International Journal of Advanced Engineering Technology
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Research Article
DESIGN GUIDELINES FOR FLEXURAL STRENGTH
OF SINGLY REINFORCED CONCRETE BEAM
STRENGTHENED WITH FIBRE REINFORCED
POLYMER LAMINATE AT BOTTOM
K. B
. Parikh
1
and
Dr. C. D. Modhera
2
Address for Correspondence
1
Department of Applied Mechanics, Government Engineering College, Surat, Gujarat, India
Research scholar, Department of Applied Mechanics, SVNIT, Surat
2
Department of Applied Mechanics, Sardar V
allabhbhai National Institute of Technology, Surat,
India
E

mail:
kbp1977@yahoo.co.in
,
cdmodhera@yahoo.com
ABSTRACT
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’
exp
erimental 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
F
iber reinforced polymer
laminate
; reinforced
concrete beam;
design guidelines;
thickness of
frp
.
INTRODUCTION
F
iber reinforced polymer laminates are
increasingly being applied for the
rehabilitation and strengthening of
infrast
ructure in lieu of traditional repair
techniques such as steel plates bonding. FRP
plates have many advantages over steel
plates in this application, and their use can
be extended to situations where it would be
impossible or impractical to use steel. For
example, FRP plates are lighter than steel
plates of equivalent strength, which
eliminates the need for temporary support
for the plates while the adhesive gains
strength. Also, since FRP plates used for
external bonding are relatively thin, neither
the we
ight of the structure nor its
dimensions are signiﬁcantly increased. In
addition, FRP plates can easily be cut to
length on site. These various factors in
combination make installation much simpler
and quicker than when using steel plates.
There were few
analytical studies available
for the prediction of flexural capacity of
reinforced concrete beam
strengthened with
external laminates.
Concrete society
technical report 55,
was
used the rectangular
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stress block for concrete.
Jones et al. used
the conventio
nal procedure
to determine the
ultimate moment capacity of RC beams
externally strengthened with bonded steel
plates. They employed rectangular stress
blocks for concrete and the
actual stress

strain curves of the internal steel
reinforcement
and external
steel plates to
evaluate the internal forces and moment.
Several researchers have come up with
techniques for attempting to predict flexural
capacities and failure modes
for FRP
reinforced structural elements. Results of
research
performed by Saadatmanesh
and
Ehsani suggested that
reasonably accurate
strength predictions of FRP reinforced
beams could be made using simple force
equilibrium
equations.
Work by Triantafillou
and Pleveris indicated that the failure mode
of FRP

reinforced beams was highly
influen
ced by the reinforcement ratios of the
FRP and steel.
Their research also offers
equations for strength based on the various
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.
This paper presents a very simple, easy and
efficient computat
ional design oriented
model for the determination of flexural
strength of reinforced concrete beam
strengthened at bottom with fiber reinforced
polymer laminate.
It also provides for the
determination of limit of laminate thickness
in order to avoid the te
nsile failure of beam
due to fiber reinforced polymer and assure
the tensile failure due to steel i.e.
reinforcement yielding.
This design oriented
model also allows for the estimation of
laminate thickness to attain a specified
limiting moment capacity. T
he results from
design oriented model compares with the
results of author’s analytical finite element
model as well as available
researches
experimental data.
DESIGN ORIENTED MODEL
IS 456:2000 is
Indian standard
code of
practice for plain and reinforced co
ncrete
.
With the help of this code, a systematic
procedure/model
had
been introduced
by
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
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For design purpose the compressive
strength of concrete in the structure
shall be assumed to be 0.67 times the
characteristics strength.
The maximum strain in concret
e at
the outermost compression fiber is
taken as 0.0035
.
The maximum strain in the tension
reinforcement in the section at
failure shall not be less than
Partial safety factor for steel is 1.15
and concrete is 1.50.
The fiber reinforced polymer sheet
or
laminate has a linear elastic stress

strain relationship to failure.
There is no relative slip between
external fiber reinforced polymer
sheet and concrete.
From the above assumptions, a stress

strain
diagram has been drawn.
Fig. 1 Stress & strain diagram for RC beam with FRP
b
D
Xu
0.0035
5
C
d
Cross section of
beam strengthened
with FRP
Strain Diagram
Stress Diagram
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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, ther
e is a linear relationship of strain diagram. So, the ratio of
can be
found as follows.
International Journal of Advanced Engineering Technology
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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 eval
uated 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,
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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)
I
ndex
L
(mm)
b
(mm)
D
(mm)
A
st
(mm
2
)
(Mpa)
(Mpa)
(Mpa)
H.
Saadatmanesh
and R. Ehsani
A
4875
205
455
1472.6
35
456
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
Yousef A. Al

Salloum
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
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VERIFICATION
EXAMPLES
In
order to evaluate the
effectiveness of the
above equation, various available
experimental research data is used.
Also, the
verification of
these equations
has been
carried by analytical model suggested by
K.B.Parikh
et. al
.
Following table 1, shows
the physical and mec
hanical properties of
materials and table 2 shows the comparison
of moment capacity of beams found from
equat
ion 1, using author finite element
model and experimental results of
researches.
The following table 3 shows the
maximum thickness and required thickness
of fiber reinforced polymer sheet under
balanced condition
The following are the comparative chart
s for the ultimate moments of beam.
Fig. 2 Comparative charts of ultimate moment
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Table
3
: Comparison of ultimate moment of beams
Author(s)
Index
Moment capacity or Ultimate Moment
Design oriented
model Results
Finite element
Model Results
(K.B.Parikh et. al)
Experimental Results
H. Saadatmanesh
and R. Ehsani
A
326.2
330
337
B
263.6
268
257.7
C
173.3
181
188.3
D
263.6
270
257.7
Yousef A. Al

Salloum
Control
8.96
12.2
15.27
G

SBL
22.15
23
23.67
C

SBL
35.25
29.8
26.60
T
able
4
:
FR
P thickness
Author(s)
Index
Under balanced
Condition
Maximum Value
Provided
Sing

Ping
Chiew et. al
A

group
2.38
3.66
1.7
Yousef A. Al

Salloum
G

SBL
1.48
1.94
1.0
C

SBL
0.86
1.13
1.19
ZHANG
Aihui
A

group
0.140
0.233
0.111
CONCLUSION
Here
s
imple and
efficient
design guidelines
for the determination
of ultimate
moment of
a beam with fiber reinforced polymer sheet
at bottom
provided w
ith the help of IS 456:
2000.
These guidelines provide
effective and
convince procedure for the determination o
f
thickness of fiber reinforced polymer sheet
under balanced condition.
This design model
validated through
analytical and researchers
experimental results of beam strengthened
with fiber reinforced polymer sheet at
bottom.
From the results following
concl
usions can be drawn:
The design oriented computational
analysis to determine the ultimate
moment capaci
ty of singly reinforced
RC beams strengthened with FRP at
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bottom proved to be efficient and
good.
The results obtained from this design
oriented model we
re 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 ba
lanced
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.
REF
E
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[1]
Sing

Ping Chiew, Qin Sun and Yi Yu,
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506.
[2]
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–
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