International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 1, January 2019, pp.112–127, Article ID: IJCIET_10_01_012
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
©IAEME Publication
Scopus Indexed
TORSIONAL BEHAVIOR OF REPAIRED
REINFORCED CONCRETE BEAMS WITH
MULTI-BOUNDARY CONDITIONS
Hayder Al-Khafaji
Lecturer: Civil engineering Department
University of Babylon, Hilla, Iraq
ABSTRACT
This paper describes a finite element analysis for reinforced concrete beams of
multi-boundary conditions end repaired by CFRP and fc85 section tested under pure
torsion, classified according boundary conditions in two types cantilever and simply
supported beams every type include 13 beams divided according repaired to three
groups and control beam. The variables considered for group one and two included
the beam faces number that will be strengthened, the effect of CFRP Strips numbers
while the third group included repaired by fc85. The results of the repaired test beams
revealed that the technique of used thefc85very effective in simply supported beam
more than cantilever beam by about 97.5% while used repaired by CFRP more than
in cantilever. The torque resistance increased in all beams which repaired by
550.65%, 137% in cantilever beams and 11.78%, 139% in simply supported beams for
CFRP and fc85respectively, while the max twist decreased in all beams by 69.46%,
79.5% in cantilever beams and 26.5%, 62.19%in simply supported beams for CFRP
and fc85respectively.
Keywords: Reinforced Concrete Beam, Torsional Strengthening, CFRP strips,
Boundary Conditions, Repaired Beam.
Cite this Article: Hayder Al-Khafaji, Torsional Behavior of Repaired Reinforced
Concrete Beams with Multi-Boundary Conditions, International Journal of Civil
Engineering and Technology (IJCIET), 10 (1), 2019, pp. 112–127.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=1
1. INTRODUCTION
The retrofitting of structures is promoted rather than demolishing and reconstruction of
deteriorated structures. Attention has also given to increase the load carrying capacity of
existing structures to increase the usage capacity or to change the intended usage so there is a
large need to strengthen concrete structures around the world. Retrofitting of structures using
fc85 and Carbon Fiber Reinforced Polymer materials is accepted as a sustainable and effective
method.
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High strength concrete was used to repair of all types of structural concrete elements in
buildings, water retaining structures, industrial plants, bridges, etc. where provide high
strength and extremely low shrinkage properties are required.
Externally bonded, CFRP sheets are currently being studied and applied around the world
for the repair and strengthening of structural concrete members [1]. CFRP materials are of
great interest to the civil engineering community because of their superior properties such as
high stiffness and strength has well as ease of installation when compared to other repair
materials.
David, E.,Djelal, C. and Buyle-Bodin , F. [2],using externally CFRP strips to bounded
beams and their results show that CFRP is very effective for flexure strengthening.
S. Panchacharam and A. Belarbi [3], makings experimental study to investigate the
torsional behavior of RC beams strengthened with externally bonded GFRP sheets. The
variables considered in this study are fiber orientation (parallel and perpendicular to the
longitudinal axis of the beam). The torsional reinforced concrete beams strengthened with
GFRP sheets exhibited significant increase in their cracking and ultimate strength as well as
ultimate twist deformations.
R.Dhanaraj and E.Chandrasekaran [4], investigated the numerical study on un retrofitted
and retrofitted reinforced concrete beams subjected to combined bending and torsion by
ANSYS. Then the study has been extended for the same reinforced concrete beams retrofitted
with carbon fiber reinforced plastic composites with ±45° and 0/90° fiber orientations. The
present study reveals that the CFRP composites with ±45° fiber orientations are more
effective in retrofitting the RC beams subjected to combined bending and torsion for higher
torque to moment ratios.
Bonfiglioli et al (2004)[5], carried out an experimental and theoretical study to evaluate
the capability of dynamic testing to give useful information about the stiffness recovery due to
external CFRP strengthening of RC beams which were previously damaged. Specimens were
damaged under cycle loading until cracks appeared. Then CFRP used for repairing cracking
specimens. The theoretical results are in good agreement with the experimental ones. The
research suggests that dynamic testing can be used to obtain useful information about the
effectiveness of the strengthening system.
Ali (2007)[6], casted twenty eight reinforced concrete beams to investigate the behavior of
using CFRP to repaired and strengthened beams failed in flexure and shear zone. All beams
had been tested as a simply supported beam under two point of loading. From the results can
see the use of CFRP as external strengthening has significant effect on ultimate load, crack
pattern and deflection. The repaired beams reach (95% to 97%) of ultimate load in
comparison with those strengthened in the same way by CFRP.
AL-Saidy et al. (2007)[7], studied behavior of corroded damaged reinforced concrete
beams repair/strengthening with CFRP sheets. Ten beams were casted and tested up to failure.
Damaged beams were repaired by bonding CFRP sheets to the tension side to restore the
strength loss due to corrosion. From the results can see The use of CFRP sheets for
strengthening corroded reinforced concrete beams increasing the ultimate strength of repaired
specimens. Deflection was increased for all repaired beams as compared with control beam.
Abed Al-Amery (2009)[8], repaired ten damaged reinforced concrete beams at flexural
region. Steel and CFRP palates used for repairing work to investigate the effect of repairing
materials in restoring the original stiffness and capacity for damage beams. Beams tested as
simply supported beam under two point loading. It was observed that ultimate can be
increased up to (121.4%) in the case of using steel plates. While deflection was decreased to
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Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
(15.4%) times .In case of using CFRP plates, the ultimate can be increased up to (64.3%).
While deflection was decreased to (28.6%) times of the original beams.
Nada S. Assi [9], using finite element method to adopted by ANSYS program for four
beams strengthened in flexure with different length of CFRP sheet to confirm the theoretical
calculations as well as to provide a valuable supplement to the laboratory investigation of
behavior of beams. Good agreement with the experimental test is obtain and this study shows
that the optimum length of CFRP plate equal to 83% of the full span length [10,11].
T.Abdo and R. Mabrouk[12],studied the behavior of simply supported RC beams with
openings subjected to pure torsion then verified using FEM analysis program ANSYS16.
Good agreement between the experimental and numerical results is found. The torque-rotation
relationship for all the beams under study was linear up to the cracking torque and after that it
became nonlinear.
2. MATERIALS CHARACTERISTICS:
The materials of the structural elements that analysis in this study include concrete, steel
reinforcing bars, Cempatch S and CFRP. The finite element models adopted have a number of
parameters, which are summarized in Table (1).
Table (1) Parameters for elements used in F.E. Model for beam
Representation
Element Type
Concrete
Solid65
Steel Reinforcement
Link180
CFRP
Shell41
Cempatch S
Solid65
Steel plate
Solid185
Characteristics
compressive strength (fc')=30 MPa
Poisson's ratio=0.2
modulus of elasticity=25742 MPa
ultimate strain=0.003
Ø16, Ø12, Ø10
Yield strength=410 MPa
compressive strength (fc')=85 MPa
Poisson's ratio=0.17
modulus of elasticity=43332 MPa
ultimate strain=0.0045
modulus of elasticity=200000 MPa
Poisson's ratio=0.3
3. NUMERICAL ANALYSIS
The finite elements representation using ANSYS16.1 program has been applied in this study
to know the validate of the numerical representation of the reinforced concrete beams
strengthening with Cempatch S and CFRP subjected to pure torsion. Twenty six reinforced
concrete beams of 500*250 mm cross-section and 2550 mm length were tested in this study
Fig (1). Schematic representations of the repairing and strengthening schemes are shown in
Fig (2) and Table (2) shows the cases of beams.
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Figure (1) Details of section beams for simply supported and cantilever
Repaired by CFRP
Repaired by strip CFRP
Repaired by CFRP
Repaired by strip CFRP
Repaired Cempatch S
Repaired Cempatch S
Figure (2) Distribution repaired of beams for simply support and cantilever
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Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
Designations:
C30= compressive strength fc'=30 MPa
C85= compressive strength fc'=85 MPa
CFRP= Carbon Fiber Reinforced Polymer
C=cut at the edge of beam
S =strip of beam length
4 , 3 =4edge and 3 edge
C4,C3 =Cover from 4 edge and 3 edge
Table (2) Details beams for simply supported
C30+CFRP4
C30+CFRP3
C30+CCFRP4
C30+CCFRP3
C30+SCFRP4
C30+SCFRP3
C30+SCCFRP4
C30+SCCFRP3
C85+C4
C85+C3
C85+C4+20
C85+C3+20
Group One
Group Two
Group Three
4. FINITE ELEMENT IDEALIZATION
A finite element analysis requires meshing of the model. In other words, the model is divided
into a number of small elements. Meshing, load and boundary conditions for beams are shown
in Fig (3).
Figure (3) Geometry of the numerical model for simply support and cantilever beams
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5. RESULTS AND DISCUSSIONS
In this section, the results obtained from ANSYS 16.1 are displayed for 26 beams divided
according boundary condition in two types cantilever and simply support each type include 13
beams. Because there is no experimental program for this research and compare it with the
results of the ANSYS. Therefore, the effectiveness of the program was verified through
another research that contains experimental results [3]. The general behavior of beams of
finite element represented in the torque-twist plots showed good convention with the data of
test from the experimentally tested. The torque-twist curves were show in Fig (4)to(6) and
Table(3).
Designations
A90W4:90 degree complete wrap
A0L4:0 degree, 4 sides
Table (3) Comparison between experimental and numerical ultimate torque and twist
Beam
reference
A90W4
A0L4
Ultimate Torque (kN-m)
Ultimate Twist (rad/mm)
Percentage
Percentage
Experimental Numerical
Experimental Numerical
Difference %
Difference %
18
19.5
-8.3
110
104
5.45
45
48
-6.67
70
63
10
29
31.25
-7.76
168
152
9.53
Figure (4) Torque-Twist relationship of reference beam
Figure (5) Torque-Twist relationship of
beam(A90W4)
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Figure (6) Torque-Twist relationship of
beam(A0L4)
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The previous tables and figures present a comparison between experimental, numerical
results related to load, deflection. This comparison shows in general that the numerical
models are stiffer, and the numerical analyses give a smaller result for the deflection and
greater for ultimate load. These differences may be due to the following reasons:

The concrete of experimental samples is not perfectly homogeneous as assumed in the
numerical models.

The compressive strength of the tested concrete cubes may not represent exactly the actual
compressive strength.
Simply support
This type of boundary condition include 13 beams divided according repaired three groups
and control beam without repaired. The result of torque and twist for control beam was
(45kN.m) and twist (0.00196 rad/mm) as show in Fig (7).
Figure(7) Torque-Twist relationship of control beam
Group one:
This group consisted of four beams were repaired by CFRP along the length of beam. the
parameters of this group number of faces strengthened of beam. CFRP was continues around
the beam and was cut off in the area of cover for anther beams for four and three faces
respectively. Torque twist curve for all beams are shown Fig (8). The beast beam for this
group was (C30+CFRP4) by increase torque by (11.78%).
Figure (8) Torque-Twist relationship of group one
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Group two:
This group consisted of four beams also repaired by CFRP. CFRP was shaped strips each
150mm along length of beam. Parameters of this group like group one. Torque twist curve for
all beams are shown Fig (9). The beast beam for this group was (C30+SCFRP4) by increase
torque by (9.11%).
Figure(9) Torque-Twist relationship of group two
Group three
This group consisted of four beams also repaired by Cempatch S. the parameters of this group
number of faces repaired and depth of repaired inside the beam. Torque twist curve for all
beams are shown Fig (10). The beast beam for this group was (C85+C4+20) by increase
torque by (139%).
Figure(10) Torque-Twist relationship of group three
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Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
Table (4) ultimate torque, percentage variation of maximum of ultimate torque and twist for simply
support beams
Control beam
Group one
Group two
Group three
Beams
simply support
C30+CFRP4
C30+CFRP3
C30+CCFRP4
C30+CCFRP3
C30+SCFRP4
C30+SCFRP3
C30+SCCFRP4
C30+SCCFRP3
C85+C4
C85+C3
C85+C4+20
C85+C3+20
T(kN.m)
45
50.3
48.2
49.4
46.7
49.1
47.3
48.6
45.9
78.4
70.4
107.55
88.1
Percentage%
------11.78
7.11
9.78
3.78
9.11
5.11
8
2
74.22
56.44
139
95.78
θ(rad/mm)
0.00196
0.00214
0.00235
0.002
0.0016
0.00201
0.00161
0.00177
0.00156
0.00208
0.00203
0.00324
0.00212
Cantilever
This type of boundary condition include 13 beams divided according repaired three groups
and control beam without repaired. The result of torque and twist for control beam was
(22.9kN.m) and twist (0.00678rad/mm) as show in Fig (11).
Figure (11) Torque-Twist relationship of control beam
Group one
Parameters in this group like group one in simply support only different in boundary
condition . Torque twist curve for all beams are shown Fig (12).the beast beam for this group
was (C30+CFRP4) by increase torque by (550.6%).
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Figure (12) Torque-Twist relationship of group one
Group two
Parameters in this group like group two in simply support only different in boundary
condition. Torque twist curve for all beams are shown Fig (13). The beast beam for this group
was (C30+SCFRP4) by increase torque by (514.6%).
Figure(13) Torque-Twist relationship of group two
Group three
Parameters in this group like group three in simply support only different in boundary
condition. Torque twist curve for all beams are shown Fig (14). The beast beam for this group
was (C85+C4+20) by increase torque by (137.8%).
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Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
60
Torque(kN.m)
50
40
30
C85+C4 Cantilever
C85+C3 Cantilever
C85+C4+20 Cantilever
C85+C3+20 Cantilever
20
10
0
0
0.002
0.004
0.006
0.008
0.01
Twist(rad/mm)
Figure(14)Torque-Twist relationship of group three
Table (5) ultimate torque, percentage variation of maximum at ultimate torque and twist for simply
support beams
Control beam
Group one
Group two
Group three
Beams
T
Cantilever
C30+CFRP4
C30+CFRP3
C30+CCFRP4
C30+CCFRP3
C30+SCFRP4
C30+SCFRP3
C30+SCCFRP4
C30+SCCFRP3
C85+C4
C85+C3
C85+C4+20
C85+C3+20
θ
22.9
Percentage%
--------
0.00678
149
113.85
146
107.55
140.7375
103.95
127.0125
95.5125
40.275
38.25
54.45
48.15
550.655
397.16
537.55
369.65
514.57
353.9
454.64
317.08
75.87
67.03
137.77
110.26
0.0319
0.0479
0.0308
0.045
0.0291
0.0427
0.0245
0.0385
0.00367
0.00775
0.00408
0.00650
Effect of variable Parameters
Through the following Fig (15) to (18), the effect of each parameter, in the present study, on
the beams behavior is studied.
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60
60
50
50
Torque(kN.m)
Torque(kN.m)
Hayder Al-Khafaji
40
40
30
30
Simply support
C30+CFRP4
C30+CCFRP4
C30+SCFRP4
C30+SCCFRP4
20
10
0
0
0.001
0.002
Simply support
C30+CFRP3
C30+CCFRP3
C30+SCFRP3
20
10
0
0.003
0
Twist(rad/mm)
0.0005
0.001
0.0015
0.002
0.0025
Twist(rad/mm)
Figure(15) the effective area of CFRP for simply supported beams
100
80
Torque(kN.m)
100
Torque(kN.m)
120
80
60
60
40
40
Simply support
C85+C4
C85+C4+20
20
0
0
0.001
0.002
0.003
Simply support
C85+C3
C85+C3+20
20
0
0.004
0
0.0005
Twist(rad/mm)
0.001
0.0015
0.002
0.0025
Twist(rad/mm)
Figure(16) the effectivedepth of Cempatch S for simply support
160
120
140
100
120
Torque(kN.m)
Torque(kN.m)
100
80
60
Cantilever
C30+CFRP4 Cantilever
C30+CCFRP4 Cantilever
C30+SCFRP4 Cantilever
C30+SCCFRP4 Cantilever
40
20
0
0
0.01
0.02
0.03
80
60
Cantilever
C30+CFRP3 Cantilever
C30+CCFRP3 Cantilever
C30+SCFRP3 Cantilever
C30+SCCFRP3 Cantilever
40
20
0
0.04
0
Twist(rad/mm)
0.01
0.02
0.03
0.04
0.05
Twist (rad/mm)
Figure(17) the effective area of CFRP for cantilever
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0.06
60
60
50
50
40
40
Torque(kN.m)
Torque(kN.m)
Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
30
20
Cantilever
10
C85+C4 Cantilever
C85+C4+20 Cantilever
0
0
0.002
0.004
0.006
30
20
Cantilever
10
C85+C3 Cantilever
C85+C3+20 Cantilever
0
0
0.008
Twist (rad/mm)
0.002
0.004
0.006
0.008
0.01
Twist (rad/mm)
Figure(18) the effectivedepth of Cempatch S for cantilever
A conclusion the curves of torque-twist which is presented in Fig (15) to (18) indicates the
following points:








The increase in ultimate torque in the case of 4 faces by (11.78 and 9.11)%for beams
(C30+CFRP4 and C30+SCFRP4,) respectively for simply supported, and (550.6 and
514.5)% for beams (C30+CFRP4cantilever and C30+SCFRP4 cantilever) respectively for
cantilever.
The increase in ultimate torque in the case of 3 faces by (7.11 and 5.11)% for beams
(C30+CFRP3 and C30+SCFRP3) respectively for simply supported, and (397and
353.9)% for beams (C30+CFRP3cantilever and C30+SCFRP3 cantilever) respectively for
cantilever.
The decrease in twist at the same torque of control beam in the case of 4 faces by (26.53
and 25.5)% for beams (C30 + CFRP4 and C30 + SCFRP4, C30) respectively for simply
support, and (67.216)% for beams (C30+CFRP4cantilever) for cantilever.
The decrease in twist at the same torque of control beam in the case of 3 faces by (25.5
and 25)% for beams (C30 + CFRP3and C30 + SCFRP3) respectively for simply support ,
and (69.16 and 69.46)% for beams (C30+CFRP4 cantilever and C30+SCFRP4 cantilever)
respectively for cantilever.
When repaired by fc85 the ultimate torque increase (74.22 and 139)% and the twist at the
same torque of control beam decrease(55.76 and 62.2)% for beams(C85+C4 and
C85+C4+20) respectively for simply support, and (75.87 and 137.77)%, (75.6 and 79.5)%
for beams (C85+C4cantilever and C85+C4+20cantilever) respectively for cantilever.
Repaired from 4 edge by CFRP have given better results from 3 edge and more stiffness
in two types of boundary conditions, but were more effective in the case of cantilever
from the simply support by (196%).
The technique of used the Cempatch S material very effective in simply support more than
cantilever of 97.5% and then when increase the depth of Cempatch S material inside the
beam was become more stiffness.
One can see that the beam of all beams for two type of boundary condition, for simply
supported (C85+C4+20) which repaired by Cempatch S material from four side and for
cantilever (C30+CFRP4 cantilever) Which repaired by CFRP.
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6. CRACK PROPAGATION
The ANSYS16.1 program registers the crack propagation at each applied load step. Cracks
patterns obtained from the finite element analysis by using the Crack/Crushing plot option, as
shown in Fig (19).
Torsional reinforced concrete beams were repaired by CFRP sheets and fc85 the
distribution of cracks has changed about the control beam this indicates that the behavior of
the beams and the distribution of the stresses have changed, where the repaired of the simply
support beams led to the decrease of cracks that was it clear through a small percentage
increase of ultimate torque (11.78%) for CFRP and (139%) for fc85 for beams (C30+CFRP4)
and(C85+C4+20)respectively while the cantilever beams increase the number of cracks due to
increase the ultimate torque high percentage (550.6%)for CFRP and (137%) for fc85 for
beams (C30+CFRP4) and (C85+C4+20)respectively.
simply supported beams
Cantilever beams
Figure(19) Crack propagation at ultimate load for simply supported and cantilever beams
7. STRESS AND MODE OF FAILURE
Fig (20) to (21) show the stress and mode of failure.
Simply
supported
beams
Cantilever
beams
Figure(20) stress at ultimate load for simply supported and cantilever beams
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Torsional Behavior of Repaired Reinforced Concrete Beams with Multi-Boundary Conditions
Simply
supported
beams
Cantilever
beams
Figure (21) mode of failure for simply supported and cantilever beams
8. CONCLUSIONS

The beams of repaired with CFRP and Cempatch S material whether, four or three faces for
two type of boundary condition were proved that an effective way, if not give the improved
properties return beam to the control beam.

The repaired with CFRP led to increase of ultimate torque force by (11.78%) for simply
support and (550.6%) for cantilever.

The repaired with Cempatch S material led to increase of ultimate torque force by (139%) for
simply support and (137.7%) for cantilever.

Torsional reinforced concrete beams were repaired by CFRP sheets and Cempatch S the
distribution of cracks has changed about the control beam this indicates that the behavior of
the beams and the distribution of the stresses have changed, where the repaired of the simply
support beams led to the decrease of cracks that was it clear through a small percentage
increase of ultimate torque while the cantilever beams increase the number of cracks due to
increase the ultimate torque high percentage.

For simply support beams were repaired with Cempatch S material were the best and which
reaches up to (91.36%), higher than beams were repaired with CFRP which reaches an
increase to (7.1%).

For cantilever beams were repaired with CFRP were the best and which reaches up to
(436.9%), higher than beams were repaired with Cempatch S material which reaches an
increase to (97.7%).

For the same torque decrease the twist deformations in beams which repaired by CFRP and
Cempatch S material (26.53%), (62.2%)respectively for simply support and (69.46%),(79.5%)
respectively for cantilever
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REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
Meier, U. : "Post-strengthening by continuous fiber sheets in Europe. Proceedings of
Third International Symposium, Non-Metallic (FRP) Reinforcement for Concrete
Structures", Vol. 1, Japan Concrete Institute, Tokyo, pp. 41–56, 1997.
David ,E.,Djelal, C. and Buyle-Bodin , F.: " Repair and Strengthening of Reinforced
Concrete Beams using Composite Materials", second Int. PhD. Symposium in Civil
Engineering, 1998 Budapest, WWW.vbt.bme.hu.
S. Panchacharam and A. Belarbi: "Torsional Behavior of Reinforced Concrete Beams
Strengthened with FRP Composites", First FIB Congress, Osaka, Japan, October 1319,2002.
R.Santhakumar R.Dhanaraj and E.Chandrasekaran "Behaviour of retrofitted reinforced
concrete beams under combined bending and torsion".
Bonfiglioli, B., Migo, S., M., Pascale, G., "Dynamic Testing of Reinforced Concrete
Beams Damaged and Repaired with Fiber Reinforced Polymer Sheets", Journal of
materials in civil engineering, ASCE, September 2004.
Ali, D., D., "Experimental and Theoretical Investigation of the Behavior of Reinforced
Concrete Beams Strengthened by Fiber Reinforced Polymer" Ph.D. Thesis, University of
Baghdad, January 2007.
Al-Saidy, A., H., Al-Harthy, A., S., Abdul-Halim, M., Al-Jabri, K., S., Al-shidi, N.,
M.,"Repair Strengthening of Corrosion Damaged Concrete Beams with Fiber Reinforced
Polymers Sheets", University of Patras, Patras, Greece, July 2007.
Abed Al-Amery, S., J., "Behavior of RC Beams Repaired with Steel and CFRP Plates",
M.Sc. Thesis, AI -Mustansiriya University, Iraq, January- 2009.
Nada S. Assi: " The Effect of Carbon Fiber Reinforced Polymer Length on the
Strengthened of Concentrically Loaded Reinforced Concrete Beams : Finite Element
Analysis", Vol. 32, Part (A), No.7, Eng. & Tech. Journal, pp. 1671-1683, 2014.
Kadhim Naief Kadhim and Ghufran A. (The Geotechnical Maps For Gypsum By Using
Gis For Najaf City (Najaf - Iraq) (IJCIET), Volume 7, Issue 44, July-August 2016.
Hassan and Kadhim Naief Kadhim (Development an Equation for Flow over Weirs Using
MNLR and CFD Simulation Approaches). (IJCIET), Volume 9, Issue 3, (Feb 2018)
T. Abdo and R. Mabrouk" Effect of web openings on the structural behavior of RC beams
subjected to pure torsion"
http://www.iaeme.com/IJCIET/index.asp
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