STRUCTURAL PEFORMANCE OF MEMBERS STRENGTHENED BY FRP JACKETING WITH HIGH FRACTURING STRAIN

T. Ueda

Division of Built Environment, Hokkaido University, Sapporo, Japan

ABSTRACT

The major advantage of FRP construction materials is high strength, while the major drawback is low material

deformability (low fracturing strain). A material with high strength/stiffness can be substituted by a material

with low strength/stiffness if the necessary amount is provided. On the other hand a material with low

deformability can never work as a substitute of a material with high deformability. Generally materials with

high deformability show low strength/stiffness but good cost performance. Based on the concept of the potential

shear strength of a member, which is a function of stiffness of tension and shear reinforcement at a given

deformation of the member, it is found that the preferable mechanical property of shear reinforcement to obtain a

high ultimate shear strength and deformability is a high fracturing strain without yielding. The jacketing with

PET fiber sheet, which is a good example of the material whose fracturing strain is high (around 10% or even

more) without yielding, proves the good enhancement of member shear strength and deformability.

KEYWORDS

FRP, RC members, jacketing, material deformability, shear strength enhancement, ductility enhancement.

INTRODUCTION

Comparing with steel, FRP (or continuous fiber) materials show high strength but low fracturing strain that

governs the shear strength and ductility (deformability) of members reinforced with FRP in according to many

experimental facts. In the past high strength/stiffness of FRP has been paid attention. However, FRP with low

strength but high fracturing strain could give higher shear strength and much better ductility than FRP with high

strength (Ueda and Sato 2002, Tuladhar et al. 2003, Jaqin et al. 2005, Ueda et al. 2006). The cost of material

with high fracturing strain is generally less than that with high strength/stiffness (Ueda et al. 2006). This paper

discloses the suitable mechanical property for shear reinforcement based on the concept of potential shear

strength (Anggawidjaja et al. 2006b), and then summarizes the experimental evidences on shear strength and

ductility enhancement of concrete linear members strengthened by jacketing of FRP with high fracturing strain.

NECESSARY MECHANICAL PROPERTY

Strength/Stiffness or Deformability

Strength and stiffness are the primary material property, so that the high strength of FRP (or continuous fiber)

material has been highlighted. Major drawbacks with FRP as construction material, however, are the material

brittleness and vulnerability to fire besides the high cost. One reason why we have been unable to remove these

drawbacks is the fact that we have been emphasizing only on strength and stiffness of the material but the others.

For example, to achieve good seismic performance, high member deformability is desired besides high member

strength/stiffness. The high member deformability can be achieved by high deformability of material. A

required member strength/stiffness is not necessarily achieved by applying high strength/stiffness materials.

Low strength/stiffness materials can satisfy the required member strength/stiffness. The difference in material

strength/stiffness only makes the difference in the required material amount. However a high deformability can

be achieved only by materials with a high fracturing strain. Materials of a low strength/stiffness generally come

with a high fracturing strain and can be produced at a low cost, while materials of a high strength/stiffness show

usually a low fracturing strain and require a high cost (see Figure 1) (Anggawidjaja et al. 2006b). The low

strength of FRP at bent is also due to the low fracturing strain.

19

Figure 1. Comparison of strength/stiffness, fracturing strain and cost of materials

Properties Necessary of Shear Reinforcement for Shear Strength

The previous study on shear strength of concrete beams with shear reinforcement (Sato et al. 1997) discloses that

strain of shear reinforcement, web at ultimate shear strength depends on various factors including both stiffness,

which is the product of elastic modulus and reinforcement ratio, of tension reinforcement and shear

reinforcement, ss E and webweb E as shown in Eq.1.

2.0

05.01000

11

0053.0c

nE

Ec

webf

eda

f webwebss

(1)

where cf is concrete compressive strength, da is shear span to depth ratio, and n is axial compressive

stress (or prestress). The above equation indicates that the less the stiffness becomes, the higher the shear

reinforcement strain at the ultimate shear strength of a member. If the shear reinforcement strain at the ultimate

is greater than the fracturing strain of the shear reinforcement material, the shear reinforcement would fracture

before the member reaches its shear capacity. It implies that a material with a high fracturing strain is a better

option for shear reinforcement.

h

str

web

cpz

Lweb

str,v

str,h

Lstr

Xe

Figure 2. Mechanical model for predicting ultimate shear strength of concrete column with shear reinforcement

The study by Sato et al. (1997) also presents the mechanical model to predict the ultimate shear strength of

concrete beams with shear reinforcement. Since main diagonal shear cracking pattern in columns is different

from beams, the mechanical model to predict the ultimate shear strength of columns, which is slightly different

from that for beams, was presented by Ueda and Anggawidjaja (2007) as shown in Figure 2 and by Eq.2.

webwebwebvstrstrcpzesvstrcpzu bLbLbxVVVV ,, (2)

where b is column width, cpz and vstr , are shear stress of concrete in compression zone and diagonal shear

cracking zone, strL and webL are as shown in Figure 2, and web ( webwebE ) is stress in shear reinforcement,

which is internally embedded and externally bonded shear reinforcement. Neutral axis depth, ex and diagonal

shear crack angle, are calculated as follows:

0

1000

2000

3000

4000

5000

0 3 6 9 12 15 18 21

Strain (%)

Str

ess(M

pa)

Carbon

Aramid (Kevlar)Aramid (Technora)

Glass

PEN

PET

Steel

Polyacetal

High strength/stiffness

Low strength/stiffness

High cost Low cost

Low fracturing strain

High fracturing strain

20

1000

08.07.0

12.0

42.0

1

2.31

125.1

4.0

ss

webweb

E

c

n

E

da

e ef

e

x

x

(3)

d

a

fV

V

c

n

mu

u 1

7.0

int,

int,tan 15.1148.28

(4)

where int,uV and int,muV are initial potential shear and flexure strength. The shear strength components of

concrete in compression zone and diagonal shear cracking zone, cpzV and vstrV , can be calculated by using the

following equations:

h

af

fa

df

d

a

d

ac

c

nccpz

5.0

211 132sin64.0tancostansin65.0

(5)

csswebwebvstr fEE sin06335.0ln0802.01206.0ln166.0, (6)

The summation of cpzV and vstrV , is the shear strength component of concrete, cV . The shear strength

component of shear reinforcement, sV can be obtained by Eq.7.

2.07721.0

1758.0

11

01658.0c

nEE

c

webwebwebwebf

eda

fEE ss

webweb

(7)

The above model for ultimate shear strength shows that the ultimate shear strength decreases with decrease in

tension reinforcement stiffness, ss E and with decrease in shear reinforcement stiffness, webweb E because the

shear strength component of concrete, cV (or vstrV , ) decreases with the decrease in reinforcement stiffness. In

order to develop the shear strength fully, the fracturing strain of shear reinforcement should be greater than the

strain calculated by Eq.7. The stiffness of shear reinforcement is also important for the shear strength. The

material stiffness (elastic modulus), however, is not the required property, because the necessary stiffness can be

achieved by providing the necessary amount of shear reinforcement in accordance with its elastic modulus. As a

summary, the more important mechanical property of shear reinforcement for the ultimate shear strength is the

fracturing strain rather than the strength/stiffness.

Force

Deformation y

Vc

Vs Vcr

Flexural yielding

Vy

cr

Shear yielding

Vu Concrete crush and shear crack widening

V

Vmu

Vu (Potential shear strength)

Vy

Figure 3. Potential shear strength reduction with deformation

Properties Necessary of Shear Reinforcement for Deformability

The mechanical model for ultimate shear strength of concrete members shown in Figure 2 and Eq.2 can be

applied to shear failure in post-flexural yielding of the member. It is known that the shear failure in post-flexural

yielding often controls the ultimate deformability of concrete members, which is smaller than that without the

shear failure. In post-flexural yielding, the stiffness of tension reinforcement decreases with the increase in

member deformation. As a result, the potential shear strength, uV would decrease as shown in Figure 3. The

initial potential shear strength, which is the potential shear strength without yielding of tension and shear

reinforcement, remains before the yielding of tension reinforcement and starts to decrease after the yielding of

tension reinforcement. The potential shear strength decreases even further after the yielding of shear

reinforcement. Once the potential shear strength becomes smaller than the potential flexural strength, muV , the

load-carrying capacity of the member is controlled by the potential shear strength and the shear failure in post-

21

flexural yielding takes place (see Figure 3). As a result, the ultimate deformation becomes smaller than in the

case where no shear failure occurs.

As shown in Figure 3, the greater stiffness of shear reinforcement, which makes the potential shear strength

greater, would result in the greater deformability of member. This fact implies that materials without yielding,

such as FRP, could be a better option than steel shear reinforcement, whose stiffness would continuously

decrease after its yielding, for shear reinforcement. After its yielding the potential shear strength with steel shear

reinforcement would decrease more rapidly than that with FRP shear reinforcement (Utsunomiya et al. 2004).

Since the tension rupture of shear reinforcement causes a sudden decrease in the potential shear strength, shear

reinforcement should have a high enough fracturing strain to achieve good ultimate deformability. Consequently,

the good mechanical property of shear reinforcement for deformability is high deformability without yielding.

STRUCTURAL PERFORMANCE OF MEMBERS WITH PET SHEET JACKETING

Duplex Jacketing

The previous section presents the necessary property for shear reinforcement to achieve high ultimate

deformability of concrete members. Based on this knowledge, a new retrofitting method was developed recently

in Japan (Ueda et al. 2006). The new method, called as A-P Jacketing (duplex jacketing), applies two kinds of

fiber: one with a high stiffness (Aramid fiber) and one with a high fracturing strain (Polyethylene Terephthalate

(PET) fiber and Polyethylene Naphthalate (PEN) fiber), to other than hinge zone and hinge zone respectively as

shown in Figure 4 (a). The ultimate strength, fracturing strain, and elastic modulus in tension of PET are 923

MPa, 13.8 % and 6.7 GPa, while those of PEN are 1028 MPa, 4.5 % and 22.6 GPa, respectively. In a hinge zone

high plastic deformation is expected, so that a material with a high fracturing strain is necessary for shear

reinforcement. In the part other than hinge zone the deformation is expected to be much less but the required

shear capacity is the same as in the hinge zone. The material with a high stiffness is selected so that required

number of jacketed sheet layers is less, which may reduce construction cost. The material with a high fracturing

strain can be applied for the part other than hinge zone as well, depending on the required amount of fiber, if the

total construction cost would be less.

Column Tests

Experimental outline

Two series of tests were conducted -- one for ductility enhancement and another for shear strength enhancement.

The first series consists of 15 bridge pier specimens whose hinge zone was jacketed with fiber sheets with PET

or PEN and the rest was jacketed with aramid fiber sheet (A-P Jacketing as shown in Figure 4 (a)) except a

reference specimen. Ten and five specimens were with a cross section of 400 × 400 mm and 600 × 600 mm,

respectively (see Table 1 and Figure 4 (b)) (Anggawidjaja et al. 2006b). Two specimens with a cross section of

250 × 250 mm were tested for the second series (see Figure 4 (c)) (Anggawidjaja et al. 2006a). Load-

deformation curves (envelopes) of some of the specimens are shown in Figure 5.

Enhance mechanism of deformability and shear strength

The ductility enhanced by PET jacketing increases with an increase in PET fiber ratio (comparing SP1, SP4 and

SP5 in Table 1 and Figure 5 (a), and SP8, SP7 and SP6 in Table 1). PEN jacketing also increases the ductility

(comparing SP1 with SP3 in Table 1). At ultimate deformation u , no fracture was observed with PET and

PEN fiber sheets even though significant plastic deformation occurred (see Figure 6), while the aramid fiber

sheet fractured in SP2. No fracture or yielding of jacketed sheets can be considered to not only improve the

ductility ratio, but also reduce negative slope of the falling branch in the load-deformation curve (see Figure 5

(a)). It is a worthy observation in SP2s that an internal steel shear reinforcement fractures at its corner bent

while the external PET fiber sheet did not show any fracture.

As the previous section (section Properties Necessary of Shear Reinforcement for Deformability) indicates,

shear strength of concrete members depends on stiffness of both flexural and shear reinforcement. If we apply

this fact to concrete columns with steel reinforcement in which the flexural yielding takes place before the shear

strength is reached, the following can be said. Once yielding of steel flexural reinforcement, which means the

reduction in stiffness, takes place, the potential shear strength starts to decrease. Yielding of steel shear

reinforcement, which means not only reduction in the stiffness but also no increase in shear force component

carried by shear reinforcement, further decreases the potential shear strength. Figure 7 (a) shows the shear force

components by concrete, steel shear reinforcement and PET fiber sheet, the last two of which were calculated

22

using their measured strains. The concrete component starts to decrease after the flexural yielding and decreases

even faster after the shear reinforcement yielding. The load-carrying capacity decreases because the load-

carrying capacity in shear (potential shear strength) becomes smaller than that in flexure. Small contribution of

PET fiber sheet can be found only after the yielding of steel shear reinforcement in Figure 7 (a).

(a) A-P Jacketing (b) Specimens SP1 to SP10

(c) Specimens SP2s and SP3s

Figure 4. Column specimens

(a) Specimens SP1 to SP5 (b) Specimens SC1s, SC3s, SP2s and SP3s

Figure 5. Load-deformation curve (Envelope)

Ø6

D19

400

JA +

8JA

+7

JA +

6JA

+5

JA +

4JA

+3

JA +

2JA

+1

JA -

1JA

-2

JA -

3JA

-4

JA -

5

T8

T7

T6

T5

T4

T3

T2

T1

1500 600

400

700

700100

400

Du

ctil

ity

stre

ng

then

ing

1-1

.5D

Aramid fiber

PET fiber

Sh

ear

stre

ng

then

ing

D

250

225

150

1000

650

1000

500

1000

650

500

500

250

1000

500

500

25065

0 75 38

Unit: mm

SP2ｓ SP3ｓ

-400

-300

-200

-100

0

100

200

300

400

-15 -10 -5 0 5 10 15

/y

V (

kN

)

SP1

SP2

SP3

SP4

SP5

Load-Envelope Curve

0

100

200

300

0 50 100Deformation (mm)

Sh

ear

Fo

rce

(kN

)

SC1 SC3SP2 SP3SC1s

SP2s SP3s

SC3s

23

Table 1. Column specimens

Specimen fc' a/d ρt

%

ρw

%

ρf

% Fiber

Vc

kN

Vs

kN

Vf

kN

Vmu

kN mu

sc

V

VV 1) Cross-

section

SP1 29.5 3 2.87 0.16 - - 151 79 - 288 0.8 5.09 12)

SP2 29.5 3 2.87 0.16 0.13 A25)

151 79 213 288 0.8 11.84 1

SP3 29.5 3 2.87 0.16 0.38 PEN 151 79 201 288 0.8 10.65 1

SP4 29.5 3 2.87 0.16 0.37 PET 151 79 184 288 0.8 11.42 1

SP5 31.7 3 2.87 0.16 0.19 PET 155 79 90 290 0.8 7.98 1

SP6 31.7 4 2.87 0.16 0.12 PET 155 79 60 223 1.05 9.05 1

SP7 31.7 4 2.87 0.16 0.06 PET 155 79 30 223 1.05 8.46 1

SP8 31.7 4 2.87 0.16 - - 155 79 - 223 1.05 7.40 1

SP9 31.7 4 3.59 0.16 0.12 PET 169 79 60 267 0.93 8.76 1

SP10 31.7 4 2.15 0.16 0.06 PET 151 79 30 177 1.3 10.41 1

SP11 31.7 4 2.82 0.2 0.25 PET 318 206 264 463 1.13 8.52 23)

SP12 31.7 4 2.82 0.2 0.125 PET 318 206 132 463 1.13 7.54 2

SP13 34.5 3 2.82 0.2 0.29 PET 327 105 308 637 0.84 7.76 2

SP14 23.7 3 2.82 0.09 0.42 PET 289 83 441 612 0.61 4.12 2

SP15 31.1 3 2.82 0.09 0.42 PEN 316 83 469 641 0.62 6.87 2

SC1s 28.4 2.9 4.5 0.15 - - 80 29 - 255 0.43 - 34)

SC3s 29.0 2.9 4.5 0.15 0.032 Carbon 81.5 29 44 255 0.43 - 3

SP2s 35.4 2.9 4.5 0.15 0.67 PET 87 29 97 257 0.45 5.19 3

SP3s 36.7 2.9 4.5 0.15 0.35 PET 88 29 50 257 0.45 2.97 3

Note: 1) Ductility ratio (=δu/δy), 2) 400×400 mm, 3) 600×600 mm, 4) 250×250 mm, 5) Aramid of high strength

type whose ultimate strength is 3246 MPa, fracturing strain is 4.1 % and elastic modulus is 79.5 GPa.

6) Notations: fc' is concrete strength, a/d is shear span to depth ratio, ρt, ρw, ρf are ratios of tension reinforcement,

stirrup and fiber sheet, Vc, Vs, Vf are concrete, stirrup and fiber sheet contribution in shear, Vmu is flexure strength

in terms of shear force.

Figure 6. High plastic deformation with PET fiber sheet jacketing

It seems that stiffness of both flexural and shear reinforcement controls the potential shear strength. This means

that FRP jacketing, which adds the stiffness of shear reinforcement, increases the potential shear strength

resulting in enhancement of ductility and more ductile manner with falling load-carrying capacity. However,

fracture of FRP would instantly eliminate the FRP contribution. PET fiber with a large fracturing strain can keep

its contribution and contribute better than steel reinforcement which is likely to yield at ultimate deformation.

24

(a) Specimen SP10 (b) Specimen SP2s

Figure 7. Shear force contributions

Similar observations can be made with specimens SP2s and SP3s, which were originally designed to fail in shear

based on the JSCE formula for carbon and aramid fiber sheet jacketing (JSCE Research Committee 2001). Both

specimens showed shear failure after flexural yielding around 220 kN (see Figure 5 (b)). The load-deformation

curves of SP2s and SP3s are compared with those of companion specimens with no jacketing (SC1s) and carbon

fiber sheet (SC3s) with stiffness greater than those in SP2s and SP3s. Specimens SC1s and SC3s show rather

brittle behavior and smaller shear strength. In specimen SC3s the carbon fiber sheet fractured. Shear force

components in specimen SP2s are shown in Figure 7 (b). After the yielding of steel shear reinforcement the

concrete component increases with a smaller rate and the component of PET fiber sheet becomes more

significant. The concrete component starts to decrease after the flexural yielding.

In order to estimate the ultimate deformation we have to predict shear deformation in hinge zone. The

experimental results indicate that shear deformation increases with total deformation and more quickly after

yielding of flexural and shear reinforcement. It can be more than 10 % of the total deformation at ultimate

deformation.

Beam Tests

Experimental outline

One reference specimen and nine specimens with PET fiber sheet jacketing were tested under monotonic and

static loading (Senda and Ueda 2008). The test parameters were PET fiber sheer ratio as the primary parameter,

beam height, shear span to depth ratio, tension reinforcement ratio and internal shear reinforcement ratio as

shown in Table 2. Strains of PET fiber sheet together with internal steel tension and shear reinforcement were

carefully measured, especially to estimate the shear force components carried by steel shear reinforcement and

PET fiber sheet. Cross sections, dimensions and strain gage arrangements of some specimens are shown in

Figures 8 and 9. Shear deformation of the tested zone was measured by using a set of displacement transducers

(see Figure 10).

300mm300mm 600mm

D6 3＠150mm

(b) 鉄筋配置図 SP1~SP6,SP9

ひずみゲージ

(c) PET繊維シート貼付け位置 SP2~SP6,SP9

600mm

PET繊維シート

ひずみゲージ

(a) 断面図

D6

D25

50mm

50

0m

m

250mm

SP7

250mm

27

0m

m

30mm

D25

D6

SP1~SP6,SP8,SP9SP1b-SP6b, SP8b, SP9b SP7b

Figure 8. Cross section of beam specimens

SP 2

0

50

100

150

200

250

300

0 20 40 60 80 100 120

Deformation (mm)

Shea

r F

orc

e (k

N)

Vtotal

Vc+Vs

Vc

SP2s

-200

-150

-100

-50

0

50

100

150

200

-150 -100 -50 0 50 100 150

Displacement (mm)

Sh

ear

Fo

rce

(kN

)

SP10 Vtotal

SP10 Vc+Vs

SP10 Vc

Yielding of shear

reinforcement

Yielding of shear

reinforcement

25

300mm300mm 600mm

D6 3＠150mm

(b) 鉄筋配置図 SP1~SP6,SP9

ひずみゲージ

(c) PET繊維シート貼付け位置 SP2~SP6,SP9

600mm

PET繊維シート

ひずみゲージ

(a) 断面図

D6

D25

50mm

50

0m

m

250mm

SP7

250mm

27

0m

m

30mm

D25

D6

SP1~SP6,SP8,SP9

300mm300mm 600mm

D6 3＠150mm

(b) 鉄筋配置図 SP1~SP6,SP9

ひずみゲージ

(c) PET繊維シート貼付け位置 SP2~SP6,SP9

600mm

PET繊維シート

ひずみゲージ

(a) 断面図

D6

D25

50mm

50

0m

m

250mm

SP7

250mm

27

0m

m

30mm

D25

D6

SP1~SP6,SP8,SP9

Strain gage Strain gage

PET fiber sheet

(a) Steel reinforcement and strain gage (b) PET fiber sheet and strain gage

Figure 9. Steel reinforcement and PET fiber sheet with strain gage

Figure 10. Instrumentation for shear deformation measurement

Table 2. Beam specimens

Specimen bh

mm

d

mm

a

mm da s

% web

%

f

%

uV

kN muV

kN muu VV exp,uV

kN

SP1b 270×250 240 600 2.50 4.22 0.17 0 205 339 0.70 178.4

SP2b 270×250 240 600 2.50 4.22 0.17 0.11 249 339 0.73 232.3

SP3b 270×250 240 600 2.50 4.22 0.17 0.17 270 339 0.80 229.3

SP4b 270×250 240 600 2.50 4.22 0.17 0.22 292 339 0.86 259.8

SP5b 270×250 240 600 2.50 4.22 0.17 0.34 324 339 0.96 248.4

SP6b 270×250 240 600 2.50 4.22 0.17 0.45 340 339 1.01 280<

SP7b 500×250 450 1125 2.50 4.50 0.17 0.34 441 668 0.66 437.3

SP8b 270×250 240 750 3.13 4.22 0.17 0.17 246 345 0.71 193.4

SP9b 270×250 240 600 2.50 3.38 0.17 0.34 236 375 0.63 255.4

SP10b 150×100 120 300 2.50 4.22 0.25 0.19 56 73 0.76 68.1

Note: bh : cross section (height ×width), d : effective depth, a : shear span, s : tension reinforcement ratio,

web : shear reinforcement ratio, f : PET fiber sheet ratio, uV : calculated shear strength, muV : calculated

flexure strength, exp,uV : tested shear strength

Enhance mechanism of shear strength and deformability

All the jacketed specimens, except for specimen SP10b which showed rather brittle failure after shear cracking

due to the tension fracture of PET fiber sheet, showed somehow ductile failure because PET fiber sheet could

carry the shear force after shear cracking (Senda and Ueda 2008). All the specimens, except for specimen SP6b

which showed the flexural yielding but the peak load before the displacement limit of loading machine was

reached, showed shear failure. Specimens SP1b to SP6b are identical except for the PET fiber sheet ratio.

26

Comparing with the reference specimen SP1b, all the jacketed specimens SP2b to SP6b showed the higher shear

strength and more ductile behaviour after the peak load (see Table 2 and Figure 11). Generally both the shear

strength and the ultimate ductility ratio (or the ratio of ultimate deformation to deformation at peak load)

increase with the increase in the PET fiber sheet ratio (see Table 2 and Figure 12).

0.05 0.1 0.15

1

2

3

4

5

0

Vf

Vs

部材角

SP4

せん断応力

(N/m

m2)

0.02 0.04 0.06 0.08

1

2

3

4

5

0部材角

Vs

Vf

せん断応力

(N/m

m2) SP2

0.04 0.08 0.12

1

2

3

4

5

0

Vs

Vf

部材角

せん断応力

(N/m

m2) SP7

Nom

inal

she

ar s

tress

, MPa

Drift angle Drift angle Drift angle

Vc

Vc Vc

Figure 11. Nominal shear stress-drift angle relationship

1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

供試体番号

μ0.8μ0.5μ0.8測定外

じん性率

(measured)(measured)(expected)

Specimen number

Duc

tility

ratio

,

Figure 12. Ultimate ductility ratio (0.8 (measured) and 0.5 (measured): measured ductility ratio when load-

carrying capacity reduced to 0.8 and 0.5 times of peak load respectively, 0.8 (measured): expected ductility

ratio when load-carrying capacity reduced to 0.8 (actual one would be greater))

The enhancement of the ultimate shear strength by the PET fiber sheet jacketing was observed due to two

reasons; the PET fiber sheet contribution and the increase in concrete contribution. The PET fiber sheet

contribution can be calculated by Eq.8.

ffffff EAEAV (8)

where Kf 005.0 (9)

606.0408.0139.1551.0dadEK ssf

(10)

The increase in concrete contribution was observed, which can be approximated by Eq.11.

0ccc VRV (11)

where cR is the multiplication factor, 0cV is the concrete contribution calculated as ordinary concrete beam, and

cc KR 6.13 (12)

766.1342.0627.0065.0 dadEK ssfc (13)

As shown in Figure 12, the ultimate ductility ratio (or the ratio of ultimate deformation to deformation at peak

load) of the jacketed specimens is greater than that of the reference specimen. Since the PET fiber sheet does not

fracture immediately after shear cracking but gradually fractures with increase in deformation, the load-carrying

capacity (or the remaining shear strength) decreases gradually. In the case of carbon fiber sheet jacketing, once

the carbon fiber sheet fractures, the shear strength is reached and the load-carrying capacity decreases rapidly.

Figure 13 (a) compares the case of SP8b with the case of specimens with carbon fiber sheet whose stiffness is

larger than that of PET fiber sheet in SP8b. The deformability of SP8b is comparable to the case with carbon

fiber sheet in which flexural yielding took place as shown in Figure 13 (b).

27

0.04 0.08 0.12

1

2

3

4

5

0部材角

せん断

応力

(N

/mm

2)

Carbon 3.8ffE

Carbon 1.4ffE

PET 9.1ffE

Nom

inal

she

ar s

tress

, MP

a

Drift angle

0.04 0.08 0.12

1

2

3

4

5

0部材角

せん

断応

力

(N/m

m2)

Nom

inal

she

ar s

tress

, MP

a

Drift angle

Carbon 1.10ffE

Carbon 1.5ffE

PET 9.1ffE

(a) Comparison with shear failure (b) Comparison with flexure failure

Figure 13. Comparison of ultimate deformation with carbon fiber sheet

CONCLUSIONS

Based on the concept of the potential shear strength of a member, which is a function of stiffness of tension and

shear reinforcement at a given deformation of the member, the preferable mechanical property of shear

reinforcement to obtain a high ultimate shear strength and deformability is the linearity with a high fracturing

strain. The jacketing with PET fiber sheet, which is a typical example of the material whose fracturing strain is

high (around 10% or even more) without yielding, proves the good enhancement of shear strength and

deformability.

ACKNOWLEDGMENTS

The author gratefully acknowledges the contribution to this research from various people, especially Mr

Dhannyanto Anggawidjaja and Mr Mineo Senda who are the former graduate students at Hokkaido University

and Mr Hiroshi Nakai of Maeda Kosen Co. Ltd.

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