DOI: 10.13140/2.1.3631.9041 It becomes a common practice to strength and repair reinforced concrete columns by wrapping them with GFRP sheets. The aim of this research is to develop a formula to describe the relation between the gain of strength of reinforced concrete square columns, their longitudinal reinforcement and number of warped layers of GFRP sheets. The research is based on simulating loading tests of a set of 12 reinforced concrete columns with different reinforcement ratios and different number of warped layers of GFRP sheets using ANSYS software. The outputs of the ANSYS models are verified using experimental tests results carried out by the author in earlier research. The results of the study are used to develop a proposed formula to correlate the axial capacity of the warped square RC column with its reinforcement ratio and the confining stress caused by the sheets. Values from both proposed formula design and formula of Egyptian Code of Practice (ECP) are compared with ANSYS outputs and experimental results. The final conclusion is that gained strength due to confining equals to (confining stress / Fcu)

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THEORETICAL STUDY FOR R.C. COLUMNS STRENGTHENED
WITH GFRP WITH DIFFERENT MAIN STEEL RATIO
Dr. Amr Hussein A. Zaher, Ass. Prof., Str. Dpt. Faculty of Engineering, Ain Shams Uni., Egypt.
Dr. Ahmed M. Ebid, Lecturer Str. Dpt., Faculty of Engineering & Tech., Future Uni. Cairo, Egypt,
ahmed.ebid@fue.edu.eg
ABSTRACT
It becomes a common practice to strength and repair reinforced concrete columns by wrapping
them with GFRP sheets. The aim of this research is to develop a formula to describe the relation
between the gain of strength of reinforced concrete square columns, their longitudinal reinforcement
and number of warped layers of GFRP sheets. The research is based on simulating loading tests of
a set of 12 reinforced concrete columns with different reinforcement ratios and different number of
warped layers of GFRP sheets using ANSYS software. The outputs of the ANSYS models are
verified using experimental tests results carried out by the author in earlier research. The results of
the study are used to develop a proposed formula to correlate the axial capacity of the warped
square RC column with its reinforcement ratio and the confining stress caused by the sheets.
Values from both proposed formula design and formula of Egyptian Code of Practice (ECP) are
compared with ANSYS outputs and experimental results. The final conclusion is that gained
strength due to confining equals to (confining stress / Fcu).
Keywords: Columns, GFRP, strengthened, specimens.
INTRODUCTION
In the last decade, the effect of external application of fiber-reinforced polymers (FRP) plates and
wraps to reinforced concrete beam-column joints to increase their performance has been
investigated theoretically and experimentally. Previous to this, steel jackets were used to reinforce
the joint area, as well as the use of R.C. jackets. The use of flat and corrugated steel plates, have
also been investigated. However, these options have been found to be labor intensive, requiring a
high level of workmanship, and often add considerable weight to the elements. Additionally, steel
plates need corrosion protection and their attachment requires either the use of epoxy adhesives
combined with bolts, or special grouting.
External application of FRP material provides a practical solution to improve the overall
performance of an R.C. frame structure without the necessity of a radical alteration to the original
structure. Externally bonded FRP may be used in a repair capacity for structures that have
undergone moderate earthquakes damage or to reinforce structures that are considered to be
vulnerable or substandard. The use of FRP offers several advantages, related to its high strength-
to-weight ratio, resistance to corrosion, fast and relatively simple application. However, FRP is to
date still rather expensive so its use must be optimized to minimize material wastage. One
disadvantage of FRP is its dependence on bond to the concrete it is to strengthen, which is a
function of the tensile capacity of the concrete and the type of surface preparation used.

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This paper aims to study the effect of longitudinal reinforcement ratio and number of warped GFRP
layers on the axial capacity of square columns. The study was carried out starting from
experimental tests results carried out by the author in earlier research. Those tests were carried out
on a set of 12 specimens with different longitudinal reinforcement ratio and number of warped
GFRP layers. All specimens were 12cm x 12 cm x 120 cm columns reinforced longitudinally with
four bars at the corners and transversally with square ties 5φ6/m. The specimens were divided into
four groups; each group has three specimens (without GFRP, with one layer of GFRP and with two
layers of GFRP). Each group has a different longitudinal reinforcement ratio (0.0%, 0.8%, 1.1% and
1.4%). The properties of the used materials are listed in table (1). Only the failure loads were
recorded for each specimen as listed in table (2). The tests results were compared with the
estimated capacities using the ECP formula, the estimated values are listed in table (3).
That earlier research was didn’t propose a relation or a formula to correlate the axial capacity with
the GFRP layers and the reinforcement ratio, also, it didn’t analyzed the failure mechanism of the
specimens. Its conclusions were as follows:
1- Warping the RC columns with GFRP sheets increasing their axial capacities regardless the
reinforcement ratio.
2- The more used GFRP sheets the more earning strength.
3- The axial capacity increased by 23% and 42% for using one and two GFRP layers
respectively.
Table (1): Properties of used materials
Ult. StrainMod. of ElasticityStrengthMaterial
0.3%E = 2470 MPaFcu = 31.5 MPaConcrete
25%E = 20000 MPaFy = 310 MPaReinf. steel
3.1%E = 70000 MPaFt = 2250 MPaGRFP
- Thickness of GRFP sheets is 0.17mm
Table (2): Recorded test results
Specimens
% of Main
Steel
Failure Load
(ton)
Control
Failure Load
(ton)
1 Layer
Failure Load
(ton)
2 Layer
Sp. 1 0.0% 28.5 34 39
Sp. 2 0.8% 32 39 45
Sp. 3 1.1% 33 41 48
Sp. 4 1.4% 35 45 51
Table (3): Estimated capacities using ECP
Specimens
% of Main
Steel
Failure Load
(ton)
Control
Failure Load
(ton)
1 Layer
Failure Load
(ton)
2 Layer
Sp. 1 0.0% 28.8 30.05 32.93
Sp. 2 0.8% 32.4 33.64 36.52
Sp. 3 1.1% 33.8 35.04 37.92
Sp. 4 1.4% 35.2 36.44 39.32

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FINITE ELEMENT MODELS
Finite element ANSYS models are used to study the confining effect of the GFRP sheets and
analyzing the failure mechanism of the specimens. Many trails were carried out to model the
specimens, the concrete always modeled as 3D solid element, while the reinforcement were
modeled in one trail as smeared in the concrete solid elements and as discrete line element in
another trail. The GRFP were modeled in three different ways in three different trials, first as shell
elements, second as line element and finally as equivalent confining pressure. The specimen’s
capacities of each trail were compared with the experimental results to determine the validity of the
modeling. This comparison indicts that the most accurate modeling technique is to model the
concrete as 3D solid element, the reinforcement bars as line elements and the GFRP as equivalent
confining load. Analyzing the output of each trail shows the following:
• Modeling the reinforcement as smeared or discrete elements gives almost the same results
since the ties have no impact on the column confining because they are widely spaced
comparing with column width (ties spacing is 200mm and column width is 120mm) this
arrangement leaves the zone between ties almost unconfined. Ties are only useful in
prevented the buckling of the longitudinal bars. However, modeling the bars as line element
has the advantage of determining the stresses at any point of the bars.
• Modeling the GFRP sheets as shell elements or line elements gives the almost the same
low results of the axial capacity because concrete fails at very low vertical strain (0.003)
which corresponding to lateral strain equals to the vertical strain times the poisson's ratio
(0.003% x 0.16 = 0.00048). At this lateral strain, the developed stresses in the GFRP
sheets equals the lateral strain times the modulus of elasticity (0.00048 x 70000 = 33.6
MPa) which is very low value compared with the tensile strength of the sheets (2250 MPa)
It means that the warped sheets has no significant effect on the axial capacity tell concrete
failure, at this point large lateral strain occurs independently from the axial strain, that lateral
strain is large enough to develop significant amount of tensile stresses in the sheets. By
increasing the vertical load the tensile stresses in the sheets increases and the collapse
occurs when the stress in the sheets exceeds the ultimate tensile strength.
Since this paper is concerned only in predicting the capacity of the warped columns not the stress-
strain relation, then modeling the GFRP sheets as equivalent confining stress to simulate the
specimens at ultimate stage is acceptable technique specially that the capacities matched the
experimental results.
The external confining pressure values due to GFRP sheets are calculated in the same way that
used to find the confining stresses due to stirrups by Park and Pauley (1975) except that the GFRP
are external confining, hence, the total column width is considered in equation. Park and Pauley
method is shown in fig. (1). Previous studies showed that this confining stresses are un-uniformly
distributed inside the non-circular columns cross section. Generally, confining stresses produce
concentrated compressive stresses at the corners of rectangle and square sections leaving the
surface areas between the corners unstressed. Rounding the corners of the non-circular sections
helps in distribute the confining stresses more uniformly and reducing the unstressed zones in the
cross section as shown in fig. (2) This pattern of stress distribution is noticed in the output of the
ANSYS models confirming that the chosen values for external pressure loads are valid.

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Fig. (1): Confining stresses provided by different arrangement of stirrups
Fig. (2): Distribution of confining stresses inside non-circular section
Based on that analysis, the final set of ANSYS 3D models were developed as follows:
Concrete: The SOLID65, 3-D reinforced concrete solid element is used to represent concrete in the
models. This element is capable of cracking in tension and crushing in compression. Cracking is
treated as a “smeared band” of cracks, rather than discrete cracks in ANSYS and occurs as soon
as stresses in the concrete exceed the tensile strength of the material. The crushing capability of
the SOLID65 element is deactivated in this study to avoid premature failure in the FE simulation.
This element can model concrete with or without reinforcing bars. If the rebar capability is used, the
bars will be smeared throughout the element. Nevertheless, in this study a discrete bar element is
used instead of the smeared reinforcing approach. The most important aspect of the SOLID65
element is the treatment of nonlinear material properties. The response of concrete under loading is
characterized by a distinctly nonlinear behavior. The typical behavior expressed in the stress-strain
relationship for concrete subjected to uniaxial loading.

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Uniaxial tensile and compressive strengths (Fcu and Ft) and the uniaxial nonlinear stress-strain
relationship for concrete are defined for the SOLID65 element. The first two parameters are
required to define the failure surface for the concrete due to a multi-axial stress state. The concrete
parameters can be calculated, based on:
Fcu = 31.5 (MPa)
Ft = 0.62 √Fcu = 3.48 (MPa)
υ = 0.16
E = 4400 √Fcu = 24.7 (GPa)
A perfectly plastic relationship is used instead of the compressive strain-softening curve in this
study. Under uniaxial tension, the material is assumed to be linearly elastic with a modulus of
elasticity of (E) up to the tensile strength.
Reinforcing Steel Bars: The BEAM188, 3-D element, is used to represent the reinforcing steel bar.
Its behavior is characterized by a uniaxial tension-compression element that can also include
nonlinear material properties. An elastic-perfectly plastic relationship is assumed in this study.
GFRP Laminates: A confining pressure on the four sides of the test columns is used to simulate
the effect of the GFRP sheets. The value of the confining stress is calculated based on the ultimate
tensile strength of the sheets as follows:
Confining stress = 2 T / b
Where: T is the ultimate tensile strength of the sheet per unit length
= sheet thickness x ultimate tensile strength per unit area
b is the column width
Analysis Assumptions:
• The bond between each element/material type is assumed perfect.
• The shear transfer coefficients in ANSYS for closed and open cracks in the SOLID65
concrete element are assumed to be 1.0 and 0.3, respectively.
• The concrete material is assumed to be isotropic prior to cracking and orthotropic after
cracking. The steel is assumed to be isotropic.
Nonlinear Analysis in ANSYS: The status transition of the concrete from an un-cracked to a
cracked state, and the nonlinear material properties of concrete in compression and for the steel as
it yields cause the nonlinear behavior of the structure under loading. Newton-Raphson equilibrium
iteration is used to solve nonlinear problems in ANSYS.
Table (4): ANSYS results
Specimens
% of Main
Steel
Failure Load
(ton)
Control
Failure Load
(ton)
1 Layer
Failure Load
(ton)
2 Layer
Sp. 1 0.0% 28.8 34.8 41.0
Sp. 2 0.8% 31.3 42.8 48.2
Sp. 3 1.1% 32.3 44.6 51.3
Sp. 4 1.4% 33.9 46.4 52.8

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Fig. (3): ANSYS models
PROPOSED FORMULA
Plotting the relation between the ultimate vertical stresses verses the confining stresses shows
perfect linear relation regardless the percentage of main steel. The confining stresses of one and
two layers of the used GFRP are 6.4 & 12.8 N/mm2
. The values of both vertical and confining
stresses are summarized in table (5) and plotted in Fig. (4). The equations of lines in Fig. (4) in
(N/mm2
) are as follows:
Ult. vertical stress = 19.3 + 0.56 confining stress For As/Ac = 0.000
Ult. vertical stress = 21.5 + 0.70 confining stress For As/Ac = 0.008
Ult. vertical stress = 22.2 + 0.80 confining stress For As/Ac = 0.011
Ult. vertical stress = 23.9 + 0.87 confining stress For As/Ac = 0.014

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Table (5): Relation between ultimate vertical stresses and confining stresses
Specimens
% of Main
Steel
Ultimate vertical stresses (N/mm2
)
Confining stress
0.0 N/mm2
Confining stress
6.4 N/mm2
Confining stress
12.8 N/mm2
Sp. 1 0.0% 19.8 23.6 27.1
Sp. 2 0.8% 22.2 27.1 31.3
Sp. 3 1.1% 22.9 28.5 33.3
Sp. 4 1.4% 24.3 31.3 35.4
Fig. (4): Relation between ultimate vertical stresses and confining stresses
The ultimate vertical stress without confining can be calculated as follows:
Ultimate vertical stress without confining = 0.66 Fcu + Fy. (As/Ac)
= 20.0 N/mm2
For As/Ac =0.000
= 22.4 N/mm2
For As/Ac =0.008
= 23.3 N/mm2
For As/Ac =0.011
= 24.2 N/mm2
For As/Ac =0.014
Those values are almost the first term in the equations of lines in fig. (4)
Dividing the second term in each equation by its first term gives almost constant value as follows:

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0.56 / 19.3 = 0.029 For As/Ac =0.000
0.70 / 21.5 = 0.033 For As/Ac =0.008
0.80 / 22.2 = 0.036 For As/Ac =0.011
0.87 / 23.9 = 0.036 For As/Ac =0.014
Hence, the four equations of lines in Fig. (4) could be summarized in one equation as follows:
Ult. vertical stress = [0.66 Fcu + Fy. (As/Ac)] x [1+ 0.033 confining stress]
= [0.66 Fcu + Fy. (As/Ac)] x [1+ (confining stress / 30)]
The formula of the ECP depends on the factor (confining stress / Fcu), similarly, the last term in the
proposed formula can be (confining stress / Fcu) since Fcu is 30 N/mm2
in this study. Hence, the
final proposed formula in (N/mm2
) is as follows:
Ult. vertical stress = [0.66 Fcu + Fy. (As/Ac)] x [1+ (confining stress / Fcu)]
Where confining stress = 2 x sheet(s) thickness x ult. tensile strength of sheets / column width
The previous equation means that the gained strength due to confining is (confining stress / Fcu).
The summarized results of applying the proposed formula are shown in table (6). The gain of
strength is (6.4/30 = 0.21) in case of one layer and (12.8/30 = 0.42) in case of two layers which
matches the conclusion of the earlier research.
Table (6): Results of proposed formula
Specimens
% of Main
Steel
Failure Load
(ton)
Control
Failure Load
(ton)
1 Layer
Failure Load
(ton)
2 Layer
Sp. 1 0.0% 28.8 34.9 41.1
Sp. 2 0.8% 32.3 39.1 46.0
Sp. 3 1.1% 33.5 40.7 47.8
Sp. 4 1.4% 34.8 42.3 49.7
COMPARISON OF RESULTS
The results of all studies are summarized in table (7) and plotted verses the experimental values in
Fig. (5). The correlation between the predicted values from each method and the experimental
values are also shown in fig. (5). Revising the sum of squared errors (R2
) of each method shows
that is the best one is the proposed formula (R2
=0.966), then the ANSYS models (R2
=0.962) and
finally the ECP formula (R2
=-.355) which indicating uncorrelated relation.

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Table (7): Comparison of results
% of Main
Steel
No. of GFRP
layers
Failure load (ton)
Experimental ECP ANSYS Proposed
0.0% 0 28.5 28.8 28.8 28.8
0.0% 1 34.0 30.0 34.8 34.9
0.0% 2 39.0 33.0 41.0 41.1
0.8% 0 32.0 32.4 31.3 32.3
0.8% 1 39.0 33.7 42.8 39.1
0.8% 2 45.0 36.5 48.2 46.0
1.1% 0 33.0 33.8 32.3 33.5
1.1% 1 41.0 35.0 44.6 40.7
1.1% 2 48.0 37.9 51.3 47.8
1.4% 0 35.0 35.2 33.9 34.8
1.4% 1 45.0 36.5 46.4 42.3
1.4% 2 51.0 39.3 52.8 49.7
Fig. (5): Correlation between experimental and predicted results

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CONCLUSIONS
The results of the study could be concluded in the following points:
1. Using of GFRP for columns repair increases their ultimate strength even without
reinforcement.
2. The proposed formula to calculate the ultimate vertical stresses of square RC column
strengthened with GFRP is as follows:
Ult. vertical stress = [0.66 Fcu + Fy. (As/Ac)] x [1+ (confining stress / Fcu)]
Confining stress = 2 x sheet(s) thickness x ult. tensile strength of sheets / column width
3. Gained strength due to confining equals to (confining stress / Fcu).
4. The proposed formula and the finite element models using ANSYS shows good matching
with the experimental results.
5. Farther studies should be conducted on rectangular columns to determine the relation
between aspect ratio and effective confining stress.
REFERENCES
1. ECP committee 208, (2005), “Egyptian code of practice for the use of fiber reinforced
polymer (FRP) in the construction fields”, housing and building national research center
“HBRC”, Cairo, Egypt.
2. ACI committee 315, (1999), “Manual of standard practice for detailing reinforced concrete
structures”, American concrete institute, Detroit MI.
3. N. Subramanian, (2011), "Design of confinement reinforcement for RC columns”, The
Indian Concrete Journal 2011, pp. 1-8.
4. Wael M. E.,(2004), "Seismic behavior of reinforced medium and high strength concrete
beam column connections", Ph.D. thesis, Faculty of engineering, Cairo university in 2004.
5. Yehia Mohamed Abd-Elmagid, (1999), "Seismic behavior of strengthen reinforced concrete
columns", Ph.D. thesis, Faculty of engineering, Cairo University in 1999.
6. Oliveto, G., Granata, M., Buda, G. and Sciacca, P. (2004b). “Preliminary Results from Full-
Scale Free Vibration Tests on a Four Story Reinforced Concrete Building after Seismic
Rehabilitation by Base Isolation”, Proceedings of the JSSI 10th Anniversary Symposium on
Performance of Response Controlled Buildings, Yokohama, Japan, Paper No. 7-2
7. Amr H. Zaher,(2013). “Behavior of reinforced concrete columns strengthened with GFRP
with different main steel ratio “Al-Azhar University Civil Engineering Research Magazine
“CERM”, 2013 Vol. (35) No. (4).
8. Park, R. and Pauley, T. “Reinforced Concrete Structures”, John Wiley and Sons, New York,
1975, p. 769.