OF REINFORCED CONCRETE BEAMS
USING CARBON FIBRE REINFORCED
YASMEEN TALEB OBAIDAT
Copyright © 2010 by Structural Mechanics, LTH, Sweden.
Printed by Wallin & Dalholm Digital AB, Lund, Sweden, May, 2010 (Pl).
For information, address:
Division of Structural Mechanics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden.
Department of Construction Sciences
ISRN LUTVDG/TVSM--10/3070--SE (1-76)
OF REINFORCED CONCRETE BEAMS
USING CARBON FIBRE REINFORCED
YASMEEN TALEB OBAIDAT
Denna sida skall vara tom!
This thesis details experimental work and finite element simulations of reinforced concrete
beams retrofitted with carbon fibre reinforced polymer (CFRP). The objectives of this study
were to investigate the behaviour of retrofitted beams experimentally, develop a finite
element model describing the beams, verifying the finite element model against the
experimental results and finally investigating the influence of different parameters on the
behaviour of the retrofitted beams.
The experimental tests were performed to investigate the behaviour of beams designed in
such a way that either flexural or shear failure will be expected. The beams were loaded in
four-point bending until cracks developed. The beams were then unloaded and retrofitted
with CFRP. Finally the beams were loaded until failure. The ABAQUS program was used to
develop finite element models for simulation of the behaviour of beams. The concrete was
modelled using a plastic damage model and two models, a perfect bond model and a cohesive
model, were evaluated for the concrete-CFRP interface. From the analyses the load-
deflection relationships until failure, failure modes and crack patterns were obtained and
compared to the experimental results. The FEM results agreed well with the experiments
when using the cohesive model regarding failure mode and load capacity while the perfect
bond model was not able to represent the debonding failure mode. The results showed that
when the length of CFRP increases the load capacity of the beam increases both for shear and
flexural retrofitting. FEM results also showed that the width and stiffness of CFRP affect the
failure mode of retrofitted beams. The maximum load increases with increased width.
Increased CFRP stiffness increases the maximum load only up to a certain value of the
stiffness, and thereafter it decreases the maximum load.
The financial support provided by the Erasmus Mundus External Cooperation Window Lot 3
is greatly acknowledged.
My most grateful appreciation goes to Professor Ola Dahlblom for his knowledgeable
insight and motivating words.
I also feel so lucky and blessed to have Dr. Susanne Heyden as my co-advisor. To me, she
is a role model for living and working.
A special thanks to Dr. Kent Persson for his assistance in using the finite element software
(ABAQUS). I would also like to thank everyone from Structural Mechanics.
Finally, I would especially like to thank my parents, brothers, sisters and close friends for
their love, vote of confidence and support throughout this time. I would also like to share this
moment of happiness with my father and mother.
Yasmeen Taleb Obaidat
Lund in May 2010
1.2 Aim and Scope...............................................................................
Retrofitting of Reinforced Concrete Beams
2.1 FRP Material...................................................................................
2.2 Application in Retrofitting..............................................................
3.1 Experimental Work.........................................................................
3.2 Modelling Work..............................................................................
Summary of the Papers
Conclusions and Future Work
5.2 Future Work....................................................................................
Retrofitting of Reinforced Concrete Beams using Composite
The Effect of CFRP and CFRP/Concrete Interface Models when
Modelling Retrofitted RC Beams with FEM.
Nonlinear FE Modelling of Shear Behaviour in RC Beam Retrofitted
FEM Study on the Effect of CFRP Stiffness and Width on Retrofitted
Reinforced Concrete Beam Behaviour.
Reinforced concrete structures often have to face modification and improvement of their
performance during their service life. The main contributing factors are change in their use,
new design standards, deterioration due to corrosion in the steel caused by exposure to an
aggressive environment and accident events such as earthquakes.
In such circumstances there are two possible solutions: replacement or retrofitting. Full
structure replacement might have determinate disadvantages such as high costs for material
and labour, a stronger environmental impact and inconvenience due to interruption of the
function of the structure e.g. traffic problems. When possible, it is often better to repair or
upgrade the structure by retrofitting.
In the last decade, the development of strong epoxy glue has led to a technique which has
great potential in the field of upgrading structures. Basically the technique involves gluing
steel plates or fibre reinforced polymer (FRP) plates to the surface of the concrete. The plates
then act compositely with the concrete and help to carry the loads.
FRP can be convenient compared to steel for a number of reasons. These materials have
higher ultimate strength and lower density than steel. The installation is easier and temporary
support until the adhesive gains its strength is not required due to the low weight. They can be
formed on site into complicated shapes and can also be easily cut to length on site.
This work is a study of the behaviour of concrete beams retrofitted with carbon FRP
(CFRP), using experiments and finite element modelling.
1.2 Aim and Scope
The overall aim of the present study is to investigate and improve the understanding of the
behaviour of reinforced concrete beams retrofitted with CFRP. Experimental tests were
performed to investigate the behaviour of beams designed in such a way that either flexural or
shear failure will be expected. The beams were loaded in four-point bending until cracks
developed. The beams were then unloaded and retrofitted with CFRP. Finally the beams were
loaded until failure. The ABAQUS program was used to develop finite element models for
simulation of the behaviour of beams. From the analyses the load-deflection relationships
until failure, failure modes and crack patterns were obtained and compared to the
experimental results. The models were then used to study how different parameters affect
retrofitted beam behaviour and investigate how CFRP should be applied in order to get
maximum increase of load capacity.
2 Retrofitting of Reinforced Concrete Beams
2.1 FRP Material
Fibre reinforced polymer (FRP) composites consist of high strength fibres embedded in a
matrix of polymer resin as shown in Figure 1.
Figure 1: A schematic diagram showing a typical unidirectional FRP plate.
Fibres typically used in FRP are glass, carbon and aramid. Typical values for properties of
the fibres are given in Table 1. These fibres are all linear elastic up to failure, with no
significant yielding compared to steel. The primary functions of the matrix in a composite are
to transfer stress between the fibres, to provide a barrier against the environment and to
protect the surface of the fibres from mechanical abrasion. Typical properties for epoxy are
given in Table 1.
The mechanical properties of composites are dependent on the fibre properties, matrix
properties, fibre-matrix bond properties, fibre amount and fibre orientation. A composite with
all fibres in one direction is designated as unidirectional. If the fibres are woven, or oriented
in many directions, the composite is bi- or multidirectional. Since it is mainly the fibres that
provide stiffness and strength composites are often anisotropic with high stiffness in the fibre
direction(s). In strengthening applications, unidirectional composites are predominantly used,
Figure 1. The approximate stiffness and strength of a unidirectional CFRP with a 65% volume
fraction of carbon fibre is given in Table 1. As a comparison the corresponding properties for
steel are also given.
Adhesives are used to attach the composites to other surfaces such as concrete. The most
common adhesives are acrylics, epoxies and urethanes. Epoxies provide high bond strength
with high temperature resistance, whereas acrylics provide moderate temperature resistance
with good strength and rapid curing. Several considerations are involved in applying
adhesives effectively. Careful surface preparation such as removing the cement paste,
grinding the surface by using a disc sander, removing the dust generated by surface grinding
using an air blower and carful curing are critical to bond performance.
Table 1. Typical strength and stiffness values for materials used in retrofitting, .
Material Tensile strength
2.2 Application in Retrofitting
For structural applications, FRP is mainly used in two areas. The first area involves the use of
FRP bars instead of steel reinforcing bars or pre-stressing strands in concrete structures. The
other application, which is the focus of this thesis, is to strengthen structurally deficient
structural members with external application of FRP.
Retrofitting with adhesive bonded FRP has been established around the world as an
effective method applicable to many types of concrete structural elements such as columns,
beams, slabs and walls. As an example, a highway RC bridge slab in China was retrofitted
using CFRP as shown in Figure 2(a) and a column in India was retrofitted using glass FRP
wrapping as shown in Figure 2(b), .
FRP plates can be bonded to reinforced concrete structural elements using various
techniques such as external bonding, wrapping and near surface mounting. Retrofitting with
externally bonded FRP has been shown to be applicable to many types of RC structural
elements. FRP plates or sheets may be glued to the tension side of a structural member to
provide flexural strength or glued to the web side of a beam to provide shear strength. FRP
sheets can also be wrapped around a beam to provide shear strength and be wrapped around a
column to provide confinement and thus increase the strength and ductility. Near surface
mounting consists of sawing a longitudinal groove in a concrete member, applying a bonding
material in the groove and inserting an FRP bar or strip.
Modulus of elasticity
Modulus of elasticity to
density ratio (Mm2/s2)
(a) Flexural strengthening of a highway RC bridge slab in China.
(b) Seismic retrofit of supporting columns for a cryogenic tank in Gujarat, India.
Figure 2. Examples of use of FRP in existing structures, .
3 Related Research
3.1 Experimental Work
Investigation of the behaviour of FRP retrofitted reinforced concrete structures has in the last
decade become a very important research field. In terms of experimental application several
studies were performed to study the behaviour of retrofitted beams and how various
parameters influence the behaviour.
The effect of number of layers of CFRP on the behaviour of a strengthened RC beam was
investigated by Toutanji et al. . They tested simply supported beams with different
numbers of CFRP layers. The specimens were subjected to a four-point bending test. The
results showed that the load carrying capacity increases with an increased number of layers of
carbon fibre sheets.
Investigation of the effect of internal reinforcement ratio on the behaviour of strengthened
beams has been performed by Esfahani et al. . Specimens with different internal steel ratio
were strengthened in flexure by CFRP sheets. The authors reported that the flexural strength
and stiffness of the strengthened beams increased compared to the control specimens. With a
large reinforcing ratio, they also found that failure of the strengthened beams occurred in
either interfacial debonding induced by a flexural shear crack or interfacial debonding
induced by a flexural crack.
A test programme on retrofitted beams with shear deficiencies was done by Khalifa et al.
. The experimental results indicated that the contribution of externally bonded CFRP to the
shear capacity of continuous RC beams is significant.
There are three main categories of failure in concrete structures retrofitted with FRP that
have been observed experimentally, Esfahani et al. , Ashour et al. , Garden and
Hollaway, , Smith and Teng, . The first and second type consist of failure modes where
the composite action between concrete and FRP is maintained. Typically, in the first failure
mode, the steel reinforcement yields, followed by rupture of CFRP as shown in Figure 3(a). In
the second type there is failure in the concrete. This type occurs either due to crushing of
concrete before or after yielding of tensile steel without any damage to the FRP laminate,
Figure 3(b), or due to an inclined shear crack at the end of the plate, Figure 3(c). In the third
type, the failure modes involving loss of composite action are included. The most recognized
failure modes within this group are debonding modes. In such a case, the external
reinforcement plates no longer contribute to the beam strength, leading to a brittle failure if no
stress redistribution from the laminate to the interior steel reinforcement occurs. Figures 3(d)-
(g) show failure modes of the third type for RC beams retrofitted with FRP. In Figure 3(d),
the failure starts at the end of the plate due to the stress concentration and ends up with
debonding propagation inwards. Stresses at this location are essentially shear stress but due to
small but non-zero bending stiffness of the laminate, normal stress can arise. For the case in
Figure 3(e) the entire concrete cover is separated. This failure mode usually results from the
formation of a crack at or near the end of the plate, due to the interfacial shear and normal
stress concentrations. Once a crack occurs in the concrete near the plate end, the crack will
propagate to the level of tensile reinforcement and extend horizontally along the bottom of the
tension steel reinforcement. With increasing external load, the horizontal crack may propagate
to cause the concrete cover to separate with the FRP plate. In Figures 3(f) and (g) the failure is
caused by crack propagation in the concrete parallel to the bonded plate and adjacent to the
adhesive to concrete interface, starting from the critically stressed portions towards one of the
ends of the plate. It is believed to be the result of high interfacial shear and normal stresses
concentrated at a crack along the beam. Also mid span debonding may take concrete cover
(a) CFRP rupture.
Loss of composite action
(d) Plate interfacial debonding.
(e) Concrete cover separation.
(b) Compression failure.
(f) Mid span debonding initiated by a flexural crack.
(c) Shear failure mode.
(g) Mid span debonding initiated by a flexural-shear
Figure 3: Failure modes in beam retrofitted in flexure.
Crack initiated in concrete
Daigonal shear crack
at plate end
3.2 Modelling Work
Many models currently exist for reinforced concrete retrofitted with CFRP. Several different
approaches have been considered. Some models use simple material models and are restricted
to 2D and others use nonlinear elasticity or plasticity models to capture the more complicated
effects and predict the behaviour of retrofitted reinforced concrete in a general sense. Each
approach has its strengths, complexity level, and complications.
A 2D model was developed by Supaviriyakit et al.  for analyses of RC beams
strengthened with externally bonded FRP plates. The RC element considered the effect of
crack and reinforcing steel as being smeared over the entire element. Perfect compatibility
between cracked concrete and reinforcing steel was assumed. The FRP plate was modelled as
an elastic brittle element. As the epoxy is usually stronger than the concrete, perfect bond
between FRP and concrete was assumed.
The orthotropic properties of FRP were taken into consideration by Hu et al.  in
modelling the behaviour of a retrofitted beam. They assumed perfect bond between the CFRP
plate and concrete.
The effect of anchorage length of near surface mounted reinforcement (NSMR) was
studied by Lundqvist et al. . They conducted numerical analyses of three different CFRP
strengthening techniques to find a critical anchorage length, where a longer anchorage length
does not contribute to the load bearing capacity. They assumed perfect bond between the plate
and concrete. The results showed that a critical anchorage length exists for plates and sheets
as well as for NSMR.
Bond is a critical parameter in strengthening systems as it provides the shear transfer
between concrete and FRP necessary for composite action. Lim et al.  presented a
numerical model to simulate the interface fracture behaviour of concrete strengthened with
external composite plates. They adapted the fictitious crack model,  with a nonlinear
fracture mechanics concept to describe the constitutive relationship at the element level. They
found that the interface material properties had significant influence on the interface stress
distributions. Furthermore, Camata et al. , investigated RC members strengthened in
flexure by FRP plates. The model considers the actual crack patterns observed in the test
using a smeared and interface crack model. The results show that debonding and concrete
cover splitting failure mode always occur by crack propagation inside the concrete. A FE
analysis was performed by Neale et al. , to simulate the nonlinear behaviour of shear
strengthened beams and two-way slabs. A plasticity–based concrete constitutive model was
used. An elastic–plastic response was assumed for the steel and the CFRP was modelled as
linear elastic until failure. A bond slip model was incorporated to the analysis to simulate the
FRP concrete interface.
Even though extensive work has been done on the use of CFRP laminates in retrofitting there
is a need for further refinement of models and further parameter studies. From the above
literature review, it can be concluded that the interface zone has been modelled with linear or
in 2D with non-linear models. The present study comprises a 3D cohesive model which is
believed to better reflect the behaviour of retrofitted beams.
In practical use of retrofitting, the structure is often damaged at the time of retrofitting. To
take account of this, the beams in the experimental study as well as in the simulations were
pre-cracked before retrofitting. This has not been done before in connection with retrofitting
in shear or investigation of influence of CFRP length.
Researchers have reported on different failure modes. It is important to understand under
what circumstances a certain failure mode will occur. To contribute to this understanding, a
parametric study of the influence of CFRP stiffness and width is included in this simulation
4 Summary of the Papers
Paper A Obaidat, Y.T., Heyden, S., Dahlblom, O., Abu-Farsakh, G., and Abdel-Jawad,
Y.: Retrofitting of reinforced concrete beams using composite laminates.
Submitted to Construction & Building Materials, 2010.
Summary: This paper presents the results of an experimental study to
investigate the behaviour of structurally damaged full-scale reinforced
concrete beams retrofitted with CFRP laminates in shear or in flexure. The
main variables considered were the internal reinforcement ratio, position of
retrofitting and the length of CFRP. The experimental results, generally,
indicate that beams retrofitted in shear and flexure by using CFRP laminates
are structurally efficient and are restored to stiffness and strength values
nearly equal to or greater than those of the control beams. It was found that
the efficiency of the strengthening technique by CFRP in flexure varied
depending on the length. The main failure mode in the experimental work was
plate debonding in retrofitted beams.
Obaidat,Y.T., Heyden, S. and Dahlblom, O.: The Effect of CFRP and CFRP/
Concrete Interface Models when Modelling Retrofitted RC Beams with FEM.
Published in Composite Structures, 2010; 92: 1391–1398.
Summary: This paper presents a finite element analysis which is validated
against laboratory tests of eight beams. All beams had the same rectangular
cross-section geometry and were loaded under four point bending, but differed
in the length of the carbon fibre reinforced plastic (CFRP) plate. The
commercial numerical analysis tool Abaqus was used, and different material
models were evaluated with respect to their ability to describe the behaviour of
the beams. Linear elastic isotropic and orthotropic models were used for the
CFRP and a perfect bond model and a cohesive bond model was used for the
concrete–CFRP interface. A plastic damage model was used for the concrete.
The analyses results show good agreement with the experimental data
regarding load–displacement response, crack pattern and debonding failure
mode when the cohesive bond model is used. The perfect bond model failed to
capture the softening behaviour of the beams. There is no significant difference
between the elastic isotropic and orthotropic models for the CFRP.
Paper C Obaidat,Y.T., Dahlblom, O. and Heyden, S.: Nonlinear FE modelling of shear
behaviour in RC beam retrofitted with CFRP. Computational Modelling of
Concrete Structures conference (EURO-C 2010), 2010.
Summary: To examine numerically the behaviour of beams retrofitted in shear
and the effects of length and orientation of CFRP in the beams, in this paper a
nonlinear 3-D numerical model has been developed using the ABAQUS finite
element program. Two models were used to represent the interface between
CFRP and concrete, a perfect bond model and a cohesive model. Validation of
the model was performed using data obtained from an experimental study. The
results showed that the cohesive model is able to simulate the composite
behaviour of reinforced concrete beams retrofitted by CFRP in shear correctly.
The model is then used to examine the influence of length and orientation of
CFRP. It is shown that the length of CFRP and the orientation strongly
influence on the behaviour of the retrofitted beams.
Paper D Obaidat,Y.T., Heyden, S. and Dahlblom, O.: FEM Study on the Effect of
CFRP Stiffness and Width on Retrofitted Reinforced Concrete Beam
Behaviour. Submitted to Composite Structures, 2010.
Summary: The finite element program ABAQUS was used to study the effect
of different parameters on the behaviour of an RC beam retrofitted with carbon
fibre reinforced polymer (CFRP). These parameters were the stiffness and
width of the CFRP. A linear elastic isotropic model was used for the CFRP and
a cohesive bond model was used for the concrete–CFRP interface. A plastic
damage model was used for the concrete. The material models were validated
against experimental work and the results showed good agreement between
experimental data and numerical results. Observations indicate that the CFRP
width to beam width ratio and CFRP stiffness influence the type of failure
mode of a beam retrofitted with CFRP. For small width and for large value of
stiffness debonding will occur before steel yielding due to stress concentration
at the end of the plate. For small values of stiffness rupture of CFRP will occur.
It was found that when the stiffness of CFRP increases the maximum load
increases until a certain value of stiffness, then the maximum load decreases
again. Simulations also show that the external load at steel yielding and the
maximum load increase with the CFRP width.
5 Conclusions and Future Work
The finite element method is a useful tool for improving the understanding of the behaviour of
reinforced concrete beams retrofitted with CFRP. Experimental tests are needed to provide
input data to the model and for the purpose of verification of simulation results. When the
model has been validated it can be used for parameter studies to clarify the influence of
The plastic damage model used for concrete and the elastic-perfectly plastic model used
for steel proved to be able to model the reinforced concrete, as was shown by comparing
simulations to tests of control beams. A uni-axial CFRP is essentially an orthotropic material,
but simulations showed that for cases where the principal stress direction coincides with the
fibre direction, an isotropic model could be used with good accuracy.
Since debonding plays an important role as a limiting phenomenon for retrofitted beams, a
perfect bond model is not suitable for the CFRP-concrete interface, at least not if the intention
is to study the fracture behaviour. The cohesive bond model, on the other hand, can capture
the debonding and simulations using this model showed good agreement with experiments
concerning stiffness, maximum load, crack patterns and failure mode.
Experiments and simulations showed that retrofitting can increase load capacity and
stiffness and the effect is larger for retrofitting in flexure than in shear. On the other hand,
simulations showed that an increase in the amount of CFRP will in some cases decrease the
maximum load. This means that understanding of the behaviour of a retrofitted structure is
very important since an unsuitable arrangement of CFRP can actually make the situation
Experiments and simulations showed that it is important to provide a sufficient anchorage
length outside the region of maximum stress to obtain full effect from the retrofitting. For
retrofitting in shear, it was also shown that the best effect is obtained it the fibre direction of
the CFRP coincides with the principal tensile stress direction.
Simulations showed that several different failure modes can occur, depending on the
geometry and stiffness properties of the CFRP. Many of the failure modes involve debonding,
associated with a stress concentration in the concrete-CFRP interface zone. An important
criterion when designing the CFRP arrangement is thus to avoid stress concentrations as far as
is possible. A high stiffness and low width of the CFRP will give a pronounced stress
concentration at the plate end. This should definitely be avoided since it will cause debonding
before steel yielding and failure will occur at low load.
A wider CFRP plate will (for constant stiffness) always give a higher maximum load,
while increased CFRP stiffness will increase the maximum load only up to a certain value of
the stiffness, and thereafter it will decrease the maximum load.
5.2 Future Work
Since debonding is such an important phenomenon when retrofitting with CFRP is concerned,
more attention should be given to the behaviour of the concrete-CFRP bond. More
experimental data on the micro-level is needed to provide the information needed for further
developing the material model used for the interface. Another interesting area when it comes
to developing the model is usage of the extended finite element method (XFEM) to represent
the cracks in the concrete.
A parametric study in this work took into consideration the effect of varying the stiffness
properties and geometry of the CFRP on the type of failure and stress concentrations. It would
also be interesting to study the effect of beam stiffness properties and geometry on the
behaviour of a beam, stress concentrations and type of failure.
This study showed that there is a stress concentration at the end of the plate causing
debonding failure. It would be interesting to study different approaches to avoid this
phenomenon. Examples are tapering at end of plate and external CFRP wrapping (stirrup) for
reducing the stress concentration at the end of the plate.
Previous experimental programmes have shown that the CFRP plate retrofitting system
enhances the capacity of deficient concrete beams. There are, however, many environmental
factors involved during the life span of a retrofitted structure that needs more attention. They
include seasonal temperature variation, degradation of material properties, creep and so on.
The durability of CFRP reinforced beams under these conditions should be investigated.
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Retrofitting Of Reinforced Concrete Beams
Using Composite Laminates
Yasmeen Taleb Obaidat, Susanne Heyden, Ola Dahlblom,
Ghazi Abu-Farsakh and Yahia Abdel-Jawad
Submitted to Construction & Building Materials
Retrofitting of Reinforced Concrete Beams using Composite Laminates
Yasmeen Taleb Obaidata,, Susanne Heydena, Ola Dahlbloma, Ghazi Abu- Farsakhb and Yahia
a Division of Structural Mechanics, Lund University, Lund, Sweden
b Jordan University of Science and Technology, Irbid, Jordan
This paper presents the results of an experimental study to investigate the behaviour of
structurally damaged full-scale reinforced concrete beams retrofitted with CFRP laminates
in shear or in flexure. The main variables considered were the internal reinforcement ratio,
position of retrofitting and the length of CFRP. The experimental results, generally, indicate
that beams retrofitted in shear and flexure by using CFRP laminates are structurally
efficient and are restored to stiffness and strength values nearly equal to or greater than
those of the control beams. It was found that the efficiency of the strengthening technique by
CFRP in flexure varied depending on the length. The main failure mode in the experimental
work was plate debonding in retrofitted beams.
Keywords: Carbon Fibre Reinforced Plastic (CFRP), Strengthening, Retrofitting,
Laminate, Reinforced Concrete Beam, Flexure, Debonding.
There are many existing structures, which do not fulfill specified requirements. This may
for example be due to upgrading of the design standards, increased loading, corrosion of
the reinforcement bars, construction errors or accidents such as earthquakes. To remedy
for insufficient capacity the structures need to be replaced or retrofitted.
Different types of strengthening materials are available in the market. Examples of
these are ferrocement, steel plates and fibre reinforced polymer (FRP) laminate.
Retrofitting of reinforced concrete (RC) structures by bonding external steel and FRP
plates or sheets is an effective method for improving structural performance under both
service and ultimate load conditions. It is both environmentally and economically
preferable to repair or strengthen structures rather than to replace them totally. With the
E-mail address: Yasmeen.Obaidat@construction.lth.se
development of structurally effective adhesives, there have been marked increases in
strengthening using steel plates and FRP laminates. FRP has become increasingly attractive
compared to steel plates due to its advantageous low weight, high stiffness and strength to
weight ratio, corrosion resistance, lower maintenance costs and faster installation time.
Earlier research has demonstrated that the addition of carbon fibre reinforced polymer
(CFRP) laminate to reinforced concrete beams can increase stiffness and maximum load of
the beams. In a study by Toutanj et al.  beams retrofitted with CFRP laminates showed an
increased maximum load up to 170 % as compared to control beams. Another study by
Kachlakev and McCurry  shows an increase of 150 % when beams were strengthened in
both flexure and shear with CFRP and glass FRP laminates respectively. Other studies have
also been conducted by David et al. , Shahawy et al. , Khalifa and Nanni , Shehata et
al. , Khalifa et al.  in an attempt to quantify the flexural and shear strengthening
enhancements offered by the externally bonded CFRP laminates. Ferreira et al.  showed
that when a beam is strengthened with CFRP sheets the stiffness increase and the tension
cracking is delayed to higher loads, and Karunasena et al.  showed that an externally
bonded composite, of either CFRP or GFRP materials, improved the moment capacity of
deteriorated concrete beams.
In spite of many studies of the behaviour of retrofitted beams, the effect of the length of
CFRP on the behaviour of pre-cracked beams retrofitted by CFRP in flexure and the
behaviour of retrofitted beams in shear after preloading have not been explored. This study
examined experimentally the flexural and the shear behaviours of RC-beams retrofitted or
strengthened with CFRP laminates. To accomplish this, laboratory testing was conducted on
full-size beams. The main variables in this study are the reinforcement steel ratio and CFRP
2. Material and methods
The experimental work undertaken in this study consisted of four point bending tests of
twelve simply supported RC beams. In addition, material tests were carried out to determine
the mechanical properties of the concrete, reinforcement steel and CFRP which were used in
constructing the beams.
An ordinary strength concrete mix was prepared using Ordinary Portland cement (Type I).
The aggregate used consisted of coarse limestone, crushed limestone and silica sand. The
gradation of coarse and fine particles met the ASTM specification (C136) .
The concrete mix was designed according to ACI method 211 , to have slump 50 mm
and 28 days cylinder compressive strength of 30 MPa. The maximum aggregate size was 10
mm and the free water cement ratio was 0.55. The concrete mix is shown in Table 1.
Table 1 Concrete mix proportions, kg per m3 concrete.
Coarse Aggregate(5 mm ≤ d ≤ 10 mm)
Fine Aggregate (d < 5mm)
The mean compressive strength was determined in compressive tests 28 days after casting
of three 300 mm by 150 mm diameter cylinders. The average concrete compressive strength
was 29 MPa. The failure of a specimen is shown in Fig. 1.
Fig. 1. Concrete specimen in cylinder compression test.
The steel bars used for longitudinal reinforcement were tested in uniaxial tension. Details of
the material properties for the reinforcing steel are given in Table 2. The average elastic
modulus was 209 GPa. The stirrups were fabricated using steel with nominal diameter 8 mm.
This steel was not tested in the experimental work.
Table. 2 .Mechanical properties of steel bars.
10 211 520
12 207 495
18 209 512
The CFRP used in this study was supplied by FOSROC . The laminate had a thickness
of 1.2 mm, a width of 50 mm and the elastic modulus 165 GPa according to the manufacturer.
The plates were supplied in a roll form as shown in Fig. 2. Three specimens were prepared
Elastic Modulus Yield Stress Ultimate Stress
and tested using a tension testing machine at a rate of 2 mm/min, to determine the ultimate
stress. The mean ultimate stress of the three specimens was 2640 MPa, with the strain
corresponding to the failure load being 0.0154. This test also showed that the behaviour of the
CFRP is linear elastic up to failure. The failure of a specimen is shown in Fig. 3.
Fig. 2. Roll of CFRP plate.
Fig. 3. The failure of a CFRP laminate specimen.
The material used for the bonding of CFRP plates to the concrete was an epoxy adhesive
with compressive strength equal to 40 MPa according to the manufacturer and it was applied
with a total thickness equal to 1 mm.
2.2 Experimental Procedure
Twelve beams were tested under four point bending after curing six months. The beams were
divided into two groups. For group RF, focus was on flexural behaviour, and for group RS
focus was on shear behaviour.
For group RF, two beams were used as control beams. The other six were preloaded until
flexural cracks appeared and then retrofitted with CFRP. Three different lengths of CFRP
were used, with two nominally equal beams for each length. Finally, the retrofitted beams
were loaded until failure and the results were compared with the control beams.
For group RS, two beams were used as control beams, and the other two were preloaded
until shear cracks appeared and then retrofitted and finally tested to failure.
2.2.1 Manufacture of beams
The beams had a rectangular cross-section of 150 mm width and 300 mm height, and were
1960 mm long. The beams in group RF were designed to have insufficient flexural strength to
obtain a pure flexural failure. They had tension reinforcement (212), compression
reinforcement (210) and the steel bars were tied together with 8 mm stirrups c/c 100 mm
along the beam, see Fig. 4(a).
The beams in group RS had the same geometry, but were cast with a reduced shear
reinforcement ratio and a larger longitudinal reinforcement ratio in order to obtain pure
diagonal shear cracks without development of flexural cracks. The beams had tension
reinforcement (218), compression reinforcement (210) and were tied with 8 mm stirrups
c/c 400 mm along the beam as shown in Fig. 4. All beams were designed according to .
In all the beams, the clear concrete cover to the main flexural reinforcement was set to 25
mm. This cover was expected to avoid splitting bond failure. Geometry and reinforcement are
shown in Fig. 4(b). The beams cured for six months before they were tested.
(a) Beams in group RF. (b) Beams in group RS.
Fig. 4. Geometry and reinforcement of beams in groups RF and RS.
2.2.2 Testing of control beams
The beams were tested in four point bending. This load case was chosen because it gives
constant maximum moment and zero shear in the section between the loads, and constant
maximum shear force between support and load. The moment was linearly varying between
supports and load. The span between the supports was 1560 mm and the load was applied at
points dividing the length into three equal parts as shown in Fig. 5. Steel plates were used
under the loads to distribute the load over the width of the beam. The testing equipment was a
testing machine of 400 kN capacity jack. A linearly variable differential transducer, LVDT,
was used to measure the deflection at midspan, as shown in Fig. 5. Fig. 6 shows the test setup
of a beam.
Fig. 5. Supports, loading and position of LVDT.
Fig. 6. Test setup.
Deflections and load were recorded during the test. The first crack appeared in the control
beams of group RF at P=60 kN and flexural cracks had formed along the beam at P=95 kN.
For the beams in group RS, shear cracks were initiated in both shear spans. The first shear
crack was the critical crack in the beam and it started to develop at P=120 kN. The load in this
group is higher than for those in group RF due to intensive flexural reinforcement. A steel
ratio around the balanced steel ratio was used.
2.2.3 Preloading of beams
In order to simulate damage, the beams were preloaded before retrofitting. The preloading
was done with the same setup as described in 2.2.2. First the beams were loaded until cracks
appeared; the load was 95 kN for beams in group RF and for beams in group RS the first
shear crack initiated at a load of 120 kN, as determined in the control beams test. Then the
load was released.
2.2.4 Retrofitting of beams
The beams in group RF were removed from the test machine and turned over to retrofit them
with CFRP as shown in Fig. 7. The soffit of the beam was retrofitted with CFRP laminates 50
mm wide and of three different lengths, 1560 mm (series RF1), 1040 mm (series RF2) and
520 mm (series RF3) as shown in Fig. 7. The laminate was positioned at the centre of the
beam width as shown in Fig.8. The laminate was applied when the beams were subjected to a
negative moment corresponding to their own dead weight. This implies a small prestressing
effect which could be obtained by a jack in the case of on-site repair.
(a) Test series RF1
(b) Test series RF2
(c) Test series RF3
Fig. 7. Lengths of CFRP laminate in test series RF1, RF2 and RF3.
Fig. 8. Application of CFRP laminate for beams in group RF.
For the beams in group RS, the web of the beam was retrofitted with CFRP laminates 50
mm wide and 300 mm long on the two faces of beams as shown in Fig. 9 and Fig. 10. The
same procedure was used as for the beams in group RF, but the position of the laminate was
520 mm 100 mm
Fig. 9. The arrangement of the CFRP laminate in group RS.
Fig. 10. CFRP laminate in test series RS1.
In order to ensure correct application of the external strengthening materials, it was
considered necessary to improve the concrete surface characteristics on the contact areas to be
bonded. The surface preparation was done according to the manufacturer’s instruction . It
included removing the cement paste, grinding the surface by using a disc sander, and
removing the dust generated by surface grinding using an air blower. After that the epoxy
adhesive was applied to both the CFRP and the concrete surface. Finally the CFRP plates
were applied to the beams.
2.2.5 Testing of retrofitted beams
After 7 days curing at ambient temperature the beams were retested under four point
bending until failure occurred. The tests were performed using the same setup as
described in section 2.2.2.
3.1 Beams in group RF
3.1.1 Control Beams
The load versus midspan deflection curves for the two control beams are shown in Fig. 11.
The beams behave in a ductile manner and gives large deflection before the final failure. This
is the typical behaviour of an under-reinforced RC member . The difference between the
two specimens is rather small, and the mean value, also indicated in the figure, will be used.
Fig. 11. Comparison between individual control beams in group RF.
The curve includes a linear response up to the load 22 kN. The appearance of a crack was
first noted at load 60 kN. The midspan deflection curve illustrates the nonlinearities at
Control beam 1
Control beam 2
cracking of the concrete. After 95 kN load flexural cracks formed and widened as loading
increased. The maximum load was 118 kN as shown in the figure. After maximum load, the
cracks did not grow in length for the remainder of the test but the flexural cracks in the
constant moment region widened. The failure of a control beam is shown in Fig 12.
Fig. 12. Flexural failure for control beam.
3.1.2 Retrofitted Beams
The load–deflection curves for the individual beams in series RF1, RF2 and RF3 are
shown in Fig. 13. The results from the two nominally equal beams in each series are close,
which indicates that the retrofitting was performed in a well-defined manner. The mean
curve will be used in the following.
The mean load–deflection curves for the retrofitted beams and for the control beams
are shown in Fig. 14. As shown in the figure the stiffness of all beams at small load is
almost the same. From a load around 60 kN -cracking stage- the stiffness of the control
beam decreases notably due to cracking. The decrease in stiffness is smaller for the
retrofitted beams since the CFRP prevents cracks to develop and widen. The longer the
CFRP the stiffer the beam. This is probably because the longer CFRP strips have a full
anchorage length outside the maximum moment region and are hence more efficient in the
cracking zone. Some contribution to the stiffness may also be due to the stiffening of the
beam caused by the CFRP outside the cracking region.
It should be noted that if a control beam would be loaded until cracking, unloaded, and
then subjected to load again, the stiffness would be somewhat lower the second time due
to the damage in the beam. This means that even if the curve of series RF3 is similar to
that of the control beam the CFRP has improved the beam and restored the stiffness to the
level of the control beam.
Fig. 13. Comparison between load-deflection curves for individual retrofitted beams in group RF. (a) series RF1,
(b) series RF2 and (c) series RF3.
Fig. 14. Comparison between mean load-deflection curves for retrofitted beams and control beam in group RF.
The curves reveal that the strengthening process has significantly increased the
maximum load in series RF1 and RF2. The maximum load in series RF1 was 166 kN,
which is a more than 33 % increase compared to the control beam. The maximum load for
series RF2 was 142 kN, 20 % higher than for the control beam. For series RF3 the
maximum load was 128 kN which corresponds to a 7 % increase in maximum load.
All beams experienced a brittle failure mechanism, however in this case sudden
debonding of the CFRP plate from the concrete occurred without concrete splitting. This
failure was due to high shear stress occurring at the ends of the CFR. The properties of the
adhesive are probably important in relation to the debonding failure. A lower stiffness and
higher fracture energy will probably weaken the tendency of debonding. For RF2 and RF3
debonding occurred earlier than for RF1. The main reason leading to this is that RF2 and RF3
do not have a full anchorage length outside the maximum moment region, hence higher shear
stress concentration will occur compared to for the longest CFRP, Fig. 15. The crack
propagation and the final crack pattern of the beam are greatly different from that of the
control beam. The control beam had few flexural cracks with large width, and the
retrofitted beam had many flexural cracks with smaller width. This indicates that the
propagation of cracks was confined by the CFRP laminates. In addition, the cracks in
series RF1 were fewer and had smaller width than in the other retrofitted beams.
Fig. 15. Debonding failures in group RF.
The results indicate that the externally bonded CFRP has increased the stiffness and
maximum load of the beam. In addition, the crack width and the deflection have
decreased. The efficiency of the strengthening by CFRP in flexure varied depending on
the length of the CFRP.
3.2 Beams in group RS
3.2 1 Control Beam
The load versus midspan deflection curves for the control beams are shown in Fig. 16. It is
clear that the beam failed in a brittle manner and has a low energy absorption before failure.
This is the typical behaviour of an ordinary RC member with insufficient shear steel . The
difference between the two specimens is rather small, and the mean value, also indicated in
the figure, will be used.
Fig. 16. Comparison between load-deflection curves for individual control beams in group RS.
The curve has linear response until 60 kN. The ultimate load of the control beams was 220
kN. The cracking patterns consist of a pure diagonal shear crack in the constant shear spans,
Fig. 17. This is due to the reduced amount of shear reinforcement.
Fig. 17. Shear failure for control beam.
3.2.2 Retrofitted beams
A debonding failure occurred for all beams also in this group. The debonding mode is due to
cracking of the concrete underneath the CFRP plate. The beam after failure appears in Fig. 18,
which clearly shows the shear crack cross the bond area in the concrete.
Control beam 1
Control beam 2
The load-deflection curves for the two beams and the mean value are shown in Fig.19.
Also here, the variation between the individual beams was small.
The load versus midspan deflection curve for the mean value of the retrofitted beams is
compared with the response of the control beams in Fig. 20.
The control beam shows more softening due to crack propagation, while in the retrofitted
beam, the cracks are arrested by the CFRP, and this makes the curve of the retrofitted beam
somewhat straighter than the control beam curve. The maximum load of the strengthened
beam was 270 kN. It may be observed that strengthening increases the maximum load by over
23 %, when compared with the control beam.
Fig. 18. Debonding and shear failures in group RS.
Fig. 19. Comparison between load-deflection curves for individual retrofitted beams in group RS.
Fig. 20. Comparison between mean load-deflection curves for retrofitted beams and control beam in group RS.
4. Concluding and remarks
The paper investigated the flexural and shear behaviour of reinforced beams retrofitted with
CFRP after preloading. The following conclusions are drawn from this experimental study:
The stiffness of the CFRP-retrofitted beams is increased compared to that of the
Employing externally bonded CFRP plates resulted in an increase in maximum load.
The increase in maximum load of the retrofitted specimens reached values of about 23
% for retrofitting in shear and between 7% and 33 % for retrofitting in flexure.
Moreover, retrofitting shifts the mode of failure to be brittle.
The crack width for the retrofitted beams is decreased compared to the control beams.
Experimental results showed that increasing the CFRP plate length in flexural
retrofitting can make the CFRP more effective for concrete repair and strengthening.
This means that insufficient strengthening lengths do not produce the intended
The results showed that the main failure mode was plate debonding which reduces the
efficiency of retrofitting.
Based on this conclusion deeper studies should be performed to investigate the behaviour
of the interface layer between the CFRP and concrete. Also numerical work should be done to
predict the behaviour of retrofitted beams and to evaluate the influence of different parameters
on the overall behaviour of the beams.
 Toutanji, H., Zhao, L., and Zhang, Y., "Flexural behaviour of reinforced concrete
beams externally strengthened with CFRP sheets bonded with an inorganic matrix".
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retrofitted for shear and flexural with FRP laminates", Composites 2000; 31: 445-452.
 David, E, Djelal, C, and Buyle-Bodin, F. "Repair And Strengthening Of Reinforced
Concrete Beams Using Composite Materials", 2nd Int. PhD Symposium in Civil
Engineering 1998 Budapest.
 Shahawy M. A., Arockiasamy T M., Beitelmant T., and Sowrirajan R. "Reinforced
concrete rectangular beams strengthened with CFRP laminates", Composites: 1996; 27:
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shear deficiencies using CFRP composites". Construction and Building Materials 2002;
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beams in flexure and shear using CFRP laminate.", Fiber-reinforced Plastic for
Reinforced Concrete Structure 2001; 1: 97-106.
 Khalifa, A., Tumialan, G., Nanni, A. and Belarbi, A., "Shear Strengthening of
Continuous RC Beams Using Externally Bonded CFRP Sheets,", American Concrete
Institute, Proc., 4th International Symposium on FRP for Reinforcement of Concrete
Structures (FRPRCS4), Baltimore, MD, Nov. 1999: 995-1008.
 Ferreira, A. J. M. "On the shear-deformation theories for the analysis of concrete shells
reinforced with external composite laminates", Strength of Materials 2003; 35(2): 128-
 Karunasena, W., Hardeo, P., Bosnich, G. Rehabilitation of concrete beams by externally
bonding fiber composite reinforcement. In Composite Systems: Macrocomposites,
Microcomposites, Nanocomposites, Proceedings of the ACUN-4, International
Composites Conference, 4th, Sydney, Australia July 21-25, 2002; 222-226.
 ASTM C136. Method of seive analysis of fine and coarse aggregate, ASTM
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weight and mass concrete. ACI Manual of Concrete Practice. Part 1, 1996.
 http: \\ www.fosroc.com. 2009, Dec, 16.
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Commentary (ACI 318-99). American Concrete Institute Detroit, MI, 1999.
 Nilson, H., Darwin, D., and Dolan, C.W. Design of Concrete structures, 13th edition..
McGraw Hill Higher Education, 2004.
 Nielsen, M. P.: Limit analysis and concrete plasticity, second edition, CRC press, 1999.
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Thesis, Jordan University of Science and Technology. 2007.
The effect of CFRP and CFRP/ concrete
interface models when modelling retrofitted RC
beams with FEM.
Yasmeen Taleb Obaidat, Susanne Heyden and Ola Dahlblom
Published in Composite Structures, 2010; 92: 1391–1398.
The effect of CFRP and CFRP/concrete interface models when modelling
retrofitted RC beams with FEM
Yasmeen Taleb Obaidat*, Susanne Heyden, Ola Dahlblom
Division of Structural Mechanics, Lund University, Lund, Sweden
a r t i c l ei n f o
Available online 14 November 2009
Carbon fibre reinforced plastic (CFRP)
Reinforced concrete beam
Finite element analysis (FEA)
a b s t r a c t
Concrete structures retrofitted with fibre reinforced plastic (FRP) applications have become widespread
in the last decade due to the economic benefit from it. This paper presents a finite element analysis which
is validated against laboratory tests of eight beams. All beams had the same rectangular cross-section
geometry and were loaded under four point bending, but differed in the length of the carbon fibre rein-
forced plastic (CFRP) plate. The commercial numerical analysis tool Abaqus was used, and different mate-
rial models were evaluated with respect to their ability to describe the behaviour of the beams. Linear
elastic isotropic and orthotropic models were used for the CFRP and a perfect bond model and a cohesive
bond model was used for the concrete–CFRP interface. A plastic damage model was used for the concrete.
The analyses results show good agreement with the experimental data regarding load–displacement
response, crack pattern and debonding failure mode when the cohesive bond model is used. The perfect
bond model failed to capture the softening behaviour of the beams. There is no significant difference
between the elastic isotropic and orthotropic models for the CFRP.
? 2009 Elsevier Ltd. All rights reserved.
Upgrading of reinforced concrete structures may be required for
many different reasons. The concrete may have become structur-
ally inadequate for example, due to deterioration of materials, poor
initial design and/or construction, lack of maintenance, upgrading
of design loads or accident events such as earthquakes. In recent
years, the development of strong epoxy glue has led to a technique
which has great potential in the field of upgrading structures. Basi-
cally the technique involves gluing steel or FRP plates to the sur-
face of the concrete. The plates then act compositely with the
concrete and help to carry the loads.
The use of FRP to repair and rehabilitate damaged steel and con-
crete structures has become increasingly attractive due to the well-
known good mechanical properties of this material, with particular
reference to its very high strength to density ratio. Other advanta-
ges are corrosion resistance, reduced maintenance costs and faster
installation time compared to conventional materials.
The application of CFRP as external reinforcement to strengthen
concrete beams has received much attention from researchers [1–5],
but only very few studies have focused on structural members
have been preloaded until cracking initiates deserves more attention,
since this corresponds to the real-life use of CFRP retrofitting.
Researchers have observed new types of failures that can re-
duce the performance of CFRP when used in retrofitting struc-
debonding of concrete layers, delamination of CFRP and shear
collapse. Brittle debonding has particularly been observed at
laminate ends, due to high concentration of shear stresses at dis-
continuities, where shear cracks in the concrete are likely to de-
velop . Thus, it is necessary to study and understand the
behaviour of CFRP strengthened reinforced concrete members,
including those failures.
Several researchers have simulated the behaviour of the con-
crete–CFRP interface through using a very fine mesh to simulate
the adhesive layer defined as a linear elastic material . How-
ever, they have not used any failure criterion for the adhesive layer.
Most researchers who have studied the behaviour of retrofitted
structures have, however, not considered the effect of the interfa-
cial behaviour at all [11–13].
In this paper, we use the finite element method to model the
behaviour of beams strengthened with CFRP. For validation, the
study was carried out using a series of beams that had been
experimentally tested for flexural behaviour and reported by
Obaidat . Two different models for the CFRP and two differ-
ent models for the concrete–CFRP interface are investigated. The
models are used for analysing beams with different lengths of
0263-8223/$ - see front matter ? 2009 Elsevier Ltd. All rights reserved.
* Corresponding author.
E-mail address: Yasmeen.Obaidat@byggmek.lth.se (Y.T. Obaidat).
Composite Structures 92 (2010) 1391–1398
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/compstruct
2. Experimental work Download full-text
Experimental data was obtained from previous work by Obaidat
. Eight identical RC beams were loaded with a four point bend-
ing configuration with a span of 1560 mm, and distance between
loads of 520 mm. All beams were 300-mm high, 150-mm wide,
and 1960-mm long. The longitudinal reinforcement consisted of
two / 12 for tension and two / 10 for compression. Shear rein-
forcement was sufficiently provided and consisted of / 8 c/c
100 mm, as seen in Fig. 1.
Two control beams were loaded to failure and the other beams
were loaded until cracks appeared, then retrofitted using different
lengths of CFRP, see Fig. 2. The CFRP was adhered to the bottom
surface of the beams with their fibre direction oriented in the axial
direction of the beam. Each CFRP plate was 1.2 mm thick and
50 mm wide. Finally the beams were retested, while the deflection
and load were monitored.
A comparison of load–deflection curves of retrofitted beams
and control beams is presented in Fig. 3. The experimental re-
sults showed that the retrofitting using CFRP increased the
strength of the beam and the effect increased with the length
of the CFRP plate. All retrofitted beams failed due to debonding
of the CFRP.
3. Finite element analysis
Finite element failure analysis was performed to model the
nonlinear behaviour of the beams. The FEM package Abaqus/stan-
dard  was used for the analysis.
3.1. Material properties and constitutive models
A plastic damage model was used to model the concrete behav-
iour. This model assumes that the main two failure modes are ten-
sile cracking and compressive crushing . Under uni-axial
tension the stress–strain response follows a linear elastic relation-
ship until the value of the failure stress is reached. The failure
stress corresponds to the onset of micro-cracking in the concrete
material. Beyond the failure stress the formation of micro-cracks
is represented with a softening stress–strain response. Hence, the
elastic parameters required to establish the first part of the relation
are elastic modulus, Ec, and tensile strength, fct, Fig. 4a. The com-
pressive strength, f0
be 30 MPa. Ecand fctwere then calculated by :
To specify the post-peak tension failure behaviour of concrete
the fracture energy method was used. The fracture energy for
c, was in the experimental work measured to
¼ 26;000 MPa
¼ 1:81 MPa
c, is given in MPa.
mode I, Gf, is the area under the softening curve and was assumed
equal to 90 J/m2, see Fig. 4b.
The stress–strain relationship proposed by Saenz  was used
to construct the uni-axial compressive stress–strain curve for
1 þ R þ RE? 2
? ð2R ? 1Þ
R ¼REðRr? 1Þ
and, e0= 0.0025, Re= 4, Rr= 4 as reported in . The stress–strain
relationship in compression for concrete is represented in Fig. 5.
Poisson’s ratio for concrete was assumed to be 0.2.
3.1.2. Steel reinforcement
The steel was assumed to be an elastic–perfectly plastic mate-
rial and identical in tension and compression as shown in Fig. 6.
520 mm 520 mm 520 mm
Fig. 1. Geometry, reinforcement and load of the tested beams.
(a) Retrofitted beam RB1
(b) Retrofitted beam RB2
(c) Retrofitted beam RB3
Fig. 2. Length of CFRP laminates in test series RB1, RB2 and RB3.
Fig. 3. Load versus mid-span deflection for un-strengthened and strengthened
Y.T. Obaidat et al./Composite Structures 92 (2010) 1391–1398