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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME 42 DUCTILITY OF TIMBER BEAMS STRENGTHENED USING CFRP PLATES Javaid Ahmad 1 , Dr. Javed Ahmad Bhat 2 1 Graduate Student, National Institute of Technology, Srinagar 2 Associate Professor, National Institute of Technology, Srinagar ABSTRACT The aim of current study is to investigate the effect of Carbon Fiber Reinforced Polymer (CFRP) composites on ductility of timber beams. Ten beams with cross section of 70mm x 120mm were tested, where two served as control beams (without CFRP strengthening). Two species of timber were used in this study based on their availability in this region viz. Cedrus Deodara (Deodar) and Pinus Wallichiana (Kail). An experimental investigation was conducted on the behavior of FRP- reinforced wood section. The strength of timber beams was significantly improved upon strengthening with maximum percentage increase being 114.28% and 140% for deodar and Kail respectively.The ductility was dramatically improved where the highest ductility index was 6.81 for Deodar beams and 4.33 for Kail beams. From this study, it was found that 0.59% is the optimum value of CFRP area to achieve maximum ductility index. All beams in this study did not fail due to peel off or de-bonding. Load–deflection curves provided an insight on the performance of the CFRP strengthened beams. Keywords: Retrofitting, Fiber Reinforced Polymers, Flexural Strengthening, Timber Failures, Ductility, Ductility Index. 1. INTRODUCTION Rehabilitation of deteriorated civil engineering infrastructure such as buildings, bridge decks, beams, girders, marine structures, roads etc. has been a major issue in last decade. The deterioration of these structures might be due to aging, poor maintenance, corrosion due to unfavorable environmental conditions, poor initial design or construction and accidental situations like earthquakes. The need to upgrade the deteriorated civil engineering infrastructure is necessitated due to the ever increasing demand e.g. unprecedented loads on buildings which have not been considered in design and likewise. INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October, pp. 42-54 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2013): 5.3277 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME
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Page 1: 20320130405006

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME

42

DUCTILITY OF TIMBER BEAMS STRENGTHENED USING CFRP PLATES

Javaid Ahmad1, Dr. Javed Ahmad Bhat

2

1Graduate Student, National Institute of Technology, Srinagar

2Associate Professor, National Institute of Technology, Srinagar

ABSTRACT

The aim of current study is to investigate the effect of Carbon Fiber Reinforced Polymer

(CFRP) composites on ductility of timber beams. Ten beams with cross section of 70mm x 120mm

were tested, where two served as control beams (without CFRP strengthening). Two species of

timber were used in this study based on their availability in this region viz. Cedrus Deodara (Deodar)

and Pinus Wallichiana (Kail). An experimental investigation was conducted on the behavior of FRP-

reinforced wood section. The strength of timber beams was significantly improved upon

strengthening with maximum percentage increase being 114.28% and 140% for deodar and Kail

respectively.The ductility was dramatically improved where the highest ductility index was 6.81 for

Deodar beams and 4.33 for Kail beams. From this study, it was found that 0.59% is the optimum

value of CFRP area to achieve maximum ductility index. All beams in this study did not fail due to

peel off or de-bonding. Load–deflection curves provided an insight on the performance of the CFRP

strengthened beams.

Keywords: Retrofitting, Fiber Reinforced Polymers, Flexural Strengthening, Timber Failures,

Ductility, Ductility Index.

1. INTRODUCTION

Rehabilitation of deteriorated civil engineering infrastructure such as buildings, bridge decks,

beams, girders, marine structures, roads etc. has been a major issue in last decade. The deterioration

of these structures might be due to aging, poor maintenance, corrosion due to unfavorable

environmental conditions, poor initial design or construction and accidental situations like

earthquakes. The need to upgrade the deteriorated civil engineering infrastructure is necessitated due

to the ever increasing demand e.g. unprecedented loads on buildings which have not been considered

in design and likewise.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 4, Issue 5, September – October, pp. 42-54

© IAEME: www.iaeme.com/ijciet.asp

Journal Impact Factor (2013): 5.3277 (Calculated by GISI)

www.jifactor.com

IJCIET

©IAEME

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(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME

43

New technology options in rehabilitation are being developed from polymers, metals,

ceramics and composites of these materials and some of these high performance materials are

already being utilized in construction. While the concept of composites has been in existence for

several millennia, the incorporation of fiber reinforced polymer (FRP) is less than a century old.

These composites combine the strength of fibers with the stability of polymer resins.

Market penetration of timber and fiber composites within the construction industry will

ultimately be determined by final cost. CFRP is more expensive. However, material cost alone is not

the prime consideration for many applications using these materials. It is important to consider the

total built cost rather than just comparing the material component costs with traditional materials but

the costs of design, manufacture, fabrication and erection need to be considered as well. Building

owners, when looking at new construction, have not given a great deal of consideration to long term

rehabilitation methods, costs or effects on projected service. Although research has been done to

strengthen timber using FRP, but the comprehensive analysis and design are not established in detail.

This is one of the reasons why the application of FRP to timber is very limited.

In the plate bonding or externally bonded technique, the FRP is situated on the external

tensile surfaces of the concrete beam to improve the flexural strength or on the vertical surfaces of

the beam to increase its shear capacity (Allbones, 1999)[3]

. Arduini and Nanni (1997) have

investigated plates in the form of flexible carbon FRP sheets, to be externally bonded to the concrete

surfaces. The strengthening technology consisting of externally bonded CFRP sheets to concrete is

easy to perform and significant improvement was found for ultimate load capacity and to a lesser

extent in flexural stiffness.[4]

Plevris and Triantafillou (1992) provided an analytical study of the short-term flexural

behavior of timber beams and beam-columns reinforced on the tension face only with epoxy-bonded

unidirectional CFRP sheets. This work demonstrated that even a small amount of fibers, as low as

1% of the cross-sectional area, of thin carbon FRP bonded to timber beams could result in a strength

increase on the order of 60%.[18]

There was another research done by Fiorelli and Antonio (2002) to evaluate the structural

behavior of timber beams strengthened with FRP. The research was focused on the experimental and

theoretical analysis of timber beams of the species Pinus Caribea Hondurensis which were reinforced

with GFRP and CFRP fabrics. The results of this research showed that the flexural stiffness (EI)

determined experimentally was greater than the theoretical values. These values are in favor of

structural safety. It shows that the increase of stiffness varied from 15% to 29% for beams

strengthened with glass and carbon fabric. The use of FRP provides better results in load capacity

and in the vertical displacement of the beam.[8]

Buell and Saadatmanesh (2005) have conducted research on creosote-treated solid-sawn

Douglas Fir strengthened with bidirectional CFRP fabric. The results show that applying carbon

fabric to the timber beams provides significant increase in the bending and shear capacity, and

nominal increase in the stiffness of the beams. The ultimate bending strength was increased between

40 to 53% and the horizontal shear strength was increased between 36 to 68%.[5]

Micelli et al. (2005) have investigated on flexural reinforcement of glulam timber beams with

CFRP rods. Flexural behavior of CFRP-reinforced beams was compared with unreinforced beams

that were used as control specimens. Experimental results showed a significant influence of the

CFRP rods because the reinforced beams demonstrated an increase in ultimate capacity and stiffness.

An increase in ultimate moment of 26% and 82% was recorded with respect to unreinforced beams

for 0.51% and 1.03% cross sectional reinforcement.[16]

The present research focuses on application of pre-fab CFRP strips for strengthening timber

beams. The strips or plates are attached to beams by means of specified adhesive. The flexural tests

are carried out on timber beams strengthened with CFRP in varying proportion with an object of

studying the improvement in load carrying capacity, modulus of rupture and flexural rigidity of these

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44

beams. However, the scope of this study was limited to seasoned dry timber only which infers the

applicability of research findings to beams used in dry condition or in the interior of structure.

The timber species used in this research includeCedrus Deodara commonly known as

Deodarand Pinus Wallichiana commonly known as Kail. These species are being widely used in

upper northern region (primarily Jammu and Kashmir) of India for structural purposes due to its

prime availability in this region. Besides, this these timber species arehaving good mechanical

properties as compared to other timber species found in northern region of India. Having been widely

used in structures constructed decades ago, it has become necessary torehabilitate the timber

structures which have suffered damage. Leaving the application of conventional rehabilitation

techniques aside, we are left with application of fiber composites as best alternatives for

rehabilitation of these structures. So, research has been conducted at National Institute of

Technology, Srinagar (NIT Srinagar) to study the feasibility of utilizing CFRP for rehabilitation or

design of new structures using Deodar& Kail.

2. METHODOLOGY

This section describes features of beam specimens, beam designation, loading equipment,

instrumentation and testing schemes. In the present study, ten timber beams were prepared for testing

among which eight beams were strengthened using CFRP Plates of different widths. The beams

without strengthening served as control beams and used as reference level for checking improvement

in properties of strengthened timber beams. As already mentioned timber species utilized for beams

wareCedrus Deodaraand Pinus Wallichiana. The ultimate tensile strength and modulus of elasticity

of specimens of Deodar were observed to be 35 MPa and 10 GPa respectively. Whereas for Kail,

ultimate tensile strength and modulus of elasticity were observed to be 20 MPa and 8 GPa

respectively. The typical geometry and testing arrangement is shown in Fig1.

Fig 1: Flexural Test – Loading Arrangement

The properties of materials used are summarized in Table 1 whereas beam designations are

shown in Table 2.

P P

1524mm(Deodar)

1473mm(Kail)

480mm(Deodar)

360mm(Kail)

480mm(Deodar)

360mm(Kail) 70mm

120mm

CFRP Strip

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Bf = 30mm Bf

ACFRP = 0.36% ACFRP

Fig 2: Graphical representation of Beam cross

Reinforcement was used in the form of CFRP strips of varying widths appli

face of the beams using adhesive. The CFRP sheets were supplied by GSP Superb Technology

(India), a New Delhi based supplier who imports it from Korea. The mechanical properties of CFRP

are shown in Table 1. Retrofitted beam specimens were

thickness 1mm and different widths in all specimens varying from 30mm to 70mm.

The tests were carried on beam models in a loading frame of capacity 500KN. Prior to testing

dial gauges were set up at mid span an

hydraulic jack till failure and deflections were noted every 4KN interval load. The failure pattern was

studied for each beam discussion regarding which is given afterwards. Fig 3 shows schematics

flexural testing.

Property

Ultimate tensile strength,

N/mm2

Ultimate tensile strain, %

Tensile modulus of

elasticity, KN/mm2

Designation

Deodar

Control Beam- D

FPD-30-1

FPD-40-1

FPD-50-1

FPD-70-1

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

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45

Table 1: Material Properties

Table 2: Beam Designation

= 40mm Bf = 50mm Bf = 70mm

CFRP = 0.47% ACFRP = 0.59% ACFRP

: Graphical representation of Beam cross-sections

Reinforcement was used in the form of CFRP strips of varying widths appli

face of the beams using adhesive. The CFRP sheets were supplied by GSP Superb Technology

(India), a New Delhi based supplier who imports it from Korea. The mechanical properties of CFRP

are shown in Table 1. Retrofitted beam specimens were strengthened with a single strip of CFRP of

thickness 1mm and different widths in all specimens varying from 30mm to 70mm.

The tests were carried on beam models in a loading frame of capacity 500KN. Prior to testing

dial gauges were set up at mid span and two alternate points. The loading was applied by means of

hydraulic jack till failure and deflections were noted every 4KN interval load. The failure pattern was

studied for each beam discussion regarding which is given afterwards. Fig 3 shows schematics

Deodar Kail CFRP

Ultimate tensile strength, 35 20 2000

Ultimate tensile strain, % 0.40 0.38 1.65

10 8 175

Designation Width of

CFRP Strip,

mm

Thickness of

CFRP Strip,

mm Kail

Control

Beam- K

- -

FPK-30-1 30 1

FPK-40-1 40 1

FPK-50-1 50 1

FPK-70-1 70 1

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

October (2013), © IAEME

= 70mm

CFRP = 0.83%

Reinforcement was used in the form of CFRP strips of varying widths applied on the bottom

face of the beams using adhesive. The CFRP sheets were supplied by GSP Superb Technology

(India), a New Delhi based supplier who imports it from Korea. The mechanical properties of CFRP

strengthened with a single strip of CFRP of

thickness 1mm and different widths in all specimens varying from 30mm to 70mm.

The tests were carried on beam models in a loading frame of capacity 500KN. Prior to testing

d two alternate points. The loading was applied by means of

hydraulic jack till failure and deflections were noted every 4KN interval load. The failure pattern was

studied for each beam discussion regarding which is given afterwards. Fig 3 shows schematics of

CFRP

2000

1.65

175

Thickness of

CFRP Strip,

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

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(a) Front View

3. DUCTILITY

The ductility of a beam can be defined as its ability

loss in its load carrying capacity prior to failure. The deformations can be deflections, curvatures, or

strains. A ductile system displays sufficient warning before catastrophic failure. Based on this

definition, ductility can be expressed in terms of deformation or energy absorption. In the case of

steel reinforced beams, where there is clear plastic deformation of steel at yield, ductility can be

calculated as the ratio of ultimate deformation to deformation at yi

However, for beam strengthened with FRP, the determination of yield point is a difficult task.

So, ductility is studied in terms of energy parameters.

Typical load-deflection beha

beam either exhibits brittle or ductile behavior. The use of material with brittle failure should be

avoided. In the extreme event of a structure loaded to failure, it should be able to undergo large

deflections at near its maximum load

before failure.

Fig 4: Load deflection curve of flexural member

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

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46

Front View (b) Side View

Fig 3: Testing Arrangement

The ductility of a beam can be defined as its ability to sustain inelastic deformation without

loss in its load carrying capacity prior to failure. The deformations can be deflections, curvatures, or

strains. A ductile system displays sufficient warning before catastrophic failure. Based on this

uctility can be expressed in terms of deformation or energy absorption. In the case of

steel reinforced beams, where there is clear plastic deformation of steel at yield, ductility can be

calculated as the ratio of ultimate deformation to deformation at yield.

However, for beam strengthened with FRP, the determination of yield point is a difficult task.

So, ductility is studied in terms of energy parameters.

deflection behavior of a flexural member (Fig4(a)) is shown in the Fig4

ither exhibits brittle or ductile behavior. The use of material with brittle failure should be

avoided. In the extreme event of a structure loaded to failure, it should be able to undergo large

deflections at near its maximum load-carrying capacity i.e. ductile behavior. This will give a warning

: Load deflection curve of flexural member

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

October (2013), © IAEME

to sustain inelastic deformation without

loss in its load carrying capacity prior to failure. The deformations can be deflections, curvatures, or

strains. A ductile system displays sufficient warning before catastrophic failure. Based on this

uctility can be expressed in terms of deformation or energy absorption. In the case of

steel reinforced beams, where there is clear plastic deformation of steel at yield, ductility can be

However, for beam strengthened with FRP, the determination of yield point is a difficult task.

vior of a flexural member (Fig4(a)) is shown in the Fig4(b). The

ither exhibits brittle or ductile behavior. The use of material with brittle failure should be

avoided. In the extreme event of a structure loaded to failure, it should be able to undergo large

ctile behavior. This will give a warning

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47

Different researcher has expressed the ductility in different quantitative basis. For instance,

Spadeaet al. (1998)[23]

, Harris et al. (1998)[12]

, Stehn and Johansson (2002)[24]

have evaluated the

ductility in terms of structural characteristics such as mid span deflection, curvature, and area under

the load-deflection diagram at two different stages, namely, the yielding of the tension material, and

at ultimate failure. The ductility indices for beams are defined on the basis of;

a) Deflection

b) Curvature

c) Area under the load-deflection curve (Spadeaet al., 1998).[23]

These are briefly explained below;

1) Deflection ductility It is defined as the ratio of ultimate deflection to yield deflection at the mid span of beams. It

is expressed as;

�� � ∆�∆� ……1

2) Curvature ductility It is defined as the ratio of curvature or slope at ultimate load to curvature at the yield load

measured at the mid span of beams. It is expressed as;

�� � ���� ……2

Where ∆u = deflection at ultimate load

∆y = Deflection at yield load

Φu = curvature at ultimate load

Φy = Curvature at yield load

3) Energy Ductility It is defined as the ratio of total energy determined as the area under load deflection curve up

to failure load, to elastic energy determined as the area under load deflection curve up to 75%

of failure load (Fig 5). It is expressed as;

� � ��� .��,��

……3

Where; Wtot = Total energy, computed as the area under the load deflection curve up to the failure

load (Fig 5(b)).

W0.75, Pu = Area under the load-deflection diagram up to 75% of the ultimate load (elastic

energy)

With FRP reinforced beams, there is no exact yield point; consequently, these definitions are not

suitable to be applied (Grace et al., 1998)[10]

. Therefore, Naaman and Jeong (1995)[17]

, stated by

(Harris et al., 1998)[12]

suggested other definition for the ductility index µEbased on energy

considerations that is applicable to FRP reinforced beam, i.e.

� � �� ������ � 1� ……4

Where

Wel = Elastic energy (Fig 5(a))

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

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Fig 5: Ductility Index a) Elastic energy b) Total Energy

4. RESULTS AND DISCUSSIONS

The beams were tested and the load deflection curves were plotted as shown in Fig 6

7. All the beams exhibited elastic behavior followed by

The results from laboratory testing for the strengthened b

strengthened) in order to study the behavior of strengthened timber beams in terms of ductility.

3 and 4 summarizes typical properties of load deflection curves

respectively.

Fig 6: Load Deflection curves for Deodar beams strengthened using CFRP

0

10

20

30

40

50

60

70

0 10

Loa

d,

KN

Midspan Deflection, mm

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

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48

Ductility Index a) Elastic energy b) Total Energy

SIONS

The beams were tested and the load deflection curves were plotted as shown in Fig 6

. All the beams exhibited elastic behavior followed by nonlinear and plastic behavior afterwards.

The results from laboratory testing for the strengthened beams are compared with control beam (un

strengthened) in order to study the behavior of strengthened timber beams in terms of ductility.

summarizes typical properties of load deflection curves for Deodar and Kail beams

: Load Deflection curves for Deodar beams strengthened using CFRP

20 30 40

Midspan Deflection, mm

Control Beam Deodar

FPD-30-1

FPD-40-1

FPD-50-1

FPD-70-1

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

October (2013), © IAEME

The beams were tested and the load deflection curves were plotted as shown in Fig 6 and Fig

nonlinear and plastic behavior afterwards.

eams are compared with control beam (un-

strengthened) in order to study the behavior of strengthened timber beams in terms of ductility. Table

for Deodar and Kail beams

: Load Deflection curves for Deodar beams strengthened using CFRP

Control Beam Deodar

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49

Fig 7: Load Deflection curves for Kail beams strengthened using CFRP

Table 3: Properties of Load Deflection Curves

Control

Beam - D FPD – 30-1 FPD – 40-1 FPD – 50-1 FPD – 70-1

Failure Load, Pu,

KN 29.05 37.35 41.5 62.25 43.16

Maximum Midspan

Deflection, δu, mm

23 22.1 17.7 16.5 36.76

Proportionality

Limit, KN 16.6 14.94 20.75 18.26 12.45

Midspan Deflection

at Proportional

Limit, mm

10.5 8.25 5.84 5.82 15.9

Table 4: Properties of Load Deflection Curves

Control

Beam - K FPK – 30-1 FPK – 40-1 FPK – 50-1 FPK – 70-1

Failure Load, Pu,

KN 20.75 29.05 41.5 49.8 33.2

Maximum

Midspan

Deflection, δu, mm

15 14.76 15.4 14.18 28.8

Proportionality

Limit, KN 16.6 16.6 22.41 25.73 12.45

Midspan

Deflection at

Proportional

Limit, mm

12.5 5.86 7.43 6.7 13.35

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Loa

d,

KN

Midspan Deflection, mm

Control Beam Kail

FPK-30-1

FPK-40-1

FPK-50-1

FPK-70-1

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As an illustration, beam FPD-70-1 is used for discussion of ductility. The Load-deflection

curve for the beam is shown in Fig 8. From the curve, the maximum elastic load, ultimate load, and

the corresponding deflections were determined.

Fig 8: Load Deflection Curve of FPD – 70 – 1

In this study none of the CFRP plate has yielded because the yield strain for CFRP is higher

than the yield strain of the timber. Hence the compressive zone of the timber will reach its yield

point before CFRP. From the curve, the elastic deflection, and the ultimate deflection were ∆e = 15.9

mm, and ∆u = 36.76 mm, respectively. The total failure occurred when the deflection at mid-span

was 36.76 mm which is considered high. This value provides good performance in the ductility point

of view where the people will have ample time to escape from the building before collapse.

Using the procedures mentioned earlier, the ductility indices were calculated based on energy

methods and the summary of the results is shown in Table 5 and Table 6.

For energy method, the equation for the curve is required to calculate the energy under the

curve. Thus, a polynomial regression analysis was carried using Microsoft Excel to determine the

equation. The order of the polynomial was decided by best fit curve of observed plot. The value for

R2 was determined and used as an indicator for the accuracy of the equation for best curve fitting.

For each curve, the energy on the elastic zone and the total energy up to failure were computed.

For the beam under consideration, elastic energy, Weis equivalent to the area under the curve

between ∆ = 0 and ∆e= 15.9 mm which is given by the following integration as;

�� � � � � �!."#

�� � $� %&1' & 05 ! � 0.0009 + & 0.0232 . � 0.2244 � � 0.1896 � 0.04432� �!."#

$

We = 110.64KNmm = 110.64Nm or 110.64 Joules

y = -1E-05x5 + 0.000x4 - 0.023x3 + 0.224x2 + 0.189x + 0.044

R² = 0.997

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Loa

d,

KN

Mid Span deflection, mm

FPD-70-1

Poly. (FPD-70-1)

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51

Similarly, the total energy, Wtotis equivalent to the area under the curve between ∆ = 0 and

∆u= 36.76 mm which is given by the following integration as;

�343 � � � � .5.65#

�343 � $� %&1' & 05 ! � 0.0009 + & 0.0232 . � 0.2244 � � 0.1896 � 0.04432� .5.65#

$

Wtot = 1224.34 KNmm = 1224.34 Nm or 1224.34 Joules

The ductility indices for all beams are shown in Table 5 & 6.

Table 5: Ductility Index for Strengthened Deodar beams Beam CFRP Area,

%

Energy Ductility index

Elastic

We

Nm or J

Ultimate

Wtot

Nm or J

Based on Energy

� � 0.5 7�343�� � 18

Control Beam-D 0 96.30 392.28 2.53

FPD-30-1 0.36 71.09 453.95 3.69

FPD-40-1 0.47 58.48 482.51 4.62

FPD-50-1 0.59 43.44 548.35 6.81

FPD-70-1 0.83 110.64 1224.34 6.03

Table 6: Ductility Index for Strengthened Kail beams

Beam CFRP Area,

%

Energy Ductility index

Elastic

We

Nm or J

Ultimate

Wtot

Nm or J

Based on Energy

� � 0.5 7�343�� � 18

Control Beam-K 0 136.27 238.08 1.37

FPK-30-1 0.36 46.12 199.76 2.66

FPK-40-1 0.47 88.27 421.32 2.88

FPK-50-1 0.59 77.75 595.91 4.33

FPK-70-1 0.83 73.00 353.83 2.92

The polynomial regression equations for the other beams are shown in Table 7. There was

significant increase in ductility when the timber beams are strengthened using CFRP plates. Even

after ultimate failure, the beams still held together. In other words, there was no catastrophic failure

when the beams were externally plated. This shows that the CFRP plates provide effective

strengthening material to the timber beams. By taking control beam as a reference, the highest

ductility index for Deodar based on energy method was 6.81 where the percentage increase was

169.17% relative to control beam.

From these results, there is a relationship between the CFRP area and the ductility index. The

relationship is shown in Fig 8. The curve shows that ductility index increased nonlinearly as the area

of CFRP plates increased. When the area of CFRP is about 0.59%, we get maximum value for the

ductility index and any increases in CFRP area beyond this value will not improve the ductility

performance. Although ductile material is important in design, consideration should not be given to

too ductile element which will lead to a decrease in the load-carrying capacity and an increase in

total deflections of the structural system. Both these effects are regarded as negative for practical

design (Stehn and Johansson, 2002). [22]

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52

It seems possible to make ductile timber beams by adequately strengthening the tension zone.

There is possibility to design the reinforced timber beams up to plastic limit as steel design does. The

plastic design approach promises an advantage in timber beam design which are strengthened in the

tension zone.

Fig 8: Ductility index Versus CFRP Area

Table 7: Polynomial Regression Equations of load deflection Curves of Beams

Deodar Beams

Control Beam-

D

y = -0.0007x3 - 0.0096x2 + 1.7841x + 0.3608;

[R² = 0.9959]

FPD-30-1 y = -0.0006x4 + 0.0286x3 - 0.4143x2 + 3.5929x - 0.2622;

[R² = 0.9976]

FPD-40-1 y = -0.0002x5 + 0.0101x4 - 0.1689x3 + 1.0258x2 + 1.5664x + 0.0659;

[R² = 0.9997]

FPD-50-1 y = -0.0002x5 + 0.0093x4 - 0.1352x3 + 0.905x2 + 0.7197x - 0.0965;

[R² = 0.9987]

FPD-70-1 y = -1E-05x5 + 0.0009x4 - 0.0232x3 + 0.2244x2 + 0.1896x + 0.0443;

[R² = 0.9974]

Kail Beams

Control Beam-

K

y = -0.0001x5 + 0.0052x

4 - 0.061x

3 + 0.2315x

2 + 1.3275x + 0.0283;

[R² = 0.999]

FPK-30-1 y = -0.0003x5 + 0.0112x

4 - 0.1703x

3 + 0.9944x

2 + 0.9387x + 0.0094;

[R² = 0.9996]

FPK-40-1 y = -0.0001x5 + 0.0049x4 - 0.0617x3 + 0.2673x2 + 2.8106x + 0.2385;

[R² = 0.9994]

FPK-50-1 y = -0.0001x6 + 0.0054x

5 - 0.093x

4 + 0.693x

3 - 1.994x

2 + 4.788x - 0.0825;

[R² = 0.9992]

FPK-70-1 y = 5E-06x5 - 0.0002x

4 + 0.0004x

3 + 0.0517x

2 + 0.4575x + 0.0224;

[R² = 0.9928]

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1

Du

ctil

ity

In

de

x

Area of CFRP, %

Ductility Index Deodar

Ductility Index Kail

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53

5. CONCLUSION

I. Ductility index obtained from energy method was observed to vary in the range 2.53 – 6.81

for Deodar beams and 1.37 – 4.33 for Kail beams.

II. It is concluded that 0.59% was the optimum value of CFRP area for maximum ductility

index. This finding was synchronized with the results for strength where the optimum value

for CFRP area that can provide maximum strength was also 0.59%.

III. All beams in this study did not fail due to peel off and also no de-bonding occurred between

CFRP plate and the bonding agent and between bonding agent and timber substrate because

the bonding length for all beams (1.5 m) was sufficient.

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