Engineering Structures 56 (2013) 2065–2075
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Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
Effectiveness of externally bonded CFRP strips for strengthening flanged
beams under torsion: An experimental study
A. Deifalla a,⇑, A. Awad b, M. Elgarhy c
a
Department of Civil Engineering, BUE, El Shorouk City, Egypt
Department of Civil Engineering, Ain Shams University, Cairo, Egypt
c
Department of Civil Engineering, Helwan University, Cairo, Egypt
b
a r t i c l e
i n f o
Article history:
Received 3 July 2013
Revised 20 August 2013
Accepted 23 August 2013
Keywords:
FRP
Strips
Anchored U-jacket
Extended U-jacket
Torsion
Ductility
Toughness
L-shaped beams and T-shaped beams
a b s t r a c t
All over the world, fiber reinforced polymer (FRP) is currently being used for strengthening concrete elements, thus improving the building sustainability. The most recent report by the American Concrete
Institute Committee 440 suggested that any proposed anchorage system should be heavily scrutinized
before field implementation [4]. A comprehensive literature review was conducted, which showed that
anchored U-jacket strips and un-anchored extended U-jacket strips were never examined for the case
of RC flanged beams under significant torsion. The objective of this study is to investigate the behavior
of FRP externally strengthened flanged beams subjected to torsion. Eleven beams were tested under significant torsion. Both the anchored U-jacket and the extended U-jacket strips were found to be more
effective strengthening techniques compared to the un-anchored U-jacket strips and as effective as the
fully wrapped strips. Using externally bonded FRP strips enhanced the torsional behavior of the flanged
beams; however, the level of enhancement depended mainly on the effectiveness of the implemented
strengthening technique.
Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Whittle reported failures in various RC buildings, a few of which
were related to torsion [1]. Torsion related problems exist in many
projects [2]. In addition, many strengthened concrete (RC) members are subjected to significant torsion, as shown in Fig. 1. The elevated cost of infrastructure replacement has urged researchers to
study the effectiveness of various external strengthening techniques for improving torsional behavior. In the late 1980s, the torsion failure of RC beams was prevented by externally
strengthening the beams with steel plates [3]. However, fiber reinforced polymer (FRP) fabrics have many advantages over steel
plates [4,5].
Most existing research has examined the effects of bending
moments or shear forces on concrete members that were externally strengthened with FRP [5,6]. A small number of studies
have focused on the torsional behavior of RC beams with FRP
as external or internal reinforcements [7–12,13,14]. Although
analytical model development is independent of experimental
work, test data can be used for validating analytical models
[15–18].
⇑ Corresponding author.
E-mail addresses: diffalaf@mcmaster.ca, ahmed.deifalla@bue.edu.eg (A. Deifalla).
0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.engstruct.2013.08.027
The literature review presented later in this paper shows that
the torsional behavior of flanged beams externally strengthened
with FRP systems (i.e., anchored U-jacket strips or unanchored extended U-jacket strips) has not been fully investigated. The objective of this study is to investigate the behavior of flanged beams
externally strengthened using FRP and subjected to torsion. A test
setup is constructed to evaluate RC beams under torsion with various cross section shapes (i.e., rectangular, T-shaped and L-shaped).
Eleven RC beams were tested and the following strengthening
techniques were used: U-jacket strips, extended U-jacket strips
and fully wrapped strips. The experimental results are reported,
analyzed and discussed. The effectiveness of the various strengthening techniques is assessed in terms of torsional strength, ductility and rigidity.
2. Literature review and research significance
Since 2001, FRP has been studied as an externally strengthening
material for beams under torsion. Prior to the initiation of this
study, existing studies with an emphasis on the effectiveness of
strengthening techniques were reviewed. It was found that: (1)
continuous jackets are more effective than strip jackets
[19,20,10]; (2) the 45° inclined fully wrapped continuous jacket
is much more effective than the vertical fully wrapped continuous
jacket [8,12]; (3) the ultimate strength of beams externally
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
total of 91 beams externally strengthened using FRP as follows:
(1) 79% have a rectangular cross-section; (2) 18% have a flanged
cross-section; and (3) 3% have a hollow box cross-section.
Although most beams are connected to a flange either as a part
of the floor slab (i.e., the slab and beam are monolithically cast together) or as an inverted flanged beam, only 18% of the tests investigated flanged beams. Several analytical models were recently
proposed for the case of FRP externally strengthened beams
[15,16]. Chalioris proposed an analytical model for the description
of the torsional response of RC beams retrofitted with FRP that
combines two different analytical methods [15]. It addressed the
development of a special truss model that utilizes softened and
FRP-confined concrete relationships and employs the contribution
of the externally bonded FRP to the torsional capacity. Deifalla and
Ghobarah proposed a model that: (1) predicted the full behavior of
RC beams wrapped with FRP; (2) accounted for the fact that the
FRP is not bonded to all beam faces; (3) predicted the failure mode;
(4) predicted the effective FRP strain using equations developed
based on testing FRP strengthened beams in torsion [16].
These models were verified using an extensive experimental database that was mainly rectangular beams rather than flanged
beams. The cross-section shape could have a significant effect
on the torsional behavior, as indicated by several researchers
[26–28].
Only 11% of the tested beams examined the usage of anchors, as
shown in Table 1. None of these tested beams was strengthened
using discrete strips; they were strengthened using continuous
jackets. Externally strengthened beams using FRP anchorage systems have been recently gaining attention [29–31]. The American
Concrete Institute Committee 440 indicated that mechanical
anchorages could be used at the termination points of FRP fabrics
to develop larger tensile forces or to increase stress transfer. However, the effectiveness of these mechanical anchorages, along with
the level of tensile stress they can develop, should be heavily scrutinized and substantiated through representative physical testing
prior to field implementation [4]. A more recent state-of-the-art
review conducted by Kalfat et al. concluded that strength improvement due to the use of anchoring FRP materials has been clearly
demonstrated [30]. However, there remains a lack of sufficient
numerical and experimental data in existing literature to develop
extensive databases with the statistical reliability for creating
strength prediction models. Therefore, it is recommended that
the future development of anchorages should focus on examining
the various anchorage types in more detail. As an example, Kalfat
et al. listed over 100 successful experimental tests for using
Brick wall
Floor Slab
Edge beam
(b)
(a)
Fig. 1. Beams under significant torsion (a) inverted flanged beam and (b) spandrel
beam.
strengthened using continuous fully wrapped jackets is significantly higher than those using a continuous U-jacket [8,12]; (4)
the usage of anchors significantly increases the torsional strength
[8,12]; and (5) The anchored extended continuous U-jacket is
much more effective compared to the anchored continuous U-jacket
and as effective as the anchored continuous fully wrapped jacket
[8]. However, a careful examination of the previous studies showed
the following caveats: (1) Both Salom et al. and Deifalla and Ghobarah
indicated that more studies were required to fully understand and
quantify the effect of anchors as well as refine their conclusions[8,12]; (2) Salom et al. studied flanges through anchors and
continuous jackets, which can be impractical and uneconomic in
many cases [8]; and (3) Both Chalioris and Deifalla and Ghobarah
studied T-shaped beams and continuous jackets, even though in
many cases continuous jackets can be uneconomic with respect
to strips and T-shaped beams are less likely to be subjected to significant torsion compared to L-shaped beams [10,12].
A survey of the previous experimental tests conducted on concrete beams externally strengthened using FRP under torsion is
presented in Table 1 [7,19–23,9,11,24,10,25]. We can see that a
Table 1
Survey of torsion testing of RC beams.
Study
Number
of tested
beams
Shape
Rectangular
Anchored
Flanged
Cross section
Fully
wrapped
Direction
Ujacket
Extended
U-jacket
Inclined
45 deg.
Longitudinal
Vertical
Strips
Continuous
Zhang et al. [7]
Ghobarah et al. [19]
Panchacharam and Belarbi [20]
Biddah et al. [21]
Sharobim and Mokhtar [22]
Salom et al. [8]
Deifalla and Ghobarah [23]
Hii and Al-Mahaidi [9]
Ameli et al. [11]
Genidi [24]
Chalioris [10]
Mohammadizadeh and Fadeel [25]
9
8
7
4
7
4
4
4
10
16
8
10
9
8
7
4
7
–
–
1
10
10
6
10
–
–
–
–
–
4
4
–
–
6
2
–
–
–
1
–
–
3
4
–
–
–
–
2
7
8
4
4
5
–
2
4
6
8
6
8
–
–
3
–
2
4
1
–
4
8
2
2
–
–
–
–
–
–
1
–
–
–
–
–
–
2
–
–
–
1
4
–
–
2
–
–
7
6
2
4
5
3
–
–
10
14
8
10
7
5
4
–
5
–
–
4
4
14
3
2
–
2
3
4
2
4
4
Total
91
72
79%
16
18%
10
11%
62
68%
26
28%
1
2%
9
10%
69
76%
48
53%
40
44%
6
2
5
8
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
anchorages in shear, but only a handful of successful experimental
tests for using anchorages in torsion [30].
Using a fully wrapped jacket technique is rarely possible due to
the flange. Therefore, unanchored U-jackets were studied but
found to perform poorly due to premature end de-bonding [10].
Furthermore, Table 1 shows that only 10% of the experimental tests
examined the 45° inclined FRP jackets. Most of the examined jackets were unanchored and/or continuous; however, anchored and/
or strips could be more effective and economic.
Available design guides [4,32] cover most cases of beams externally strengthened using FRP systems subjected to flexure and
shear. However, the case of flanged beams externally strengthened
using an FRP system while subjected to significant torsion is not
addressed. More testing of beams externally strengthened using
FRP systems under torsion is required, with an emphasis on investigating flanged beams, U-jackets, anchors, strips and inclined
jackets.
3. Experimental program
Fig. 2a and b show a schematic diagram and a photo for the test
setup. All tested beams had a length of 1600 mm. The beams were
vertically supported at a distance of 1450 mm center to center.
These supports ensured that the beams were free to twist at both
ends but elongate longitudinally at one end only. The load was applied through a stiff steel beam that was placed diagonally above
the tested beam. The steel stiff beam split the applied load equally
at the free ends of two 400 mm steel arms that were rigidly connected to both ends of the tested beam. From Fig. 2a, we can see
that the beginning and end parts of the tested beam were subjected to combined torsion, shear and flexure. On the other hand,
the middle part (the test region) was subjected to significant torsion. To insure the failure is within the test region the tested beams
were heavily strengthened at the beginning and end of the beam.
For the tested beams, the typical dimensions and the reinforcements (as well as the dial and strain gauge locations) are shown in
Fig. 3. The concrete cover was 25 mm for the web and 15 mm for
the flange and the spacing between the longitudinal bars was
20 mm. The total applied load was measured by a load cell. Electrical strain gauges were used to measure strain in the transversal
and the longitudinal steel reinforcements, as shown in Fig. 3. Dial
gauges were used to measure the vertical deflection and angle of
twist, as shown in Fig. 3.
3.1. Materials
The concrete mix used for the tested beams had a nominal compressive strength of 25 MPa. The longitudinal steel reinforcements
were high tensile steel with a nominal yield stress of 360 MPa and
the shear reinforcements were mild steel with a nominal yield
strength of 240 MPa. Sikawrap Hex-230 carbon fiber reinforced
polymer (CFRP) sheets were used and the resin was Sijadur-41CF.
The CFRP fabric without resin, had thickness and ultimate strain
values of 0.12 mm and 1.7%, respectively. The recorded ultimate
strength for the CFRP coupons impregnated with resin was
700 MPa.
3.2. External strengthening using FRP
During the strengthening procedure, special attention was paid
to attaining a full bond between the RC beam and the FRP fabrics.
The same standard procedure was executed for preparing each
specimen as follows:
(a)
(b)
Fig. 2. Test setup; (a) schematic diagram and (b) photograph.
(1) The concrete surface was leveled and the aggregate was
exposed using a hand held grinder, which benefits the bond
between the FRP fabrics and the concrete.
(2) The concrete edges and corners were rounded to a minimum
radius of 20 mm with the grinder, minimizing the stress
concentration in the fibers.
(3) The concrete surface was cleaned of loose particles or dust
using compressed air.
(4) The prepared concrete surface was impregnated with the
resin, especially at the re-entrance between the flange and
the web.
(5) Each CFRP layer was impregnated with the resin.
(6) These resin impregnated CFRP layers were rolled over the
concrete surface and pressed using a steel roller to eliminate
air bubbles.
(7) Each beam was cured for at least 7 days before testing.
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
(a)
(b)
Fig. 3. Details, and dial and strain gauges of the tested; (a) L-shaped beams and (b) T-shaped beams.
In this study, three strengthening techniques were selected (i.e.,
the U-jacket, the extended U-jacket and the fully wrapped jacket),
as shown in Fig. 4. In the U-jacket, the FRP fabrics are bonded to the
web of the beam with either continuous or discrete strips. In addition, the anchors can be used below the intersection of the web and
the flange. The U-jacket can be normal or inclined with respect to
the longitudinal axis of the tested beam. This technique can be
used in situations where the flange or the slab is inaccessible.
In the extended U-jacket, first introduced by Deifalla and
Ghobarah, the FRP fabrics are bonded to the web and further extended to the flange with either continuous or discrete strips
[23]. In addition, the anchors can be used in the flange [23], or at
the re-entrant corner of the web and the flange [33,34]. The extended U-jacket can be normal or inclined with respect to the longitudinal axis of the tested beam. This technique can be used
where only one side of the flange or the slab is accessible.
In the fully wrapped jacket, the FRP fabrics are wrapped all
around the perimeter of the cross section with either an anchorage
system or an overlap to tie the termination points of the jackets to-
gether. The fully wrapped jacket can be normal or inclined with respect to the longitudinal axis of the tested beam. This technique
has limited applications, such as the case of unrestricted access
to the entire cross section. It is used primarily as a reference for
comparison to provide valuable insight for the effectiveness of
the other tested strengthening techniques.
In this study, eleven beams (RB1, RB1ER6-50, RB1ER6-100, TB1,
TB1ER1, TB1ER5, LB1, LB1ER2, LB1ER3, LB1ER4 and LB1ER7) were
externally strengthened using FRP fabrics and tested under torsion.
The rectangular beams, T-shaped beams and L-shaped beams are
referred to as RB, TB and LB, respectively. Each externally strengthened beam is referred to by a unique label, depending on the
strengthening technique used for this beam: vertical U-jacket
strips (ER1); anchored vertical U-jacket strips (ER2); inclined
U-jacket strips (ER3); anchored inclined U-jacket strips (ER4); extended vertical U-jacket strips (ER5); vertical fully wrapped strips
(ER6); and inclined fully wrapped strips (ER7). The strengthening
techniques used in this investigation were chosen to represent various practical applications. Table 2 shows the details of all the
FRP sheet
Anchor rod
U-jacket
Continuos wrapping
FRP sheet
Anchor rod
Vertical strips
Extended U-jacket
FRP sheet
Inclined strips
(a)
Fully wrapped
(b)
Fig. 4. Externally reinforcing techniques; (a) longitudinal direction and (b) around cross section.
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
Table 2
Details of all tested beams.
Shape
Beam
Strengthening technique
Steel Stirrup ratio
(%)
FRP strip width (Wf)
(mm)
FRP strip spacing (Sf)
(mm)
FRP strips ratio
(%)
Rectangular
RB1
RB1ER6-50
RB1ER6-100
Control beam
Vertical fully wrapped jacket
0.545
–
50
100
–
200
200
–
0.07
0.13
L-shaped
LB1
LB1ER2
LB1ER3
LB1ER4
LB1ER7
Control beam
Anchored vertical U-jacket
45° inclined U-jacket
Anchored inclined U-jacket
45° inclined fully wrapped jacket
0.348
–
100
100
100
100
–
200
200
200
200
–
0.10
0.10
0.10
0.10
T-shaped
TB1
TB1ER1
TB1ER5
Control beam
Vertical U-jacket
Vertical extended U jacket
0.571
–
100
100
–
200
200
–
0.14
0.14
Table 3
Summary of experimental results.
h
(°)
et
(°/m)
6.7
7.84
8.98
2.81
3.55
3.7
44
49
53
0.23
0.27
0.30
Mode I
Mode III
0.24
0.32
0.38
0.50
0.78
8.16
11.56
10.20
12.92
14.96
3.13
4.09
3.91
4.38
5.09
29
39
36
44
52
0.20
0.36
0.39
0.42
0.48
Mode
Mode
Mode
Mode
Mode
0.38
0.53
0.75
11.7
15.23
19.2
3.44
4.69
5.10
43
47
52
0.30
0.29
0.31
Mode I
Mode II
Mode II
GK
(kN m2)
GKcr
(kN m2)
Tcr
(kN m)
wcr
RB1
RB1ER6-50
RB1ER6-100
417
400
441
134
175
175
1.60
1.75
2.89
0.22
0.25
0.38
LB1
LB1ER2
LB1ER3
LB1ER4
LB1ER7
520
640
530
650
692
168
304
170
170
190
2.10
2.72
3.40
4.08
4.76
TB1
TB1ER1
TB1ER5
470
554
575
233
228
197
3.10
5.25
6.71
Beam
(°/m)
tested beams, including cross-section shape, beam designation,
strengthening technique, steel stirrup ratio, FRP strip width (wf),
FRP strip spacing (Sf) and FRP strips ratio. The FRP strips ratio
(qft) is calculated such that:
qft ¼
wf t f pf
Sf Aof
ð1Þ
where tf is the thickness of the FRP sheets, pf is the cross-section
perimeter and Aof is the area of the cross-section.
Tu
kN m
wu
Failure mode
(%)
I
I
II
I
I
the beam resistance significantly dropped down (i.e. load readings
were not increasing). The strength and angle of twist at both the
cracking and the ultimate state were unique for each tested beam.
The cracking was observed at an applied torque and a corresponding angle of twist values of Tcr and wcr, respectively, as shown in Table 3. The recorded values of the ultimate torque resistance and the
corresponding angle of twist were Tu and wu, respectively and are
listed in Table 3.
4.2. Transversal reinforcement strain
4. Experimental results
The behavior of all tested beams is described in this section. Table 3 contains a summary of the experimental results for all of the
tested beams. The table shows the different strengthening techniques versus the initial torsional rigidity (GK), the post-cracking
torsional rigidity (GKcr), the cracking strength (Tcr), the angle of
twist at cracking (wcr), the ultimate strength (Tu), the angle of twist
at ultimate strength (wu), the stirrup strain at ultimate strength (et)
and the failure mode. The relationships between the applied torque
and the angle of twist for all the tested rectangular, L-shaped and
T-shaped beams are shown in Fig. 5a–c, respectively.
4.1. Torsional behavior
The torsional behavior of all tested beams was similar. At the
beginning of the loading, the behavior was linear, with a relatively
large torsional rigidity (GK) until cracking. The value of GK for each
beam was unique and is listed in Table 3. After cracking, the behavior continued to be linear, but with a relatively lower post-cracking
torsional rigidity (GKcr), as shown in Table 3. Before achieving the
ultimate capacity, the behavior became nonlinear with a significantly lower torsional rigidity. The loading was terminated when
The stirrup strain versus the applied torque for the tested rectangular, L-shaped and T-shaped beams is shown in Fig. 6a–c,
respectively. As expected, strain values were very small up till
the onset of cracking. After cracking, stirrup strain values increased
rapidly. The recorded values of the stirrup strain at the ultimate
resistance were listed in Table 3. For the rectangular beams, the recorded values of the transversal reinforcement strain were 0.23%,
0.27% and 0.30% for beams RB1, RB1ER6-50 and RB1ER6-100,
respectively. For the L-shaped beams, the recorded values of the
transversal reinforcement strain were 0.20%, 0.36%, 0.39%, 0.42%
and 0.48% for beams LB1, LB1ER2, LB1ER3, LB1ER4 and LB1ER7,
respectively. For the T-shaped beams, the recorded values of the
transversal reinforcement strain were 0.30%, 0.29% and 0.31% for
beams TB1, TB1ER1 and TB1ER5, respectively. The transversal reinforcement strain values were increased due to the usage of various
FRP strengthening techniques; however, the percentage of increase
was different for each strengthening technique.
4.3. Cracking pattern and failure mode
Due to torsion, beams resist a wave of diagonal compressive
and tensile forces. Both the FRP and steel carry the tensile forces
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
25
LB1
LB1ER2
LB1ER3
LB1ER4
LB1ER7
Applied torque (kN.m)
RB1
20
RB1ER6-50
RB1ER6-100
15
TB1
TB1ER1
TB1ER5
10
5
0
0.00
1.00
2.00
3.00
4.00 0.00 1.00 2.00 3.00 4.00 5.00 0.00
Angle of twist (°/m)
Angle of twist (°/m)
(a)
(b)
1.00
2.00
3.00
4.00
5.00
Angle of twist (°/m)
(c)
Fig. 5. Torsion behavior of tested beams; (a) rectangular, (b) L-shaped and (c) T-shaped.
while the concrete carries compressive forces. Failure was defined
as complete collapse and no ability to sustain any loads (i.e. the
concrete is broken whether by concrete crushing due to compression or section is separated due to excessive cracking). All tested
beams exhibited diagonal spiral cracking (i.e. cracks were propagating all around the cross section in a continuous form) combined
with steel stirrups yielding before failure. However, the cracking
pattern and the failure mode were dependent on the implemented
strengthening technique. Three failure modes were observed:
Mode (I); Mode (II); and Mode (III). Mode (I) is characterized by
steel stirrup yielding followed by diagonal failure (i.e. either concrete strut crushing due to compression forces or excessive diagonal cracking due to diagonal tension forces). Mode (II) is
characterized by steel stirrup yielding followed by FRP end debonding and finally diagonal failure. Mode (III) is characterized
by steel yielding followed by FRP peeling off (intermediate FRP
de-bonding, along the crack direction and at the crack location)
and finally diagonal failure.
For the rectangular beams, the control beam (RB1) experienced
diagonal cracking (as shown in Fig. 7a) with an average angle of
inclination of 44° with respect to the longitudinal axis of the beam.
The beam failed due to Mode (I). Beams RB1ER6-50 and RB1ER6100 experienced diagonal cracking with an angle of inclination of
49° and 53°, respectively, which was larger than that of beam
(RB1) (as shown in Fig. 7b and c). This could be because adding
0.50%
RB1
0.45%
TB1
RB1ER6-50
0.40%
Stirrup strain (%)
the FRP strips increased the transversal reinforcement ratio. They
failed due to Mode (III), accompanied with FRP ripping at the peeling off location, as shown in Fig. 7d.
For the L-shaped beams, the average angles of inclination of the
cracks were 29°, 39°, 36°, 44° and 52° for beams LB1, LB1ER2,
LB1ER3 LB1ER4 and LB1ER7, respectively. The control beams
(LB1, LB1ER2, LB1ER4 and LB1ER7) failed due to Mode (I), while
no FRP de-bonding or rupture was observed (as shown in
Fig. 8a–e). However, beam (LB1ER3) failed due to Mode (II), as
shown in Fig. 8f.
For the T-shaped beams, the average angles of inclination of the
cracks were 43°, 47° and 52° for beams TB1, TB1ER1 and TB1ER5,
respectively. The control beam (TB1) failed due to Mode (I), accompanied by concrete spalling as shown in Fig. 9a. Beams (TB1ER1
and TB1ER5) failed due to Mode (II), accompanied with concrete
flange cover spalling as shown in Fig. 9b and c.
The beams that were strengthened using anchored U-jacket
strips did not fail due to FRP debonding similar to the unanchored
strips; they failed due to diagonal cracking in the flange similar to
the fully wrapped strips. In addition, the rectangular beams
strengthened with fully wrapped strips exhibited diagonal peeling
off at concrete cracking and finally failed due to diagonal cracking
between the strips, while the L-shaped beams strengthened using
fully wrapped strips failed due to diagonal cracking in the flange
without any observed peeling off.
TB1ER1
RB1ER6-100
0.35%
TB1ER5
0.30%
0.25%
0.20%
LB1
LB1ER2
LB1ER3
LB1ER4
LB1ER7
0.15%
0.10%
0.05%
0.00%
0
10
20 0
10
20 0
10
Applied torque (kN.m)
Applied torque (kN.m)
Applied torque (kN.m)
(a)
(b)
(c)
Fig. 6. Strriup strain versus torque of tested beams; (a) rectangular, (b) L-shaped and (c) T-shaped.
20
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
(a)
(b)
Major diagonal
cracks
(c)
(d)
Fig. 7. Cracking pattern of; (a) RB1, (b) RB1ER6-50 and (c) RB1ER6-100, and (d) failure mode of both RB1ER6-50 and RB1ER6-100.
5. FRP contribution
To evaluate the contribution of the FRP external reinforcements
on the torsional behavior, the measured experimental data recorded during the tests will be analyzed. The FRP contribution
for each measured response (i.e., cracking torque; ultimate torque)
was calculated as the difference between the measured value for
the response of the beam externally strengthened using FRP and
that of the control beam. To minimize the effect of the cross-section
shape, dimensions and internal reinforcements on the analysis of
the results, the FRP contribution had to be normalized. Thus, the
percentage ratio of the FRP contribution of any response was calculated as the percentage ratio between the FRP contribution divided
by the response of the control beam having the same cross-section
shape, dimensions and steel reinforcements. The percentage ratios
of the FRP contributions for the cracking strength (denoted as
DTcr), the ultimate strength (denoted as DTu), the angle of twist
(denoted Dwu) and the initial rigidity (denoted as DGK) of the
rectangular, the L-shaped and the T-shaped beams are shown in
Table 4.
5.1. Cracking strength
All of the beams externally strengthened using FRP systems
exhibited an increase in the cracking torque over the control specimen with the same cross-section (DTcr), which was due to the FRP
strips arresting the concrete cracks. However, each strengthening
technique yielded a different level of improvement. From Table 4,
we can determine the following:
(1) For the rectangular beams, the cracking torque of beams
RB1ER6-50 and RB1ER6-100 improved by 9% and 81%,
respectively, over the control beam RB1.
(2) For the L-shaped beams, the cracking torque of beams
LB1ER2, LB1ER3, LB1ER4 and LB1ER7 improved by 30%,
62%, 94% and 127%, respectively, over the control beam LB1.
(3) For the T-shaped beams, the cracking torque of beams
TB1ER1 and TB1ER7 increased by 69% and 116%, respectively, over the control beam TB1.
The degree of cracking strength improvement depends on the
effectiveness of the chosen external strengthening technique.
5.2. Ultimate strength
In general, using FRP as an external reinforcement confined the
concrete and arrested the cracks, thus causing a delay in the failure
and an increase in the ultimate torque (DTu). From Table 4, we can
determine the following:
(1) For the rectangular beams, the ultimate torque of beams
RB1ER6-50 and RB1ER6-100 improved by 17% and 34%,
respectively, over the control beam RB1. We can conclude
that the ultimate torque improvement is linear with the
value of the FRP strips ratio.
(2) For the L-shaped beams, the ultimate torque of beams
LB1ER2, LB1ER3, LB1ER4 and LB1ER7 improved by 42%,
25%, 58% and 83%, respectively, over the control beam LB1.
(3) For the T-shaped beams, the ultimate torque of beams
TB1ER1 and TB1ER7 increased by 30% and 64%, respectively,
over the control beam TB1.
Externally strengthening the beams with FRP improved the ultimate strength of all tested beams. However, the level of improvement is dependent on the selected strengthening technique.
5.3. Ductility improvement (Dwu)
Although FRP fabrics have been successfully implemented in
various civil engineering applications over the last few decades,
ductility has been a serious concern commonly raised by designers
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
Major diagonal
cracks
(a)
(c)
Major diagonal
cracks
(b)
(d)
Major diagonal
cracks
(e)
(f)
Fig. 8. Cracking pattern of; (a) LB1 and (b) LB1ER2, and failure modes of; (c) LB1, (d) LB1ER2, (e) LB1ER7 and (f) LB1ER3.
[31]. Thus, the growth of the FRP market requires comprehensive
investigations into the ductility of various applications.
Ductility in FRP (i.e., brittle material with no yield plateau)
externally strengthened members arises from providing concrete
confinement (i.e. columns and fully wrapped beams) and arresting
cracks as well as resisting tensile forces [23,12]. For beam in torsion, the diagonal concrete struts are subjected to compression
similar to columns. Having FRP strips wrapped around the beams
improve the compression behavior through providing a lateral
hoop pressure. This lateral pressure confines the concrete struts
which increases both the stress and strain. For the current, the observed increase in the transversal strain is evidence of increase in
the compressive diagonal strain by Mohr circle [16]. Redefining
ductility as the increase in the ability of the beam to sustain larger
deformations before failure due to the external FRP reinforcements
was first introduced by Deifalla and Ghobarah [23]. Moreover,
Chalioris and Karayannis have used indices-ratios of the rotation
at the point of 85% of the maximum torsional moment (assumed
as the end of the reliable response range) to the rotation at the
maximum torsional moment (or to the rotation at the cracking torsional moment) to measure the torsional ductility [28]. Furthermore, a recent comprehensive literature review concluded that in
the case of FRP wrapping, ductility can be achieved through
enhancing the energy absorption ability of the existing non-FRP
materials such as concrete and steel [31].
In this study, the ratio between the increase in the maximum
deformation of the beam externally strengthened using FRP to that
of the control beam with the same cross-section shape and details
was used as an indication of improved ductility (Dwu). From
Table 4, we can determine the following:
(1) For the rectangular beams, the ductility of beams RB1ER6–
50 and RB1ER6–100 improved by 26% and 32%, respectively,
over the control beam RB1 (control beam). We can conclude
that ductility improvement is not linear with the reinforcement ratio of FRP strips (qft).
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
(a)
(b)
Concrete spalling
Peeling off at
diagonal cracks
(c)
Fig. 9. Cracking pattern and failure mode of; (a) TB1, (b) TB1ER1 and (c) TB1ER5.
The ductility improvement for each beam is significantly dependent on the effectiveness of the strengthening technique.
Table 4
FRP contribution for all beams.
DTcr
(%)
DTu
(%)
Dwu
(%)
9
81
17
34
26
32
4
6
LB1ER2
LB1ER3
LB1ER4
LB1ER7
30
62
94
127
42
25
58
83
31
25
40
63
23
2
25
33
TB1ER1
TB1ER5
69
116
30
64
36
48
18
22
Specimen
RB1ER6-50
RB1ER6-100
DGK
(%)
(2) For the L-shaped beams, the ductility of beams LB1ER2,
LB1ER3, LB1ER4 and LB1ER7 improved by 31%, 25%, 40%
and 63%, respectively, over the control beam LB1.
(3) For the T-shaped beams, the ductility of beams TB1ER1 and
TB1ER7 increased by 36% and 48%, respectively, over the
control beam TB1.
5.4. Initial torsional rigidity
The initial torsional rigidity was calculated as the rate of change
of the applied torque with respect to the unit angle of twist before
cracking. In general, the effect of FRP external reinforcements
(DGK) was insignificant, ranging between 4% and 33%. From Table 4, we can determine the following:
(1) For the rectangular beams, the torsional rigidity of beam
(RB1ER6-50) decreased by 4% and the torsional rigidity of
beam (RB1ER6-100) improved by 6% over beam RB1. Thus,
we can conclude that torsional rigidity of the rectangular
beams was slightly affected by the FRP reinforcement.
(2) For the L-shaped beams, the torsional rigidity of beams
LB1ER2, LB1ER3, LB1ER4 and LB1ER7 improved by 23%, 2%,
25% and 33%, respectively, over the control beam LB1.
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A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
Fig. 10. Torsion gain versus FRP-ER ratio for different reinforcing techniques.
(3) For the T-shaped beams, the torsional rigidity of beams
TB1ER1 and TB1ER7 increased by 18% and 22%, respectively,
over the control beam TB1.
The initial torsion rigidity was slightly improved due to externally strengthening the beams using FRP systems. However, the level of improvement depends on the strengthening technique.
strength and ductility of 213% and 133%, respectively, when compared to those of the U-jacket strips technique (TB1ER1). The extended U-jacket strips improved the ability of the beams to
sustain more twist without further load capacity reduction when
compared to the U-jacket strips. Extending the FRP to the flange arrested the flange cracks, consequently enhancing the behavior.
6.3. Strengthening technique versus FRP Strip Ratio
6. Effectiveness of strengthening techniques
6.1. Anchored U-jacket
Beams that are externally strengthened using an FRP U-jacket
while subjected to torsion fail prematurely due to end de-bonding.
Thus, many researchers have suggested the use of anchorage systems [8,10,12,23]. However, it was suggested that further testing
be conducted to quantify the effect of the anchors and refine the
conclusions [8,12].
In this study, using anchored inclined U-jacket strips (LB1ER4)
significantly increased the strength and ductility over the regular
inclined U-jacket strips (LB1ER3) by values of 232% and 160%,
respectively. When comparing the anchored inclined U-jacket
strips (LB1ER4) with the inclined fully wrapped strips (LB1ER7),
the strength and ductility of the anchored U-jacket strips were
70% and 63.3% of the fully wrapped strips, respectively. However,
using the inclined U-jacket strips (LB1ER3) for externally strengthening RC beams increased the strength and ductility in a limited
capacity, achieving values of only 30% and 39.7%, respectively,
when compared with the inclined fully wrapped strips (LB1ER7).
Using the anchored inclined U-jacket strips led to significant
improvements over the inclined U-jacket strips.
6.2. Extended U-jacket
Although the FRP U-jacket strips are suitable as a strengthening
technique for most practical situations, their effectiveness is poor
when compared with other techniques. In addition, the anchored
extended continuous U-jacket, first proposed by Deifalla and
Ghobarah, was found to perform better than the anchored continuous U-jacket and as effective as the continuous fully wrapped jacket
[23]. However, this strengthening technique required anchorage in
the flange (i.e., slab), which is impractical in many situations.
In the current study, an unanchored extended U-jacket strip
(TB1ER5) was implemented. It was found to be more effective than
using the U-jacket strips (TB1ER1), resulting in an increase in the
All of the relevant previous experimental results [8,10,12] and the
results from the current study were gathered and analyzed. Fig. 10
shows the percentage of normalized FRP contributions to the ultimate
torsion (DTu) versus the FRP strips ratio (qft) for different strengthening techniques as previously shown. Fig. 10 shows that the ultimate
torsion gain has a direct relationship with the FRP reinforcement ratio
for the same strengthening technique. However, at the same FRP reinforcement ratio, the ultimate torsion gain significantly depends on
the effectiveness of the strengthening technique.
7. Conclusions
Eleven RC beams were tested under torsion and the following
conclusions were reached:
Using the same FRP reinforcement ratio, for vertical U-jacket,
inclined U-jacket, anchored inclined U-jacket, extended
vertical U-jacket, vertical fully wrapped and inclined fully
wrapped, the torsion gain due to FRP was 6%, 25%, 30%, 42%,
64% and 83%. The level of torsional behavior enhancement
for flanged beams externally strengthened with FRP was
not only dependent on the ratio of the FRP reinforcement
but also on the effectiveness of the implemented strengthening technique.
The anchored inclined U-jacket strip is significantly more
effective than the regular inclined U-jacket strip. It increased
the ultimate strength and ductility over the regular inclined
U-jacket strip by 232% and 160%, respectively.
The anchored inclined U-jacket strip is comparable with the
inclined fully wrapped strip. Using the anchored inclined
U-jacket strip increased the ultimate strength and ductility
by 70% and 63.3%, respectively, relative to the inclined fully
wrapped strip.
The extended vertical U-jacket strip is more effective than
the vertical U-jacket strip, resulting in an increase in the ultimate strength and ductility of 213% and 133%, respectively,
compared to that of the vertical U-jacket strip technique.
A. Deifalla et al. / Engineering Structures 56 (2013) 2065–2075
Acknowledgment
The authors would like to express their gratitude for the Civil
Engineering Department, Mataria Branch, Helwan University for
using their lab facility in order to conduct this experimental study.
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