DESIGN GUIDELINES FOR FLEXURAL STRENGTH OF SINGLY REINFORCED CONCRETE BEAM STRENGTHENED WITH FIBRE REINFORCED POLYMER LAMINATE AT BOTTOM

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Nov 26, 2013 (3 years and 9 months ago)

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International Journal of Advanced Engineering Technology


E
-
ISSN 0976
-
3945


IJAET/Vol.I/ Issue
II
/
July
-
Sept.,
2010/
274
-
282






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

International Journal of Advanced Engineering Technology


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IJAET/Vol.I/ Issue
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2010/
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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


E
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ISSN 0976
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3945


IJAET/Vol.I/ Issue
II
/
July
-
Sept.,
2010/
274
-
282






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





International Journal of Advanced Engineering Technology


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2010/
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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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ISSN 0976
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3945


IJAET/Vol.I/ Issue
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Sept.,
2010/
274
-
282




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,



International Journal of Advanced Engineering Technology


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ISSN 0976
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IJAET/Vol.I/ Issue
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Sept.,
2010/
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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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Sept.,
2010/
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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



International Journal of Advanced Engineering Technology


E
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ISSN 0976
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3945


IJAET/Vol.I/ Issue
II
/
July
-
Sept.,
2010/
274
-
282




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

International Journal of Advanced Engineering Technology


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ISSN 0976
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3945


IJAET/Vol.I/ Issue
II
/
July
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Sept.,
2010/
274
-
282




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
RENCES

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Sing
-
Ping Chiew, Qin Sun and Yi Yu,
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