Tbeams.
Finite element analysis (using ANSYS) will be used in this study where appropriate to
provide insight into various structural behavioural characteristics.
43