International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Research Article
DESIGN GUIDELINES FOR FLEXURAL STRENGTH
OF SINGLY REINFORCED CONCRETE BEAM
STRENGTHENED WITH FIBRE REINFORCED
POLYMER LAMINATE AT BOTTOM
K. B. Parikh1 and Dr. C. D. Modhera2
Address for Correspondence
Department of Applied Mechanics, Government Engineering College, Surat, Gujarat, India
Research scholar, Department of Applied Mechanics, SVNIT, Surat
2
Department of Applied Mechanics, Sardar Vallabhbhai National Institute of Technology, Surat,
India
E-mail: kbp1977@yahoo.co.in, cdmodhera@yahoo.com
ABSTRACT
1
The design guidelines for the determination of limiting moment capacity of reinforced concrete beam
strengthened with fiber reinforced polymer laminate at bottom is presented. The results derived from this
design oriented model compared with analytical finite element model and others available researchers’
experimental data. This study also presents the design of laminate thickness to attain a specified limiting
moment capacity in a given beam. The results show that the design guidelines presented in this study,
performed well in the prediction of experimental results.
KEYWORDS Fiber reinforced polymer laminate; reinforced concrete beam; design guidelines;
thickness of frp.
INTRODUCTION
Fiber reinforced polymer laminates are
strength. Also, since FRP plates used for
increasingly
external bonding are relatively thin, neither
rehabilitation
being
and
applied
for
the
strengthening
of
the
weight
of
the
structure
nor
its
infrastructure in lieu of traditional repair
dimensions are significantly increased. In
techniques such as steel plates bonding. FRP
addition, FRP plates can easily be cut to
plates have many advantages over steel
length on site. These various factors in
plates in this application, and their use can
combination make installation much simpler
be extended to situations where it would be
and quicker than when using steel plates.
impossible or impractical to use steel. For
There were few analytical studies available
example, FRP plates are lighter than steel
for the prediction of flexural capacity of
plates
reinforced concrete beam strengthened with
of
equivalent
strength,
which
eliminates the need for temporary support
external
for the plates while the adhesive gains
technical report 55, was used the rectangular
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
laminates.
Concrete
society
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
stress block for concrete. Jones et al. used
This paper presents a very simple, easy and
the conventional procedure to determine the
efficient
ultimate moment capacity of RC beams
model for the determination of flexural
externally strengthened with bonded steel
strength
plates. They employed rectangular stress
strengthened at bottom with fiber reinforced
blocks for concrete and the actual stress-
polymer laminate. It also provides for the
strain
steel
determination of limit of laminate thickness
reinforcement and external steel plates to
in order to avoid the tensile failure of beam
evaluate the internal forces and moment.
due to fiber reinforced polymer and assure
Several researchers have come up with
the
techniques for attempting to predict flexural
reinforcement yielding. This design oriented
capacities and failure modes for FRP
model also allows for the estimation of
reinforced structural elements. Results of
laminate thickness to attain a specified
research performed by Saadatmanesh and
limiting moment capacity. The results from
Ehsani suggested that reasonably accurate
design oriented model compares with the
strength predictions of FRP reinforced
results of author’s analytical finite element
beams could be made using simple force
model as well as available researches
equilibrium equations. Work by Triantafillou
experimental data.
and Pleveris indicated that the failure mode
DESIGN ORIENTED MODEL
of
highly
IS 456:2000 is Indian standard code of
influenced by the reinforcement ratios of the
practice for plain and reinforced concrete.
FRP and steel. Their research also offers
With the help of this code, a systematic
equations for strength based on the various
procedure/model had been introduced by
curves
of
FRP-reinforced
the
beams
internal
was
modes of FRP-reinforced beam failure.
Perhaps the most accurate method of
predicting strength of FRP-reinforced beams,
for flexural, is through the use of finite
element modeling programs, as suggested by
some researchers. A critical factor for
flexure capacity design is the adhesion
between the concrete and the composite.
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
computational
of
tensile
reinforced
failure
due
design
oriented
concrete
to
steel
beam
i.e.
K.B.Parikh et al. for the determination of
flexural strength of singly RC beam
strengthened with fiber reinforced polymer
at bottom. For the determination of this
model following assumptions should be
made.

The tensile strength of the concrete is
ignored.
International Journal of Advanced Engineering Technology

For design purpose the compressive

The fiber reinforced polymer sheet
strength of concrete in the structure
or laminate has a linear elastic stress-
shall be assumed to be 0.67 times the
strain relationship to failure.

characteristics strength.


E-ISSN 0976-3945
There is no relative slip between
The maximum strain in concrete at
external fiber reinforced polymer
the outermost compression fiber is
sheet and concrete.
taken as 0.0035.
From the above assumptions, a stress-strain
The maximum strain in the tension
diagram has been drawn.
reinforcement in the section at
failure shall not be less than

Partial safety factor for steel is 1.15
and concrete is 1.50.
0.0035
5
b
C
Xu
d
D
Cross section of
beam strengthened
with FRP
Stress Diagram
Strain Diagram
Fig. 1 Stress & strain diagram for RC beam with FRP
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
From the above stress and strain diagram of RC beam moment capacity of beam can easily
determined from the following equation.
The depth of neutral axis is to be determined from the following equation.
t thickness of frp laminate/plate/sheet
DESIGN THICKNESS OF FRP LAMINA
Balanced Condition
The thickness of fiber reinforced polymer sheet can be determined for balanced condition. As per
above assumption, there is a linear relationship of strain diagram. So, the ratio of
found as follows.
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
can be
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Using equation (2), it is very easy to obtain an equation of thickness of fiber reinforced polymer
lamina in balanced condition.
For,
hence the equation for the thickness of FRP laminate becomes as,
For,
hence the equation for the thickness of FRP laminate becomes as,
Maximum Thickness of FRP Sheet
The maximum thickness of fiber reinforced polymer sheet can be evaluated by using the criteria
of minimum value of percentage of reinforcement as per IS 456:2000. The basic equation of
minimum percentage of reinforcement for beam as per code is as follows.
.
Using the equation (8), modified the equation (5), (6) and (7) are as follows.
Using, various grade of concrete and grade of reinforcement, the equation of thickness of sheet
under balanced condition with minimum reinforcement can be generated as,
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Where the k is the multiplication factor, as shown in table 1.
Table 1: multiplication Factor ‘k’
Grade of Concrete/Grade of
Reinforcement
M15
2.1225
1.8526
M 20
3.0765
2.7166
M 25
4.0305
3.5806
M 30
4.9845
4.4446
General Equation
The general equation for the determination, of thickness of fiber reinforced polymer sheet can be
expresses as follows.
If moment capacity
is known, then it is very easy to determine the depth of neutral axis from
following equation,
Table 2: Physical and Mechanical properties of materials
Author(s)
H.
Saadatmanesh
and R. Ehsani
Yousef A. AlSalloum
A
L
(mm)
4875
b
(mm)
205
D
(mm)
455
Ast
(mm2)
1472.6
(Mpa)
35
(Mpa)
456
(Mpa)
400
B
4875
205
455
981.8
35
456
400
C
4875
205
455
265.5
35
456
400
D
4875
205
455
981.8
35
456
400
Control
1350
150
200
157
40.1
412
--
G-SBL
1350
150
200
157
40.1
412
540
C-SBL
1350
150
200
157
40.1
412
930
Index
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
VERIFICATION EXAMPLES
materials and table 2 shows the comparison
In order to evaluate the effectiveness of the
of moment capacity of beams found from
above
equation 1, using author finite element
equation,
various
available
experimental research data is used. Also, the
model
and
experimental
verification of these equations has been
researches. The following table 3 shows the
carried by analytical model suggested by
maximum thickness and required thickness
K.B.Parikh et. al. Following table 1, shows
of fiber reinforced polymer sheet under
the physical and mechanical properties of
balanced condition
The following are the comparative charts for the ultimate moments of beam.
Fig. 2 Comparative charts of ultimate moment
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
results
of
International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Table 3: Comparison of ultimate moment of beams
Author(s)
Index
A
Moment capacity or Ultimate Moment
Finite element
Design oriented
Model Results
Experimental Results
model Results
(K.B.Parikh et. al)
326.2
330
337
H. Saadatmanesh
B
263.6
268
257.7
and R. Ehsani
C
173.3
181
188.3
D
263.6
270
257.7
Control
8.96
12.2
15.27
G-SBL
22.15
23
23.67
C-SBL
35.25
29.8
26.60
Yousef A. AlSalloum
Table 4: FRP thickness
Author(s)
Index
Under balanced
Condition
Sing-Ping
Maximum Value
Provided
A - group
2.38
3.66
1.7
Yousef A. Al-
G-SBL
1.48
1.94
1.0
Salloum
C-SBL
0.86
1.13
1.19
A - group
0.140
0.233
0.111
Chiew et. al
ZHANG
Aihui
CONCLUSION
Here simple and efficient design guidelines
experimental results of beam strengthened
for the determination of ultimate moment of
with fiber reinforced polymer sheet at
a beam with fiber reinforced polymer sheet
bottom.
at bottom provided with the help of IS 456:
conclusions can be drawn:
2000. These guidelines provide effective and

From
the
results
following
The design oriented computational
convince procedure for the determination of
analysis to determine the ultimate
thickness of fiber reinforced polymer sheet
moment capacity of singly reinforced
under balanced condition. This design model
RC beams strengthened with FRP at
validated through analytical and researchers
IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282
International Journal of Advanced Engineering Technology
bottom proved to be efficient and
good.

The results obtained from this design
oriented model were well compared
with finite element model results and
experimental results.

One can easily determine the moment
capacity of a beam strengthened with
FRP at bottom by using simple
approach.

It also very easy to determine the
thickness of FRP sheet under balanced
condition.

The design of FRP sheet thickness to
attain a desired moment capacity in a
given beam can be found out easily.

The
results
showed
that
all
computational models presented here
performed well for the determination
of experimental results.
REFERENCES
[1] Sing-Ping Chiew, Qin Sun and Yi Yu,
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[2] K.B.
Parikh
and
C.D.
Modhera,
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