SP 188-59

Interaction between Fiber Reinforced Polymer
Sheets and Concrete under Biaxial Stress Fields
by T. Furuta, T. Kanakubo, M. Uemura, and H. Yoshizawa

Synopsis:
In this research, the interaction behavior between fiber and concrete wasinvestigated by biaxial plain loading experiments on mortar panels strengthened
with various fiber sheets (carbon, aramid and glass) and analyses based on the
Modified Compression-Field Theory. As result of the experiment and analysis, it
was confirmed that ( 1) pure shear and pure tensile strengths of the strengthened
panels are in proportion to the tensile strength of the fiber, (2) analysis based on
the Modified Compression-Field Theory can express the experimental results
excellently, and (3) in the case of fibers with small elastic modulus, there is a vastdifference between local shear strains and average strains. Further analysis was
conducted with the elastic modulus and weight per unit area set as the variablefactors.

Keywords: biaxial properties; continuous fiber sheet; interaction; mortar panel

671

672 Furuta et al.
Tomoki Furuta is a research associate in the Department of Architecture at the
Akashi National College of Technology.
Toshiyuki Kanakubo is an assistant professor in the Institute of Engineering
Mechanics at the University ofTsukuba.
Masahiko Uemura is a sinior fellow in the TOW SHEET division at the Nippon
Steel Composite Co., Ltd.
Hiroyuki Yoshizawa is a chief engineer in the TOW SHEET division at the
Nippon Steel Composite Co., Ltd.
INTRODUCTION
Currently, the strength and deformation performance of reinforced concrete
members strengthened aseismatically with continuous fiber sheets (hereinafter tobe referred to as sheet) are, in most cases, evaluated by utilizing the existing
formulas used for reinforced concrete. That of fiber in these formulas substitutes
the strength of shear reinforcements. However, in actual members, it is assumed
that, in addition to tensile stresses, complicated stresses are acting as well as
concrete. While in the case of reinforced concrete members, the reinforcing bars
yield with increasing of the deformation of member, it is possible to use the yieldstrength of reinforcing bars for stress evaluation. In the case of members
strengthened with continuous fiber sheets this is not possible. Because the fiber
stress increases as same as the increasing of fiber strain that accompanies member
deformation. Therefore, for continuous fiber sheet-strengthened members, it isnecessary to develop the strength evaluation method based on a detailed failure
mechanism that takes into account the deformation of the members.
In order to develop the strength and deformation evaluation method based on the
failure mechanism, basic data such as the interaction between the sheet andconcrete are obtained and investigated in this research. This interaction involves
the basic properties such as the bond, shear and tensile strengths under multidirectional stresses. To achieve these purposes, a biaxial plain loading experimentand analysis based on the Modified Compression-Field Theory are carried out.
OUTLINE OF BIAXIAL LOADING EXPERIMENTAs shown in Fig. 1 the test pieces are 300x300x15mm fiber sheet-strengthenedmortar panels provided with 24 holes to fix to the loading system, and bolts to set
displacement transducers. 4 types of sheets were applied on both surfaces of themortar panel. As variable factors, the type of sheet, sheet application direction andweight per unit area were mainly selected. Loading stresses to be applied to themortar panel were pure shear stress and pure tensile stress. Table I shows
correspondence between each variable factor and test piece identifications. Fig. 2
shows the sheet direction of the respective test pieces. Four types of sheets were
employed: commonly used E=230GPa carbon fiber sheets (hereinafter to bereferred to as SCF), high-elasticity (E=500GPa) carbon fiber sheets (hereinafterreferred to as HCF), ararnid fiber sheets (referred to as ARF) and glass fiber
sheets (referred to as GLF). These are prepreg sheets with a weight per unit area

Fiber Reinforced Polymer Reinforcements 673
of 75g/m2 . For SCF, additional test pieces of small weight (55g/m2 ) and large
weight (150g/m2) sheets were fabricated. In SCF pieces for pure shear loading,
sheets were applied in the directions of 45°+ 135°, 0°+90° and 25°+ 115° in relation
toward the side directions of the panel. For others, in the directions of 45o + 135°
and 0°+90°. Meanwhile, for test pieces for pure tensile loading, sheets wereapplied in the 0°+90° direction in relation toward the direction of the panel sides.
Three test pieces were fabricated for each one variable factor. Total numbers oftest pieces are 48.
Premixed mortar was used with the compressive strength set to 50MPa. The
mechanical characteristics of the fiber sheets and mortar are presented in Table 2
and Table 3, respectively.
For the pure shear loading, tensile forces (north-south direction) andcompressive forces (east-west direction) of the same magnitudes were applied in
the diagonal directions of the test pieces, using a total of 24 oil jacks (6 for eachside of the panel). For pure tensile loading, tensile forces of the same magnitudes
were applied by 12 oil jacks installed at the north-west and south-east positions.
Displacement transducers were installed on the front surface of the test pieces in 5
directions. 3-direction strain gauges were put on the sheet surface at the center ofthe front and back surfaces. Fig. 3 shows the loading method, and Fig. 4 shows
the positions of the displacement transducers and strain gauges.
EXPERIMENTAL RESULTS
Table 4 lists the experimental results. Photo 1 shows typical modes of failure. Fig.
5 shows the relation between shear stress and shear strain ("!xy-Yxy, measured bystrain gauges) for each test piece. In the test pieces subjected to pure shear
loading, 2 modes of failure were observed, i.e., sheet rupture and edge failure
where failure occurred at the attachment position to oil jacks. No crushing ofmortar was observed. The test pieces, which failed by edge failure, were SCFH
series with large-unit-weight. Though cracking observations during loading could
not be carried out, the "!xy-Yxy relation for all test pieces was found to be linear up
to the point where cracking is assumed to occur. In all test pieces excepting thehigh-elasticity HCF's, shear strain rapidly increased after the cracking. As for the
HCF's, it is considered that the sheet ruptured at almost the same time withcracking. After the loading, the sheets were peeled off, and then fine hair-cracks
as shown in Photo 1 (d) was observed on the putty applied on the mortar surface.
The cracks, however, did not pass throughout the mortar.
Fig. 6 shows the variable factors-maximum stress relation of the test pieces. The
relation between the various types of sheets with the same unit weight andmaximum shear stress is shown in the Fig. 6 (a), and those for maximum tensilestress, in the Fig. 6 (b). As for SCF, the application direction of sheets of the same
weight per unit area and maximum shear stress relation is presented in the Fig. 6(c), and those for each weight per unit area and maximum shear stress, for SCF in
the Fig. 6 (d). Fig. 6 (a) shows that the maximum shear stress increases, as thesame as the tensile strength increases. A similar tendency is also observed in (b).

674 Furuta et al.
From Fig. 6 (c), no significant difference in maximum shear stress due to theapplication direction of the sheet was observed. As can be seen from (d), a
significant tendency was observed, in which, the maximum shear stress increased
as the weight per unit area also increased.
ANALYSIS BASED ON THE MODIFIEDCOMPRESSSION-FIELD THEORY
To understanding the behavior of test pieces, analytical program based on the
Modified Compression-Field Theory (1) is conducted. To adapt this method fortest pieces of this research, two considerations are taken into account (2). One is
the multiple-axis conversion and the other is the bond condition between fiber andmortar. The experimental results obtained by the test pieces for pure shear loading
are compared with analytical results. After that, a comparative analysis is carriedout for the unit weight of sheets as a variable.
The assumptive values used in the analysis are given in Table 5. As the mortar
properties, values obtained by a uniaxial compression test conducted on 50-mm
dia.xlOOmm cylinder pieces were used. For yield bond stress and slip at yieldbond stress, the values obtained from Reference (3) were applied. For the sheet
rupture strength, values obtained on panel test pieces subjected to pure tensileloading were used.
Table 6 compares the experimental results with the analytical results for all test
pieces. The experimental results of the failure mode show full agreement with theanalytical results, excepting for the test pieces that had edge failure. It is assumed
that the SCFH test pieces might have crushing failure, if those had the enoughcapacity at the edge of attachment. The ratio of the experimental results to theanalytical results on maximum shear stress ranges from 0.99 to 1.05. This meansthat this analysis is capable of representing the experimental results excellently.
Fig. 7 shows the analytical results of shear strain - shear stress relation for
typical test pieces. The experimental results roughly agree with the analyticalresults. The differences between the experimental and analytical values found at
the first turning point of the curves are due to the fact that the experimental values
for shear strain are measured by the strain gauges, whereas, the analytical values
represent mean strains. This difference was found in ARF test pieces especially.
The reason for this is the fact that the difference between means strain and local
one increases, as the smaller the elastic modulus of the fiber becomes.

Since the elastic modulus of fiber influences on the difference between local andmean strains, further analysis is conducted for the unit weight of sheets as avariable. Basing on the SCF's elastic modulus, unit weight of ARF and GLF ischanged to have equal rigidity to SCF. As a result, unit weight of ARF and GLF ischanged to 122.3 and 220.5 from 75 g/m 2 , respectively.
The analytical results are shown in Table 7 and Fig. 8. The failure mode for both
ARF and GLF in equal rigidity changes to crushing. The maximum shear stress ofboth exceeds that of SCF. For test pieces with fiber direction of set to 451135°, theFiber Reinforced Polymer Reinforcements 675
maximum shear stress quite exceeds that of SCF. From Fig. 8, for example, if
ARF's unit weight is equivalent to that of SCF, the maximum shear stress isalmost the same. However, the corresponding shear strain at the same stressincreases. For 451135° test pieces, the shear stress corresponding to same strain
increase in equal rigidity results. The maximum stress increases to 1.74 times ofthat of SCF.
It is considered that the shear strain - shear stress behavior of fiber sheets must
be taken account as well as the deformation of RC members.
SUMMARY
As a result of studying the interaction between fiber and concrete, based on
biaxial plain loading experiments using mortar panels strengthened with various
fiber sheets (carbon, aramid and glass) as well as by analysis based on the
Modified Compression-Field Theory, the following findings were obtained.
( 1) In cases of shear rupture, the pure shear and pure tensile strengths of thestrengthened panel are proportional to the tensile strength of the fiber.
(2) Analysis based on the Modified Compression-Field Theory is capable ofrepresenting the experimental results excellently.
(3) For fibers with small elastic modulus, there is a difference between local shear
strain and mean strain. Based on the results obtained by comparative analysis
with the elastic modulus of sheets and the unit weight as the variable factors,
elastic modulus influences the shear stress and strain relationship.
REFERENCES(1) Vecchio, F. J., and Collins, M. P., "The Modified Compression-Field Theory

for Reinforced Concrete Elements Subjected to Shear, " ACI Structural Journal,
Vol. 83, No.2, Mar.-Apr. 1986, pp. 219-231.
(2) Kanakubo, T., "Analysis of Modified Compression-Field Theory for MultiAngle Reinforcements," Summaries of Technical Papers of Annual Meeting
Architectural Institute of Japan, C-2 Structure •, Sept. 1998, pp. 511-512. (inJapanese)(3) Sato, Y.; Kimura, K; and Kobatake, Y., "Bond behavior between cfrp sheet
and concrete (part2)- Improvement of bond strength by out-of-plane confinement-, " Journal of Structural and Construction Engineering (Transactions of AU), No.
509, July 1998, pp. 127-134. (in Japanese)676 Furuta et al.
TABLE 1-LIST OF TEST PIECES.
Sheet application
direction
SCF-0/90-CT
0°+90°--s-cF-45/i_3_5-~:r-·- --45 °+ m
rsc·F-25/1 is".:cT -25 °+ 115 °o +9oTest piece

Loading method0---scF-"0/9o-.:r-·----- -

0

_____

Pureshear:::=~~~~t;;ar ::=:~
Pure shear

Lot No.
6/10-2_!5123-1 ____ _6/10-1_p~~;"t~-;;-~ik-----r------------6/i0-:3·------------

0

scFL-o/90-cT
0 °+90 °Pure shear
6/10-2-------------------------------------- -----------------------------------------------------------------------------------------SCFH-0/90-CT
0 °+90 °Pure shear
6/10-2
HCF-45/135-CT
45 · + 135 ·Pure shear
7/13-1·--HcF-.:o/9o::-c:r·------------ ------------ci-~90_'"" __________ -----------i>~~~-~;;;~~----------r-------------711 ~-----i=icF::-o/9o::-:r·--------------- ---------- o + 90 ° ----------- ----------i>~~~-i-~~~ii~---------- --------------;7Ti3-:2____ _0

AFF-45/135-cT
45°+135°
Pureshear
6/23-1
f-ARF::-o/9o=-c:r·-------- ------- o +9o------"P~~;~h-~~;-------- -----------6/23-=2·-------------rn:o/9o..:r·---------- --~+90°___ ------i=,-~;t~~;;------r------7-il-=-~-------0

GLF-45/135-cT
r-GLF-0/9o=cT_________

r--oi,F-0!9o=:r·---------

0--45 °+ 135 °Pure shear

6/23-3o +9or~-"t~~;i~----r---7/i~-----------~90-;--- -----Pure sh;~-r--r-----------6/23".:2 ______ _
0

0

scF
:Normal carbon fiber sheet (Unit weight- 75g/m")
SCFL : Unit weight= 55 g/m2
SCFH :Unit weight= 150g/m2
HCF : High elasticity carbon fiber sheet (Unit weight= 75g/m 2)
ARF : Aramid fiber sheet (Unit weight= 75g/m 2)
GLF :Glass fiber sheet (Unit weight= 75g/m 2)CT: Pure shear stressT: Pure tensile stress
45/135, 0/90, 25/115: Sheet application direction

TABLE 2-FIBER SHEET PROPERTIES.
Material

Strength(MPa)

Elastic
modulus
(GPa)

SCF

4,145

228.3

HCF
ARF
GLF

2,500
3,500
2,224

500.0
140.0
83.3

Unit fiber
weight(g/m')
55
75
150
75
75
75

Fiber Reinforced Polymer Reinforcements 677

TABLE 3-MORTAR PROPERTIES.
Lot No.
5/28
6/10
6/10
6/10
6/23
6/23
6/23
7/01
7/0!
7113
7/13

-I
-I
-2
-3
-I
-2
-3
-I
-2
- I
-2

Compressive
strength
(MPa)
46.6
59.7
63.4
69.0
60.5
57.9
6!.3
55.5
55.6
56.9
58.2

. .
Elastic modulus
(GPa)
22.2
30.!
30.2
30.7
29.4
28.2
28.6
25.2
26.5
25.6
26.6

Strain at maximum
stress
(%)
0.364
0.296
0.294
0.3!6
0.278
0.272
0.286
0.329
0.3!9
0.321
0.297

678 Furuta et al.
TABLE 4-LIST OF EXPERIMENTAL RESULTS.
Test pieceType of sheet

SCF-0/90-CT~

SCF-45/135-CT

~
~_
1-3

3

Carbonrj-(normal)SCF-25/1 15-CT
SCF-0/90-T

Loading
methodMaximum shear stress(MPa)

Failuremode-----H~--i ~A~j r=--i~~~~:::-

~--

5.52
4.36

Pure shear 1--

!

·

!

6:J.r-=:
5.52_::=:::Hl=

:;r-

(Av.)
5 ·28

4.25
4.34

-1

J:

Pure tensile

(A )
v4
53

(Av.)
4_69

:::::::IfF:=:

RI!Q!ure---~_!!E}ure _R~!P_tureEdge-~:g:::~
R!!Q!ure___ _Ruptu~------~~~%~~--~~

Carbon___ __±j_!______ j(Av.)---~!!P!_ll.l:~---SCFL-0/90-CT ~3 (light weight)
Pure shear--~---:1..~-l 3.55-------~.<Jg_~------l-------t-7-+--------------t-----t------:4""'.,_14,__-+-!----+--"'R""IJill""t""u"'""'re~Carbon____ _2_].§. __-l(Av.)------~E.g_e__ _SCFH-0/90-CT ~:.) (heavy weight) Pure shear ----~~-~~:
7.92----~~~-----

c:}-____ll_?_____ I~J-______ z_._~_?____ ::::j
1
2 ·00
Pure shear-------~!_?______ ~

(Av.)
2.40

__ Ruptur~_
EdgeRll]:>ture

HCF-0/90-CT~~3

HCF-45/1 35-CT

rj-- (high-elasticity)-----+~t----j 2.62--~~~---~~Pure tensile -:=::-f -"-_-_3<t~J ~:~~~t~;_;___
1 6.~ 9r---:~:.)---~1
RuptureHCF-0/90-T
ARF-0/90-CT=-l-

Carbon

-1

5. 98

r:l-

-1

----5.49--l:T:T

Pure shear-_-TI_r---1--:
4 _99

ARF-45/1 35-CT-2
1-:3"-

ARF-0/90-T

8-32

GLF-0/90-CT:2

Pure tensile __ __l_&?_ ______ j
3.92_____ ]3_·:__3?_65____ _j~_1

Pure shear

GLF-45/135-CT
GLF-0/90-T

Aramid-J-1----us- i

:;r-T

·:3

---5-:47--i-----~-'~

Glass"-=-_:23_,

Pure tensile

Ruptu~-(Av.)----~!!.1?!_!1_~~----

5 74

.

(Av.)
5 48

·

(Av.)
3 _78
(Av.)
3 03

·

-------I27 ______l

(Av.)
3 22

1.12
:
--1.07 ____1

(Av.)
1· 12

-----3])2____!
_____L!l____~

-1
, ~

3_37

(Av.)

·

----~!!.1?!_!1!~----~upture______ !!P!_ll.l:~-----~!!.l?!_ll!~Rll]:>ture~!!.l?!.ll.l:~----

RuptureRupture-~!!!?!.!!.'"~---~upture___ _Rupture----~!!.1?!_!1!~---~!!.l?!_ll.l:~----

Rtt]:>ture----~!!.l?!_ll.l:~----___ .13:!!.1?!_1!~~---Rtt]Jture

Fiber Reinforced Polymer Reinforcements 679

TABLE 5-ANAL YTICAL VALUES.
Test piece

E,
%

O"s

MPa

E,
GPa

_$.g_~:2{?_9_:~I________ ---~?.:~---- ___ }2:~---- ___ Q,~2~--- _____ !_!}_____ ----~'~L- ____ L2L ___ _!_,~~L ---~-~~,L-~-gE:~-~{!}_~:~L- ---~2:~---- ___ }2:~---- ___ Q,~1-~--- _____ !_~_L_ ----~'~L- ____!_~~L ---~~~}___
SCF-25/115-CT
59.7
30.1
0.296
162
4.56
1.97
1,686
228.3
SCFL-0/90-CT
63.4
30.2
0.294
94
4.56
1.97
1,686
228.3

Ln______·scji}i:o7'io:cr_____ ---63:4____ ---'Joj____ ---oj94--- -----i-62 ____ ----4:56-------~-:97____---~-:686___ ---228:3---

HcF-ot9o-cT

56.9

25.6

0.321

283

4.56

1.97

591

50o.o

ARF-45/135-CT
GLF-0/90-CT

60.5
57.9

29.4
28.2

0.278
0.272

226
70

2.03
0.91

0.88
0.39

1,100
574

140.0
83.3

WcF:4s/T3-s-:cr--- ---56~9---- ----25~6---- ---o~32T- ------io _____ ----4:56---- ----1':97---- ----5-9i____ ---s-oo:o--~\~f-~Qt22~g_I_______ ---~1:2____ ----~~:~-- ___ Q,~!L ______ !_~~---- ----~,Q?.__ ______ Q,~~---- ___!_,!_QQ____ __!_~Q,Q __ _a'LF::4sTi35-:c--r·-- ---6i3____----28~6-------oj86___ ------94 _____----o:9-~-----o:39---- ----57_4_____ ----83:3 ___0" 8 : Compressive mortar strength

E,: Elastic modulus of mortar
Sm: Mean crack spacing (45°-direction)r by: Yield bond stress (per unit length)
Sb,: Slip at the yield bond stress
fru: Sheet rupture strength
E,: Elastic modulus of sheet
E ,: Strain at compressive mortar strength

TABLE 6-COMPARISONRESULTS.
Test piece

BETWEENANALYTICAL

t.xoenmental resu ts
JYiaXImum
Failureshws~fss
mode
MPa

SCF-0/90-CT~-~i--- ---~~~~-::1 ~AJJ ---~!!R!!!!:~------5:sz--·---Rtl~llf~{--

SCF-45/135-CT(Av.) * ---~!!R!!!!:~--~i--- --til--l---:;32----! 5.25 -----~§~[-~---

SCF-25/115-CT---~=tf----1 ~~2J~~i--- ---,n:;---·1.~T-

Ana lie
JYiaximum
Failureshw st;)ss
mode
MPa

Ex~erimentI

nalytic--{1}~-~ 1.00

Rupture5.18

Rupture --H&---j 1.0 I*---Rtl~llf~~---

5.17

Rupture--H~---i 1.02

"RuiJftfre--

4.11

Rupture:::::~~:=j 1.00*---104"--

8.81

crushing-----=-----, -~~T --Too----1

2.39

Rupture2.79

Rupture:-T-

l~T

HCF-0/90-CT

EXPERIMENTAL

5.61.-~'3------~!!R!!!!:~---* ---~~§!¥~--SCFL-0/90-CT t~i- ---Hi---! (Av.~-4:1'4'"1 4.1
SCFH-0/90-CT

AND

L:j--1r-~------t.fi7-::J SA~) ----ggg_~--------Ea~e------~~§!¥~--~+- ---N-5---I (Av-r
2.3"Ruiilllre___--~!!R!!!!:L---u~gg-_____________ J
I---(J~82"'i

II------------~-__!_J:~---i 1.00*--u~&J---1

HCF-45/135-CT(Av-j*
1-~i--- --++1----!
---:z·.ur--1 2.9

ARF-0/90-CT

L:j--- ---H~----1 ~A?J --~tlR!li~~-b-- "T75---!
---Rii~turr

5.55

Rupture ---b~~~---~ I .0 3

~AXJ

5.28

Rupture---H}--1 1.04--TG'I"'i

3.01

Rupture--Ht-~ 1.01

3.24

Rupture--+gi---1 0.99-~'3---

1-l- --H~---:j
ARF-45/135-CT~~T.-~J---

GLF-0/90-CT
GLF-45/135-CT---:;:47"'

1-1r::z-- ---H%---1

tT- ---rs'B'---1---~!!R!!!!:L''Rli~Itl~~----~!!R!!!reWli ---Rtl§llif~--___

1-~i--- ---H+--:J ~A2)---3:DT-h---* : Except edge failure-----~§lff~-----~!!R!!!!:~-----Rtl§Itl~~------&~M---j_____________ j 1.o5•-

I-r:u'l---~---u~go----u~g:J---1

680 Furuta et al.
TABLE 7-ANALYTICAL RESULTS OF UNIT WEIGHTS OF FIBER INCREASED BY
ELASTIC MODULUS RATIO.
Analytic results
Elastic
modulus
ratio

Unit weight(glm')

SCF-0/90-CT-

ARF-0/90-CT

Type of fiber(Test piece)r max
I SCF r max

Maximumshear stress(M?a)

Failure mode

75.0

5.61

Rupture

-

1.63

75.0

5.55

Rupture0.99

ARF equal rigidity

1.63

122.3

6.90

Crushing

1.23

GLF-0/90-CT

2.94

75.0

3.01

Rupture0.53

GLF equal rigidity

2.94

220.5

5.63

Crushing

1.00

SCF-45/135-CT

-

75.0

5.18

Rupture-ARF-45/135-CT

1.63

75.0

5.28

Rupture1.02

ARF equal rigidity

1.63

122.3

9.05

Crushing

1.74

GLF-45/135-CT

2.94

75.0

3.24

Rupture0.63

GLF equal rigidity

2.94

220.5

7.65

Crushing

1.48

. . .

..

ARF equal ngtdtty : ARF umt wetght IS mcreased to have same ngtdtty of SCF.
GLF equal rigidity : GLF unit weight is increased to have same rigidity ofSCF.

Fig. 1-Shape of test piece.

Fiber Reinforced Polymer Reinforcements 681

Fig. 2-0utline of each test piece.

(a) Pure shear(b) Pure tensile

Fig. 3-loading direction.

(a) Displacement transducers(b) Strain gauges

Fig. 4-Position of displacement transducers and strain gages.

682 Furuta et al.

-SCF0/90CT-- -SCF45/135CT------SCF25/115CTo~~~~~~~~~~

0
2
4
6
8
Shear strain(G) r xy (x10" 3)(c) ARF, GLF- Pure shear-ARF0/90CT-- -ARF45/135CT------GLF0/90CT----GLF45/135
0 ~0~~2~~4~-76~~8
Shear strain(G) r xy (x10"3)(a) SCF- Pure shear

Fig_ 5-Shear stress: shear strain relation.

-SCFL0/90CT-- -SCFH0/90CT------HCF0/90CT--HCF45/135CT
0 ~o~~~2~~4--~6~~8

Shear strain(G) r xy (x10" 3){d) SCF, HCF, ARF, GLF- Pure tensile

QL-0~~2~~4~~6~~8
Shear strain(G) r xy (x10" 3)(b) SCFL, SCFH, HCF- Pure shear

Fiber Reinforced Polymer Reinforcements 683

iii'~ 10.-----.--,-....-,-...,,---.,---,

! 8

iii'
~12.5.----,-, - . , ,. -............,-...,,---,·---0 I 90 Av.
451135 Av.

b
.. 10

0

~

e\

i 7.5

·---- Av.

/8\

\

U)

\

-i

5

/

\

\

/

'

' ,
~~

§

2

\

\

b

E 2.5

~ 0'---:-:':=-:-:7::--:=--=-"-=---'

o~~SC~F~H~C~F~A~R~F-G~L~F~
Type of fiber (Unit weight: 75glm 2 )-SCF HCF ARF GLF

Type of fiber (Unit weight: 75glm 2, Pure tensile)(a) Type of fiber- Maximum shear stress(b) Type of fiber - Maximum tensile stress

iii'
~ 10

iii'

..
i!l

~ 10

~

8

....
. 4

.1>

6

&----l_____g
D

t:>

.c:

-

!

-

~. sr-

-

."
:e

2

·---- Av.

><

0

~

§

E

.§

....

0190

251115 451135

I

0

,.D
,.,•

_if,.

4r

9//

2r-

0

0

SCFL

D

'

·---- Av•
SCF

SCFH

(Unit weight: 75glm 2)

SCF fiber weight (Application direction: 0190)(c) Fiber direction- Maximum shear stress(d) Fiber weight- Maximum shear stress

SCF fiber application direction

Fig. 6-Relation between each variable factor and maximum stress.

684 Furuta et at.

;;;-

5

\

4

0..

...

SCF45/135CT--1--- -2--3-Analytic--1--- -2--3-Analytic
40Shear strain

4r xy(x1rJ 3)

Shear strain(a) SCF-0190-CTr zy(x1rJ3)(b)SCF-45/135-CT

;;;-

~

3

v------------I HCF45/135CT--1--1--- -2--3-Analytic

0

0.5

1.5

Shear strainr xy(x1U3)--- -2--3-Analytic

4
Shear strainr xy(x1U 3)(d) ARF-45/135-Cf(c) HCF-451135-Cf

Fig. 7-Shear stress: shear strain relation.
10

10
iii"

iii"

0..

0..

\...

\...

8

II)
II)

II)
II)

g

g

II)

II)

."'

8
6

.

....

....

-SCF

:--~~ ~

""
.c:
CJ)

ti

__ ................
equal rigidl--·-G L F

- G L F equal rigidity

0

5

10

15

0

5

10

Shear strain rxy(x1U 3)

Shear strain r xy(x1U 3)(a) 0/90-CT(b) 451135-CT

Fig. 8-Shear stress: shear strain relation (analysis).

15

Fiber Reinforced Polymer Reinforcements 685(a) SCF-0/90-CTI(b) HCF-451135-CTI(c) ARF-45/135-CT3(d) Detail of crack

Photo 1-Failure mode.