Repair of Pre-cracked Reinforced Concrete (RC) Beams with Openings Strengthened Using FRP Sheets Under Sustained Load
International Journal of Concrete Structures and Materials
Repair of Pre-cracked Reinforced Concrete (RC) Beams with Openings Strengthened Using FRP Sheets Under Sustained Load
Bashir H. Osman
Suhaib S. Abdulhameed
Strengthening reinforced concrete (RC) beams with openings by using aramid fiber reinforcement polymers (AFRP) on the beams' surfaces offers a useful solution for upgrading concrete structures to carry heavy loads. This paper presents a repairing technique of the AFRP sheets that effectively strengthens RC beams, controls both the failure modes and the stress distribution around the beam chords and enhances the serviceability (deflection produced under working loads be sufficiently small and cracking be controlled) of pre-cracked RC beams with openings. To investigate the possible damage that was caused by the service load and to simulate the structure behavior in the site, a comprehensive experimental study was performed. Two unstrengthened control beams, four beams that were pre-cracked before the application of the AFRP sheets and one beam that was strengthened without pre-cracking were tested. Cracking was first induced, followed by repair using various orientations of AFRP sheets, and then the beams were tested to failure. This load was kept constant during the strengthening process. The results show that both the preexisting damage level and the FRP orientation have a significant effect on strengthening effectiveness and failure mode. All of the strengthened specimens exhibited higher capacities with capacity enhancements ranging from 21.8 to 66.4%, and the crack width reduced by 25.6-82.7% at failure load compared to the control beam. Finally, the authors present a comparison between the experimental results and the predictions using the ACI 440.2R-08 guidelines.
pre-cracked; RC beaam; AFRP strengthening; beam with openings
Transverse openings in reinforced concrete (RC) beams
are facilities that allow for the passage of utility lines
through a structure. Due to sudden changes presented in the
cross section of the beam, the opening edges are, for the
most part, subjected to high stress concentrations, which
inadvertently leads to induced transverse cracks in the beam;
resulting in a significant reduction in the beam shear capacity
and stiffness (Mansur 1998; Mansur et al. 1999; Yang et al.
2006). The external bonding of different materials, such as
high–strength fiber reinforced plastics (FRP) or steel plates,
has gained wide popularity in recent years to strengthen the
RC structural (Hawileh et al. 2012).
In recent years, FRP has been increasingly used as a
substitute for traditional steel reinforcements in RC structures
due to its superior material properties, such as; light weight,
immunity to the corrosive effects of acids, alkalis, salts and
similar aggressive materials under wide range of
temperature, and excellent mechanical strength and stiffness
(Deborah 1994). These advantages account for the FRP‘s superior
strength when compared with alternative materials such as
steel plates, steel rods or FRP reinforcing bars (rebars) (Lin
and Zhang 2013). Furthermore, it has been found that the
orientation of the FRP also plays a significant role in the
behavior of RC beams and failure mode (Singh 2013). The
external plate bonding technique for structural rehabilitation
is now well established as a convenient repair method for
increasing the shear strength and stiffness of reinforced
concrete beams. The advantage of this technique is the speed
of the upgrading process, which makes the technique more
economical in most cases compared with other strengthening
techniques, such as concrete jacketing or complete
replacement of the member. More importantly, this repair technique
can be performed while the structure is still in use (Hussein
et al. 2013). Within the past decade, there has been numerous
studies conducted regarding the strength and behavior of RC
deep beams with openings (Ashour and Rishi 2000;
Campione and Minafo` 2012; El Maaddawy and Sherif 2009;
Mansur and Alwis 1984; Shanmugam and
Swaddiwudhipong 1988; Zhang et al. 2004). Hussain and Pimanmas
(2015) conducted an extensive experimental program to
elevate the shear strength of RC deep beams with openings
strengthened with Sprayed Glass Fiber Reinforced Polymer
(SGFRP) composites. Both circular and square openings of
varying sizes were investigated. To prevent debonding
failures, a mechanical anchoring system was introduced to
secure the SGFRP to the beam‘s surface. They reported that
the failure mode was changed from debonding to inclined
crack rupture in the fibers due to the presence of anchor bolts.
Alternatively, El Maaddawy and Sherif (2009) examined the
potential use of externally bonded carbon fiber reinforced
polymer (CFRP) composite sheets as a strengthening
solution to upgrade reinforced concrete (RC) deep beams with
openings. The strength gain caused by the CFRP sheets was
in the range of 35–73%. Furthermore, others studies have
reported a significant increase in both shear strength and
stiffness when the RC deep beams with openings are bonded
by fiber reinforced polymer (FRP) system; whilst limiting the
resulting shear crack width within these beams (Chaallal
et al. 2002; Dias and Barros 2008; Etman 2011; Hoult and
Lees 2009). The results of these investigations have
demonstrated the effectiveness of different opening
geometries and different FRP systems such as sheet, wrap and strips
to attain the desired effects. It should be noted that most
studies presented in literature focus on the shear behavior and
strength of RC shallow beams with openings (Mansur 2006;
Osman et al. 2016; Torunbalci 2002; Aykac et al. 2013).
Two different pre-repair loading histories in RC beams
were simulated by Richardson and Fam (2014) using cracking
within the elastic range and overloading in the plastic range.
Their beams were repaired with either high or ultrahigh
modulus (210 or 400 GPa) carbon fiber reinforced polymer
(CFRP) sheets or a hybrid sheet and were then reloaded to
failure. Alternatively, tests conducted by El-Ashkar et al.
(2012) showed that loading the beams to their first cracking
loads before the application of FRP sheets strengthening has
virtually no effect on the repair efficiency; however, no
discussions were found on the effect of increasing the preloading
level and the associated increase in crack width and length.
The experimental and FE-method-based studies modeling the
effect of various pre-cracked loads on the shear behavior of
FRP-strengthened RC deep beams with openings are scarce.
However, very few researchers have considered pre-cracked
RC beams that have been strengthened in terms of shear via
externally bonded FRP reinforcement (Dirar et al. 2013;
Vecchio and Bucci 1999; Kim and Vecchio 2008).
Accordingly, no researchers have investigated the
potential use of an externally bonded AFRP system as an external
repair upgrade of pre-cracked RC deep beams with openings
under sustained load. This paper demonstrates that the
AFRP-strengthening sheets can significantly increase the
efficiency of pre-cracked RC deep beam with openings. The
experimental data provided by this paper helps to gain a
better understanding and enhance the experimental database
of the shear behavior of preloaded RC deep beams with
openings strengthened with the AFRP sheet.
2. Experimental Program
For the experimental investigation, seven rectangular
reinforced concrete beams with openings (the openings were
created before concrete casting using circular tubes) were
fabricated and tested. Two un-strengthened control beams
were considered, four beams that were pre-cracked before
the application of the AFRP sheets and one beam that was
strengthened without pre-cracking were tested. Cracking was
first induced, and then repairs were performed using an
epoxy injection with varying orientations of the AFRP
sheets, followed by testing of the beams to failure. This load
was kept constant during the strengthening process till full
curing of the AFRP epoxy adhesive; once the epoxy had
cured, it was continuously loaded till failure of the beam.
The following sections provide details of the experimental
2.1 Test Specimens and Parameters
In this paper, a total of seven RC deep beam specimens
with circular openings were tested. The specimens included
five repaired beams and two control beams (solid and with
opening) without strengthening. All specimens had a
rectangular cross section of 120 mm wide and 300 mm high,
with a total length of 1800 mm. All beams were tested under
a shear span-to-depth ratio of 1.6 in order to ensure that deep
beam action will develop. The specimens had a similar
default internal shear reinforcement that was designed to
ensure failure in shear. To guarantee that shear failure would
occur only within the shear span of all of the beams, the
internal longitudinal reinforcement (tension steel) was
increased in the bottom of the beam. Steel stirrups of
6-mmdiameter spaced every 100 mm were implemented as shear
reinforcement. All tension and compression reinforcement
were kept the same for all the specimens. Two of the 20-mm
diameter deformed bars were used as bottom reinforcement
(in tension the face), and two of 10 mm deformed bars were
used as top reinforcement. Details and dimensions (in mm)
of the test beams are shown in Fig. 1.
A clear cover at the top and bottom of the beam was
20 mm, whereas a clear cover of 15 mm was maintained on
the beam’s vertical sides. All specimens had two circular
openings, one in each shear span, that were placed
symmetrically about the mid-point of the beam (Fig. 1). The
opening size was 140 mm, which corresponded to opening
height-to-effective depth ratio of 0.5. The beams were cast in
a horizontal position using plywood molds.
Table 1 summarizes the test matrix, including various
parameters. Specimen B1 and B2 were considered control
beams and were tested to failure load without any damaging
or AFRP strengthening, and B3 was strengthened with
AFRP sheets and loaded to failure without preloading.
Specimens B4 and B5 were brought to a damage level
within the elastic range by cracking up to 50% of the failure
load of the control beam (B2) and were then strengthened
with different AFRP schemes. Beam B6 was strengthened
with AFRP after being loaded up to 70% of B2, and beam
B7 was loaded as in beam B6, but the load was released to
the cracking load of the control beam (B2). The load was
kept constant during the strengthening process in beams
B4B7. The strengthening process was took at least three days
Fig. 1 Specimen’s details (in mm).
Table 1 Test matrix.
Opening size mm
50% of B2
50% of B2
70% of B2
70% of B2
(72 h) to ensure full curing of AFRP epoxy (Abdulhameed
et al. 2013).
The AFRP sheets were applied to three faces of the beam
in a U wrap shape and had a consistent bond length of
350 mm, a 120 mm width and a 300 mm height. Specimens
B3 and B4 were strengthened with vertical AFRP, and the
diagonal AFRP (60 ) was used in the other beams (B5-B7).
Figure 2 presents the layout of the AFRP sheet arrangements
on the beam faces.
2.2 Materials’ Properties
The properties of the steel reinforcement and the concrete
that were used in this research were obtained experimentally.
All test beams were prepared at the same time and cured
under the same conditions to ensure that the compressive
strength was approximate in nature. The cube‘s compressive
strength was obtained by testing nine cubes with dimensions
of 150 9 150 9 150 mm using Compressive Testing
Machine (CTM).The average tested compressive strength of
Fig. 2 AFRP layout a U wrap vertical strengthening (B3 and B4), b U wrap diagonal strengthening (B5-B7).
concrete at 28 days was 39.3 MPa. The yield strength of
steel reinforcement was obtained by testing three bars with
diameters of /20 mm, /10 mm and /6 mm, respectively,
using Tensile Testing Machine (TTM). The longitudinal steel
reinforcement was Grade 480 and 450 deformed steel bars
for tension (/20 mm) and compression (/10 mm)
reinforcement, respectively, and the web reinforcement was
Grade 330 deformed bars. The AFRP sheet (type C1-AK-40)
has a tensile strength of 2100 MPa, an elastic modulus of
120 GPa, and a thickness of 0.193 mm. The properties of the
epoxy adhesive, primer, putty, and FRP were provided by
the manufacturers and are given in Table 2.
2.3 Specimen Preparations and Test Setup
The concrete surface was prepared before the bonding of
the U-shaped AFRP sheets. The three surfaces of the beam
were sandblasted and cleaned before FRP application until
the aggregates were exposed. The corners of the beam were
rounded with a radius of 10 mm to avoid stress
concentration in the U wrap. Longitudinal AFRP sheets that were
60 mm wide by 350 mm long were bonded to the concrete
chords above and below each opening, with the fibers
oriented in a direction parallel to the longitudinal axis of the
beam (Fig. 2) to prevent any delamination occurring during
shear that would have concentrated in the chords.
The surface dust was removed by an air blower. Next, the
surface was cleaned with acetone. A thin layer of primer
[type Telesun Epoxy Adhesive (TLS)-501] was applied to
the prepared surface of the reinforced concrete beam. The
primer was allowed to cure for 24 h before the epoxy
adhesive was applied to the concrete. The purposes of the
primer are as follows: to strengthen the surface of the
concrete, prevent the epoxy from being absorbed by the concrete
instead of wetting fibers, penetrate the concrete via the pores,
and enhance the bond for the fibers. Putty is used to fill
larger holes and irregularities on the surface of the concrete.
A layer of epoxy adhesive (TLS-503) was applied by a
paintbrush to the surface of the concrete and AFRP sheet
(Abdulhameed et al. 2013).
All beams were tested under four-point bending in the
structural testing frame, as shown in Fig. 3. To provide
bearing and frictionless rotational, the beams were supported
on two heavy-duty rollers during the test. The clear span
between the supports was 1500 mm. The beams were
subjected to two monotonic loadings using a steel spreader
beam that conveyed the load from a 500-kN capacity jack to
the beam. The load was measured by a 500-kN capacity load
cell. The load was applied at an increment of 5 kN using the
load cell machine. The distance between the loads was
600 mm. The deflection values were recorded at each load
increment up to failure. The load that caused the crack was
recorded, and its crack pattern was marked on the beam
surfaces (Fig. 4).
2.4 Instrumentation of LVDTs and Strain Gauges
The tested RC beams were instrumented with linear
variable differential transducers (LVDTs) to monitor the
deflection and the crack width during the test (Fig. 3). The
deflection during testing was measured using LVDTs located
under the two load points and at mid-span. Measurements of
the strains in the reinforcing bars and concrete were made
using electrical-resistance strain gauges with gauge lengths
of 5 and 100 mm, respectively, as shown in Fig. 3a. Strains
in the AFRP were made using electrical-resistance strain
gauges with gauge lengths of 5 mm, as shown in Fig. 3b.
3. Experimental Results and Discussions
3.1 Failure Mode and Cracks Pattern
Table 3 gives a summary of the load capacity and failure
modes of all of the tested beams. The observation of
specimens during the tests and detailed discussions are presented
in the following. It was noted that the control beam B1
experienced failure due to the shearing off of the concrete in
the load path, located between the load points and the
supports, as illustrated in Fig. 6. As the load increased, inclined
diagonal shear cracks (at approximately 45 from the
supports) appeared at the line connecting the load points and the
supports. A further load increase resulted in the widening of
diagonal cracks as well as the initiation of new flexural and
diagonal cracks, whereas the shear cracks were inactive. Due
to failure in the shear region, the beam finally failed at a load
of 251 kN. The load-mid-span deflection curve and the
failure mode of the beam are illustrated in Figs. 5 and 6,
Beam B2, which was tested to failure without
strengthening, failed at a load 50% lower than that of the control
beam B1. Failure occurred by shear off of the concrete. The
Table 2 Material Properties.
Ultimate strain (%) Elastic modulus
Curing time (h)
CMax (2.5, ftk)
CMax (2.5, ftk)
CMax (2.5, ftk)
Areal density (g/m2)
Fig. 3 Test setup a LVDT positions and steel strain gauges and b AFRP strain gauges location.
Fig. 4 Crack width of tested beams.
first shear crack appeared at a load of 40 kN, followed by the
first flexural crack at 55 kN located at mid-span. As the load
increased, a diagonal crack passing through the center of the
opening was formed at 90 kN. Two additional cracks formed
in the top and bottom chords of the opening during the
application of load. As the loading continued to progress, the
cracks widened with several minor cracks appearing along
the fac¸ade of the beam, as shown in Fig. 6. Finally, the beam
failed due to the presence of these cracks in the bottom
chords of the opening at a load of approximately 124 kN.
For strengthened beams, the bond interface is generally
considered the weakest link in the element and debonding at
this interface will usually experience what is known as the
critical failure mode (Zhou et al. 2010).
In beam B3, the shear crack followed by the first flexural
crack occurred at approximately the same load of that in
beam B2. To evaluate the effect of preloading on the
strengthening efficiency, the beam (B3) was strengthened
without preloading. For beam B3, attaining the
measurements of the first shear crack width was not feasible, due to
the concealment of cracks by the fiber wrap. The first
flexural cracks appeared in the constant moment region at
61 kN (1.5 times the cracking load of beam B2). As
loading progressed, the developed flexural cracks widened,
and the flexural cracks stopped increasing. The specimen
finally failed in a brittle manner at a load of approximately
178 kN in the top chord of the opening at the top
AFRPstrengthening sheet. At failure, a partial debonding of the
fiber wrap was noted. Beams B4 and B5 were initially
loaded to 50% of the control beam (B2) capacity to
simulate the initial cracks. In this loading phase, the formation
of cracks was very similar to that of the control beam, and
at the completion of this loading phase, the load was kept
without release for repairing. Before reloading up to failure,
the U wrap (90 ) and diagonal (60 ) AFRP shape (with
respect to the beam axis) strengthening approaches were
used for B4 and B5, respectively. Next, the cracking and
ultimate loads in the second loading phase of these beams
were determined, as shown in Table 4. The vertical
orientation of AFRP in beam B4 proved to yield a lower
performance than the diagonal orientation of AFRP seen in
other strengthened beams. This is attributed to: deep beam
failure action, and failure of the beams’ chords due to
First shear crack (kN)
First flexural crack (kN)
Failure load (kN)
vertical cracks parallel to the FRP axis which helps for
Beams B6 and B7 were initially loaded up to 70% of the
control beam (B2) capacity to simulate the initial cracks.
The load in Beam B6 was kept without release, whereas,
the load in B7 was released to the cracking load of control
beam B2. The load was then kept constant for both beams
during FRP strengthening process. The diagonal AFRP
strips were then used to strengthen both the upper and
lower chords of these beams. After this strengthening
procedure, the beams were subjected to a continuous load.
It was observed that there were no critical diagonal cracks
present in beams B6 and B7; the maximum crack width
measured for these beams, therefore, remained minor
during the entire loading history. Additionally, when compared
to beam B4, no debonding failure was observed at the end
of the AFRP in these beams up to the failure loads. The
cracking, failure loads and modes of failure of these beams
are shown in Table 3 and Fig. 6. Compared to beam B1,
the reduction in shear capacity was caused by the early
formation of a diagonal crack around the chords of the
opening due to the stress concentration and the reduced
ability of the web area to resist high shear.
3.2 Cracking Behaviors
A special microscope with 0.02-mm accuracy was used to
measure the crack width at different locations. The loads
corresponding to the appearance and progression of cracks at
the different loading stages are presented in Table 4. The
first crack appeared at approximately the shear span of the
beam, with, new cracks forming progressively towards the
supports. Diagonal shear cracks appeared next, which were
propagated downwards to the inner edge of the support and
upwards to the loading point. With its appearance, the width
of the shear cracks began to exceed that of those formed in
the flexural zone. As load increased, the existing cracks
advanced further and new cracks began to form inside the
openings, which ultimately lead to the failure at the beam‘s
chords. During the course of this study, all major cracks
were inspected (visually) and their maximum widths
measured and recorded up until failure. The measured crack
widths against the applied load are plotted in Fig. 4.
The measured cracking width of beam B1 was
approximately 0.15 mm at 88 kN. As loading progressed, the crack
width augmented from approximately 0.33 to 1.45 mm at
125 and 251 kN (failure load), respectively. In beam B2,
cracks appeared early during the loading process, with a
width of approximately 0.04 mm at a load of 40 kN. After
increasing the load, the crack width increased exponentially,
especially in areas near the opening. Beam B2 experienced
failure in shear at 124 kN, with a maximum crack width of
3.31 mm. The crack patterns of the remaining beams (B3–
B7) before strengthening showed very similar crack patterns
to those in the control beam (B2); however, the maximum
measured crack width for all AFRP strengthened beams was
lower. Furthermore, the attained ultimate loads were much
higher than that of the control beam, as illustrated in Table 3.
Figure 4 shows the crack width of the tested beams.
By increasing the pre-damaged load before strengthening,
the crack width increased rapidly especially during failure
stage. In beam B5, lower pre-damaged loads resulted in a
remarkable decrease in the crack width by 15.8 and 60% at
corresponding loads of 80 kN and 125 kN, respectively,
compared to the control beam B2. When the pre-damage was
increased to 70% of B2, the crack width increased
considerably, and hence a significant reduction in the beam
stiffness was recorded. At 80 and 125 kN, the crack width of
specimens B6 (with pre-damages of 70% of B2) was about 7
and 9.8%, respectively, and resulted in lower crack widths
than those of beam B5 (with lower damage) as shown in
In the strengthened beams, the main flexural crack formed
at a load of approximately 65 kN. After a load level
corresponding to approximately 85% of the ultimate load was
attained, no more flexural cracks appeared, and only
widening of the existing vertical flexural cracks could be
observed. Next, the beam started to fail, mainly by brittle
shear failure, in which the diagonal shear cracks that formed
at the top and bottom chords of the beams led to concrete
crushing or AFRP debonding or peeling. Most of the failures
Fig. 5 Load deflection relationship of the tested beams a B1,
B2, B3 and B4, b B2, B3 and B5, and c B5, B6 and B7.
of the tested beams occurred in the concrete thin layer
adjacent to the sheet (in direct contact with the FRP sheet),
not in the adhesive epoxy (Fig. 6) (Hussein et al. 2013).
3.3 Deflection Behavior
To investigate the deflections and stiffness of the
reinforced concrete beams with openings strengthened with
AFRP sheets, the load deflection curves were studied. Four
LVDTs were used to measure the displacement: one at the
top of the beam located at the mid-span and three at the
bottom of the beam (one at the mid-span and two under the
loading points) (Fig. 3a). The three LVDTs at the bottom
read almost the same displacement values, and even the two
LVDTs at the top and bottom (mid-span) exhibited no clear
difference. The mid-span deflection at the maximum load for
the tested reinforced concrete beams with the opening is
illustrated in Fig. 5. The load deflections of the beams tested
can therefore be generalized to those of typical RC beams,
which like the beams tested, fail mainly due to shear. All
beams demonstrated a nearly linear trend up to
approximately 65% of the failure load.
From Fig. 5, the changes in the slope of the curves
indicate that the cracking of the concrete has occurred and the
AFRP sheet started to carry load. The ultimate loads of the
test beams proved to be different from the control beam, this
difference is dependent upon the loading behavior. After a
load of 65% of the ultimate load was applied, the beams
experienced a reduction in stiffness, and soon after, complete
failure. Strengthening of pre-cracked beams showed
increases in the initial stiffness, ultimate load, and deflection,
compared to the equivalent control beam. The strengthening
of beams after pre-damage ultimately leads to an increase in
the external force required to produce cracks in the concrete
at ultimate. Additionally, the experiments conducted showed
that by increasing the pre-damage load, a decrease in the
ultimate load by 11% in beam B6 was experienced when
compared to the equivalent pre-damaged beam B5.
For pre-damaged strengthened beams, it was observed that
the stiffness of the beams were increased after strengthening.
This strengthening restrained the cracks that were previously
generated due to the application of loads prior to the FRP
application, which reduced the magnitude of displacement
between the two halves of the main crack by transferring the
failure to the FRP sheet.
3.4 Strain Distribution
The results of some failed strain gauges during testing
were discarded due to the erroneous data that they provided.
The strain gauges locations are illustrated in Fig. 3.
3.4.1 Reinforcement Strain
The main steel strain was recorded at the mid-span and at
the region surrounding the openings. For all beams, the
strains along the reinforcement bars varied in a manner
similar to the bending moment up to the formation of the
diagonal shear crack. Figure 7 shows the strain distribution
of the longitudinal steel in the tension face at different
loading level. The linear strain distribution in the
longitudinal steel was observed and did not reach its ultimate strain
until beam failure; which was attributed to the shear failure
of the beams and early contribution of the FRP. Finally, by
load increasing, the load-strain curves slope increased with a
linear trend till failure of the concrete.
Figure 8 shows the load versus vertical reinforcement
strain for the tested beams. The vertical steel strain was
measured around the openings in two stirrups (before and
Fig. 6 Typical failure observed for both un-strengthened and repaired beams (B1–B7).
Table 4 Maximum shear crack width (mm) at 80, 125, 150 kN, and at failure load.
At 125 kN
At 150 kN
after the opening). The load versus longitudinal
reinforcement strain for the tested beams is shown in Fig. 7.
From Fig. 8, the strain values before first crack was
smaller and almost close to the vertical axis with values near
to zero. In loads that generated approximately 80% of failure
load for the control beam, the slope of the strain distribution
experienced an increase, which was attributed to the increase
of the load that was carried by the vertical reinforcement.
Fig. 9 Concrete strain in the bottom of the beams at
and B4, and at loads more than 100 kN for the beams B5 and
B7. This signifies that the stirrup steel present in the tested
beams have yet to reach their yielding points before concrete
failure has occurred. This is mainly due to the presence of
AFRP, and its ability to carry loads once the structural
integrity of the element begins to weaken (Ferreira et al.
3.4.2 Concrete Strain
The strains in the concrete were measured using
electricalresistance strain gauges with gauge lengths of 100 mm, as
illustrated above in Fig. 3. Figure 9 shows the load-strain
plots for the tested specimens. It can be observed that the
strains at low load levels appeared to increase linearly after
increasing non-linearly until the first diagonal cracking load
was reached. Accordingly, it has been projected that the
concrete will fail, as such the AFRP will carry the bulk of the
load. After this point, the values increased gradually up to
Some of the strain values in Fig. 9 were more than 2000
micro, this may be attributed to that when the steel start to
yield explains the large concrete strains. Furthermore, may
be due to several factors such as cracks may be occurring at
the interfaces between the cement and aggregate, due to their
differences in elastic modulus, thermal coefficient of
expansion, and response to change in moisture content when
the concrete is hardened (Damian et al. 2001).
3.4.3 FRP Strain
The positions of the FRP strain gauges are given in
Fig. 3b. The shear force-strain curves for the externally
bonded AFRP sheets in the shear spans where failure
occurred are shown in Fig. 10. In the first stage, the FRP
sheets started to resist the further opening of the existing
shear cracks at the inception of the final reloading stage, and
they continued to develop tensile strain with an increased
load up to approximately the peak loads. Then, the sheets
started to peel off or debond, or the concrete was crushed.
Figure 10 shows that at any load before first crack, the
beams shows smaller strain values. Till the first crack, the
FRP has not taken much load as the strain is almost close to
Fig. 7 Tensile steel strain a at mid-span (T2) and b below the
opening at the bottom chord (T1).
Fig. 8 Stirrups steel (vertical reinforcement) strain (S2).
Lately, the curve had started to show some reasonable
inclination, this means that the strain value which
corresponding to the applied load is big compared to previous
loading stages increment.
According to the strain values predicted in Fig. 8, the
transversal reinforcement starts to carry loads at almost 48
kN for the case of the control beams, at 90 kN for beams B3
Fig. 10 AFRP sheet strain a F1, b F2, c F3, and d F4.
zero in this stage and the curve is almost close to the vertical
axis. From this stage, the FRP starting to take load, by the
fact that the curve had started to show some reasonable
inclination. From this point it was clear that the curve has
taken a slope which indicates the FRP has started to take
As seen from Figs. 10a and 10d, it was observed that the
ultimate tensile strain from openings’ sides in F1 and F4
which lie in the shear path (line connected the load point and
the support) equal to approximately 10,000 le, which is
greater than the tensile strain at the beams’ chords (F2 and
F4) which is equal to approximately 2000 le. This increase
in the tensile strain is attributed to the concentration of the
stresses along the shear path (line connecting the load point
and the support) due to the relative displacement between the
two of the main cracks.
4. Performance of the Current Analytical
Equations Used in this Study
Shear strength and shear forces in RC beams following the
ACI approach (ACI 318 2014; Mansur 1998) was able to
develop the following equations for beam type failure.
Equation (1) can be used for calculating shear strength of
RC beam containing opening as proposed by Mansur
where, Vc and Vs are the contribution of the concrete and
steel reinforcement respectively; fc is the concrete strength;
b is the beam width; d is the effective depth; do is the
depth of opening; dv is the distance between the centroids
of extreme tension and compression reinforcement layers;
s is the stirrup spacing; Ast is the area of stirrups; Ad is the
cross-sectional area of the diagonal reinforcement within
the failure surface; fyst is the yield strengths of the stirrups
reinforcement; Asl is area of tension steel and a is shear
Ptheo. and Pexp. are ultimate load for theoretical and experimental tests, respectively.
4.1 FRP Contribution
The contribution of the FRP sheet to shear strength of RC
beams is based on the orientation of the fiber and an assumed
crack pattern (ACI-440.2R-08 2008). The shear strength
provided by the FRP contribution can be determined by
calculating the force resulting from the tensile stress in the
FRP across the assumed crack. The shear contribution of the
FRP shear reinforcement is given by the following equations
Table 5 Comparison of the experimental and analytical results.
where, df is the depth of FRP shear reinforcement, k2 is
modification factor applied to kv to account for the wrapping
scheme, Le is active bond length of FRP laminate, and k1 is
modification factor applied to kv to account for the concrete
In Table 5, the values obtained using these equations were
compared to those obtained experimentally. For beam B6,
the ACI equation has underestimated the shear strength of
FRP contribution for RC beams subjected to high damage
(70% of B2) by approximately 28% error band. For beam
B4, an orientation of vertical FRP sheet crossed by the shear
crack might have caused the low value of the
FRPstrengthening-sheet contribution, subsequently the
strengthening sheet debonded prematurely at a relatively low
magnitude of applied load compared to that calculated from ACI
440.2R-08 (2008) equation by approximately 26%. This
variation between analytical and experimental results may be
due to the residual strain in the concrete before
strengthening; the ACI 440.2R-08 equation, is therefore, unsuitable for
the estimation of the shear capacity of high damaged RC
beams under sustained loads.
According to the results obtained from the present
experimental work, the design value of the contribution of
the FRP shear reinforcement can be estimated using the
recommendations proposed by ACI guidelines
(ACI440.2R-08 2008; ACI-014 2014) for damage levels not
exceeding a 70% capacity of equivalent unstrengthened
Experiments were performed to study the effects of
different pre-cracking loads on the shear strength of RC deep
beams with openings. Based on the experimental results and
discussions, the following conclusions could be drawn,
/Vn ¼ /ðVc þ VsÞ þ 0:7Vf
Shear capacity of FRP RC beam can be determined from
where / = the strength-reduction factor required by ACI
that for shear strengthening of concrete elements has a value
of 0.85 (Khalifa et al. 1998); sf is the spacing of the wet
layup strips of FRP sheets; and Afv is the area of FRP shear
reinforcement within spacing, sf; tf, n, and wf are the
thickness of a layer, the number of layers per strip, and the width
of the strips, respectively. If continuous or one FRP sheets
are used, the width of the strip, wf and the spacing of the
strips, sf should be equal (sf = wf) (Khalifa et al. 1998).
The effective stress in the FRP, ffe obtained multiplying the
elasticity modulus of the FRP, Ef by the effective strain
0:004 ðfor U-wrapÞ
where, kv is a bond-reduction coefficient that is a function of
the concrete strength, the type of wrapping scheme used, and
the stiffness of the FRP.
(1) The pre-cracked RC deep beams with openings
strengthened by AFRP sheets displayed a higher level
of stiffness and ductility; with reductions in the crack
width between 25.6 and 82.7% at failure load when
compared with the control beam. This is predominately
due to limiting the development of shear cracks by
using the epoxy resin prior to the application of the
AFRP strengthening strip. This is demonstrated most
clearly in beam B7, which was loaded up to 70% and
reduced to cracking loads of those loads subjected to
(2) Damage levels have an effect on the ultimate capacity
of the reinforced concrete deep beam strengthened with
AFRP sheet by a decrease in failure load of
approximately 11.5%, when the damage level was increased
from 50 to 70% of control beam B2. Beam B7 failed
with load capacities lower than that of beam B5 by
2.5%, this is attributed to the residual stress in beam
(3) All of the strengthened specimens exhibited higher
capacities than the equivalent unstrengthened control
beams, with capacity enhancements ranging from 21.8
to 66.4%, thus confirming the potential effectiveness of
the FRP sheets.
(4) Strengthening the more damaged RC deep beams with
openings by AFRP sheets decreased the mid-span
deflection at the ultimate load by 22.5% when
compared with the control beam. This is primarily
due to the AFRP’s ability to carry additional loads
when the concrete begins to experience failure and its
ability to limit further development of exiting cracks.
(5) AFRP strengthening of pre-cracked RC deep beam with
opening can enhances a beam’s capacity (Fig. 5) and
stiffness after repairing, and decreases the crack width
spatially (as seen in beam B7). Furthermore, loading the
beams to less than their cracking loads prior to the
application of the FRP strengthening had almost no
effect on the repair efficiency (El-Ashkar et al. 2012).
(6) The orientation of AFRP sheets used for shear
strengthening (reducing the stress concentration on
the top and bottom chords of the opening) and the
crack width both play a significant role in the behavior
of RC beams with openings. The AFRP sheets installed
at 60 to the axis of the beam are found to be most
efficient for shear-strength enhancements, whereas the
vertical AFRP sheets are less effective (B4 and B5).
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Abdulhameed , S. S. , Wu , E. , & Ji , B. ( 2013 ). Mechanical prestressing system for strengthening reinforced concrete members with prestressed carbon-fiber-reinforced polymer sheets . Journal of Performance of Constructed Facilities , 29 ( 3 ), 04014081 .
ACI- 014 . ( 2014 ). Building code requirements for structural concrete and commentary . Farmington Hills, MI.
ACI-440. 2R - 08 . ( 2008 ). Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures . Farmington Hills, MI.
Ashour , A. F. , & Rishi , G. ( 2000 ). Tests of reinforced concrete continuous deep beams with web openings . Structural Journal , 97 ( 3 ), 418 - 426 .
Aykac , B. , Kalkan, I. , Aykac , S. , & Egriboz , Y. E. ( 2013 ). Flexural behavior of RC beams with regular square or circular web openings . Engineering Structures , 56 , 2165 - 2174 .
Campione , G. , & Minafo`, G. ( 2012 ). Behaviour of concrete deep beams with openings and low shear span-to-depth ratio . Engineering Structures , 41 , 294 - 306 .
Chaallal , O. , Shahawy , M. , & Hassan , M. ( 2002 ). Performance of reinforced concrete T-girders strengthened in shear with carbon fiber-reinforced polymer fabric . ACI Structural Journal , 99 ( 3 ), 335 - 343 .
Damian , K. , Thomas , M. , Solomon , Y. , Kasidit , C. , & Tanarat , P. ( 2001 ). Finite element modeling of reinforced concrete structures strengthened with FRP laminates . Salem, OR: Report for Oregon Department of Transportation .
Deborah , D. C. ( 1994 ). Carbon fiber composites (1st ed .). Waltham, MA: Butterworth-Heinemann Publisher .
Dias , S. J. , & Barros , J. A. ( 2008 ). Shear strengthening of T cross section reinforced concrete beams by near-surface mounted technique . Journal of Composites for Construction , 12 ( 3 ), 300 - 311 .
Dirar , S. , Lees , J. M. , & Morley , C. ( 2013 ). Phased nonlinear finite-element analysis of precracked RC T-beams repaired in shear with CFRP sheets . Journal of Composite for Construction , 17 ( 4 ), 476 - 487 .
El Maaddawy , T., & Sherif , S. ( 2009 ). FRP composites for shear strengthening of reinforced concrete deep beams with openings . Composite Structures , 89 ( 1 ), 60 - 69 .
El-Ashkar , N. , A. Morsy , & K. Helmi , ( 2012 ). FRP repair technique for RC beams pre-damaged in shear . In Proceedings of 14th International Structural faults and repair . Edinburgh: Engineering Technics Press.
Etman , E. ( 2011 ). Strengthening of T-section RC beams in shear using CFRP . In Proceedings of concrete solutions. 14th international conference on concrete repair . Dresden, Germany.
Ferreira , D. , Oller , E. , Mar´ı , A. , & Baira´n, J. ( 2013 ). Numerical analysis of shear critical RC beams strengthened in shear with FRP sheets . Journal of Composites for Construction , 17 ( 6 ), 04013016 .
Hawileh , R. A. , El-Maaddawy , T. A. , & Naser , M. Z. ( 2012 ). Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites . Materials and Design , 42 , 378 - 387 .
Hoult , N. A. , & Lees , J. M. ( 2009 ). Modeling of an unbonded CFRP strap shear retrofitting system for reinforced concrete beams . Journal of composites for construction , 13 ( 4 ), 292 - 301 .
Hussain , Q. , & Pimanmas , A. ( 2015 ). Shear strengthening of RC deep beams with openings using Sprayed Glass Fiber Reinforced Polymer Composites (SGFRP): Part 1. Experimental study . KSCE Journal of Civil Engineering , 19 ( 7 ), 2121 - 2133 .
Hussein , M. , Afefy , H. M. E.-D. , & Khalil , A.-H. A.-K. ( 2013 ). Innovative repair technique for RC beams predamaged in shear . Journal of Composite for Construction , 17 ( 6 ), 04013005 .
Khalifa , A. , Gold , W. J. , Nanni , A. , & Abdel Aziz , M. I. ( 1998 ). Contribution of externally bonded FRP to shear capactiy of RC flexural members . Journal of Composites for Construction , 2 ( 4 ), 195 - 202 .
Kim , S. , & Vecchio , F. J. ( 2008 ). Modeling of shear-critical reinforced concrete structures repaired with fiber-reinforced polymer composites . Journal of Structural Engineering , 134 ( 8 ), 1288 - 1299 .
Lin , X. , & Zhang , Y. ( 2013 ). Bond-slip behaviour of FRPreinforced concrete beams . Construction and Building Materials , 44 , 110 - 117 .
Mansur , M. ( 1998 ). Effect of openings on the behaviour and strength of R/C beams in shear. Cement & Concrete Composites , 20 ( 6 ), 477 - 486 .
Mansur , M.A. ( 2006 ). Design of Reinforced Concrete Beams with Web Openings . In Proceedings of the 6th ASI-pacific Structural Engineering and Construction Conference (APSEC 2006 ). 5 - 6 September 2006 , Kuala Lumpur , Malaysia.
Mansur , M. , & Alwis , W. ( 1984 ). Reinforced fibre concrete deep beams with web openings . International Journal of Cement Composites and Lightweight Concrete , 6 ( 4 ), 263 - 271 .
Mansur , M. , Tan , K.-H. , & Wei , W. ( 1999 ). Effects of creating an opening in existing beams . Structural Journal , 96 ( 6 ), 899 - 905 .
Osman , B. H. , Wu , E. , Ji , B. , & Abdulhameed , S. S. ( 2016 ). Shear behavior of reinforced concrete (RC) beams with circular web openings without additional shear reinforcement . KSCE Journal of Civil Engineering . doi: 10.1007/s12205- 016 - 0387 -7.
Richardson , T. , & Fam , A. ( 2014 ). Modulus effect of bonded CFRP laminates used for repairing preyield and postyield cracked concrete beams . Journal of Composite for Construction , 18 ( 4 ), 04013054 .
Shanmugam , N. E. , & Swaddiwudhipong , S. ( 1988 ). Strength of fibre reinforced concrete deep beams containing openings . International Journal of Cement Composites and Lightweight Concrete , 10 ( 1 ), 53 - 60 .
Singh , S. B. ( 2013 ). Shear response and design of RC beams strengthened using CFRP laminates . International Journal of Advanced Structural Engineering (IJASE) , 5 ( 1 ), 1 - 16 .
Torunbalci , N. ( 2002 ). Behaviour and design of large rectangular openings in reinforced concrete beams . Architectural Science Review , 45 ( 2 ), 91 - 96 .
Vecchio , F. J. , & Bucci , F. ( 1999 ). Analysis of repaired reinforced concrete structures . Journal of Structural Engineering , 125 ( 6 ), 644 - 652 .
Yang , K.-H. , Eun , H.-C. , & Chung , H.-S. ( 2006 ). The influence of web openings on the structural behavior of reinforced high-strength concrete deep beams . Engineering Structures , 28 ( 13 ), 1825 - 1834 .
Zhang , Z. , Hsu , C.-T. T., & Moren , J. ( 2004 ). Shear strengthening of reinforced concrete deep beams using carbon fiber reinforced polymer laminates . Journal of Composites for Construction , 8 ( 5 ), 403 - 414 .
Zhou , Y.-W. , Wu , Y.-F. , & Yun , Y. ( 2010 ). Analytical modeling of the bond-slip relationship at FRP-concrete interfaces for adhesively-bonded joints . Composites Part B Engineering , 41 ( 6 ), 423 - 433 .