SHEAR BEHAVIOR OF FIBER-MESH REINFORCED PLATES
Toshiyuki KANAKUBO*1 and Masaharu SHINDO*2

ABSTRACT : To investigate the fundamental behavior of fiber-mesh reinforced plates,
pure shear test is carried out for 11 specimens. Carbon and aramid fiber meshed in two, threeand four directions are used as reinforcements for 300×300×15mm mortar panels. Testvariables are fiber type, amount of fiber, mesh configuration, and mesh layers. From the test
results, two failure processes, compression failure and rupture of fiber, are observed.
Measured fiber strains correspond with the directions of fiber in regard to applied load
direction. The analytical study is carried out based on the modified compression-field theory
given by Collins. The shear stress versus shear strain relationships obtained by experiments
show a good correlation with analytical results.
KEYWORDS: mesh, panel, configuration, pure shear, tension stiffening

1 INTRODUCTION
Continuous fibers, such as carbon and aramid fiber are materials with high strength anddurability. However, all-elastic and brittle behavior have made it difficult to use as a
substitute for steel reinforcement, especially in seismic areas. One of the effective use is in
the development of composite structures consisting of concrete, steel reinforcement, andcontinuous fibers. In members of this type, ductile behavior should be given by thelongitudinal steel reinforcement, while the high strength of continuous fiber is effective foruse as shear and confining reinforcement. The fiber also has the merit of high durability
when arranged at the surface of members.
Fig. 1 shows examples of the use of fiber-mesh reinforced panels as a shell for members.
The panels are about 10-15mm thick, and used as a substitute for wooden forms. After
concrete casting, the panels are not removed and become a portion of the member. Thesepanels are expected to carry loads, especially for shear and confinement. Composite RC
structures profiled by continuous fiber-mesh reinforced plate seem to be one of the mosteffective construction systems to utilize continuous fibers. In this paper, shear behavior offiber-mesh plates, which is one of the fundamental properties, is investigated and evaluatedthrough experimental and analytical studies.

*1 Institute of Engineering Mechanics, University of Tsukuba, Japan, Ph.D.
*2 Graduate School, University of Tsukuba, Japan

Steel Reinforcement

Core RC
Fiber-mesh Panel

Fig. 1

Examples for effective use of fiber-mesh reinforced plates

2 TEST PROGRAMS
2.1 SPECIMENS AND LOADING
Specimens are 300mm square with a thickness of 15mm. Each specimen has a total of 24
holes along the edges to fix 12 attachment plates. Two oil jacks are connected to one
attachment panel via pins. In this test, monotonic pure shear loading is achieved by applying
equal pressures to 24 oil jacks. Fig. 2 shows the loading system and details of the setting.
North

West

East

South

Fig. 2

Loading system and setting of specimen

2.2 MATERIALS AND TEST VARIABLES
Test variables are fiber type (aramid, carbon), filament number of yarn (2k, 4k, 6k), meshconfiguration (2, 3, 4 directions) and mesh layers (1, 2 layers). Aramid fiber, which has 2k(30 denier) and 4k (60 denier) filaments, and carbon fiber with 6k filaments per one yarn are
Table 1 Mechanical properties of fiber (nominal values)
Elastic
Ultimatefor one yarn
Fiber type
modulusstrength
Filaments
Sectional
(MPa)
(MPa)
per one yarn area (mm2)*2k
0.452
Aramid70 000
3 500
4k
0.905
Carbon230 000
3 500
6k
0.462
* includes binder volume

Strength
(N)
790
1 580
810

Table 2

Specimen identification

N4 - C A 30 x2
number of layers : nothing=1 x2=2
amount of fiber : 30=2k 60=4k 06=6k
fiber type : A=aramid C=carbon
configration : C=2 T=3 D=4 directions
mortar with 40MPa strength

used as reinforcements. Mechanical properties of fiber are summarized in Table 1. Thesefiber are arranged in mesh with 2, 3 or 4 directions (see Fig. 4). The spacing of each yarn isfixed at 10mm. Epoxy resin is used for binder. Mortar with specified compressive strengthof 40 MPa was cast vertically. The measured compressive strength at the loading was 55.1
MPa. By combining test variables, a total of 11 specimens are tested. The relationships
between specimen identifications and test variables are shown in Table 2.
2.3 MEASUREMENTS
Load, displacements and fiber strains were measured. Load was obtained by a load cell
set at an oil jack. Five displacement transducers were set up to four bolts fixed in thespecimen as shown in Fig. 3. Four or six strain gages were attached as shown in Fig. 4.
North

3 directions

3
D4

D1
D5

West
D3

1

1

2

2 directions1
3 2 central portion
4 side portion

East

6

4 directions

4
2

D2

North

4

3

5
South

Fig. 3

Displacement transducers set up

South

Fig. 4

Positions of strain gages

3 TEST RESULTS AND DISCUSSIONS
3.1 FAILURE PROGRESS
Test results are summarized in Table 3. In all specimens, first crack took place at over
2MPa of shear stress. Specimen N4-CC06 failed by rupture of fiber at essentially the first
crack load. In other specimens, cracks took place step by step and diagonal displacement
became larger. Two failure pattern were observed, rupture of fiber and compression failureof mortar. Two specimens that showed typical failure patterns, rupture and compression, andtheir shear stress versus shear strain curves are shown in Fig. 5.

Table 3 Test results
Shear stress at
Maximum
Reinforcement
Specimenfirst crack
shear stressType Aspect*
(MPa)
(MPa)
N4-CA30
2d-2k
2.11
2.45
N4-TA30
3d-2k
2.43
3.25
N4-DA30
4d-2k
2.63
3.49
N4-CA60
2d-4k
2.24
2.88
Aramid
N4-TA60
3d-4k
2.42
4.01
N4-DA60
4d-4k
2.28
4.07
N4-CA30x2
2d-2k-2
2.66
3.42
N4-DA30x2
4d-2k-2
2.73
6.08
N4-CC06
2d-6k
2.24
2.26
Carbon 3d-6k
N4-TC06
2.31
2.50
N4-DC06
4d-6k
2.03
2.71
* direction - filament - layer

Failure pattern
RuptureCompression
RuptureEdge failure
Compression
Compression
Compression
RuptureRuptureRuptureRuptureShear stress τ (MPa)5N4-TA60

4
3

N4-CA30

2
1
0

0

10

20

30
-3

Shear strain γ (x10 )Fig. 5

Typical failures and shear stress - shear strain curves

3.2 STRAIN OF FIBER
Shear stress versus fiber strain curves of specimens using 4k-aramid are shown in Fig. 6.
The left, middle and right graph shows specimen of 2-direction, 3-direction and 4-direction
mesh, respectively. The numbers correspond with the gage numbers shown in Fig. 4.

4
3

3

4

2

1
2

1
0

0

0.5

1

1.5

Strain εr (%)

Fig. 6

5

N4-TA60
44 1

2 5 3 6

3
2
1
0

0

1
2
Strain εr (%)

Shear stress τ (MPa)5N4-CA60

Shear stress τ (MPa)Shear stress τ (MPa)5N4-DA60

4

2 1 3

4

3
2
1
0
-0.5

Shear stress versus fiber strain curves

0

0.5

1

Strain εr (%)

1.5

Since these specimens were not failed by rupture of fiber, maximum strains are smaller
than the ultimate strain of 5%. In specimen N4-CA60, all strain-curves behave similarly.
Fibers of 2 directions are under the same conditions to applied loads. On the other hand,each curve is different in specimen N4-TA60 and N4-DA60. These phenomena correspondwith fiber direction to applied load. No.1 and 4 gages of N4-TA60 and No.4 gage of N4DA60 are placed on fibers that run along the compressive direction (see Fig. 4). No.2 and 3
gages of N4-TA60 and No.1, 2, 3 gages of N4-DA60 show the same tendency.

4 ANALYTICAL PROGRAM
The analysis based on the “Modified Compression-Field Theory” proposed by Collins[1] is carried out to obtain shear behavior of fiber-mesh reinforced panels. Analytical
relationship between shear stress and shear strain of panels can be obtained by solving
compatibility conditions and equilibrium conditions using proposed stress-strain relationshipfor concrete. In addition, tension stiffening effect is also considered in this paper.
4.1 ANALYTICAL METHOD
The analysis is carried out according to the following process (notation is in appendix).
Step 1 : Choose principal tensile strain ε1 to analyze.
Step 2 : Estimate average stress of reinforcement (fiber) f r .
Step 3 : Calculate principal tensile stress of concrete f c1 by formula (1) (Fig. 7).
2 ⋅ f c ⋅ ε1
(ε 1 ≤ ε cr )
 f c1 =
f ⋅ε
εc

,
f cr = 0.33 − f c ,ε cr = cr cf cr
2 ⋅ fc(ε 1 ≥ ε cr )
 f c1 =
ε
1
+
200
⋅

1

( 1)

Step 4 : Calculate shear stress τ xy from equilibrium (Fig. 8).
τ xy = f c1 + ρ ⋅ f r( 2)

Step 5 : Calculate principal compressive stress of concrete f c2 from equilibrium.
f c 2 = f c1 − 2 ⋅ τ xy

( 3)

Step 6 : Calculate f c2 max for given ε 1 by formula (4).
f c 2 max / f c = 1 / (0.8 − ε 1 / ε c ) ≤ 10
.

( 4)

f c1

Tensionf cr

negative

Compression

fc
f c2max

εcr
Fig. 7ε1εc
negative
Proposed stress-strain relationship for mortar

y

fr

τby

f r・A rf r・A r/√2

f r・A rτxy

Fig. 8√3・fr ・A r

y
x

f c1
τxy
Equilibrium conditions

Fig. 9s by
Bond assumption

3 direction

4 direction

Fig. 10 Effective area for ρ

Step 7 : Calculate principal compressive strain ε 2 by formula (5) (Fig. 7).
2
f c2 
ε  ε f
Q c2 = 2  2  −  2 
f c 2 max
f c 2 max  εc   εc Step 8 : Calculate strain in y-direction ε y ( = ε x ) from geometry.

ε 2 = ε c ⋅ 1 −

1−

( 5)

ε y = (ε 1 + ε 2 ) / 2( 6)

Step 9 : Calculate f r .
f r = Er ⋅ ε y( 7)Step 10 : Check if f r calculated agrees with estimated f r . If not, return to Step 2 withnew estimate of f r .
Step 11 : Check that f c 2 < f c 2 max . If not, then mortar crushing by compression.
Step 12 : Calculate tensile force of reinforcement at a crack Prcr (Fig. 9 [2]).

Prcr =(1 + nρ ) ⋅ Prm ⋅ sm,nρ ⋅ sm + 2 / k ⋅ tanh( k ⋅ sm / 2)

Prm = f r ⋅ Ar ,k=

(1 + nρ ) ⋅ τ byE r ⋅ Ar ⋅ sby( 8)

Step 13 : Calculate tensile stress of reinforcement at a crack f rcr .
f rcr = Prcr / Ar
( 9)
Step 14 : Check that f rcr < f ru . If not, then reinforcement breaks (rupture of fiber).
Step 15 : Calculate γ xy from geometry.
γ xy = 2 (ε y − ε 2 )( 10)

To obtain the complete stress-strain relationship, these calculations are repeated for arange of values of ε 1 , from small ε 1 and increasing until recognizing crush or break.
In this analysis, formula (4) is re-modified to adapt the reduction factor for concrete
strength to 55MPa class mortar, because the reduction factor proposed by Collins wasdetermined from test results of concrete with 27MPa strength. Formula (8) represents theeffect of tension stiffening as the force in reinforcement at a crack is bigger than the averageforce. Reinforcement ratio, ρ , is calculated using the following formulas based on
consideration of effective sectional area of yarns to y-direction (Fig. 10). Other common
data for analysis are : f c = −551
. MPa , ε c = −0.0035, n = 14
. (aramid), n = 4.6 (carbon),2
τ by / sby = 4300 N / mm

2-direction :

Ar
,
s⋅t

3-direction :

3Ar
,
s⋅t

4-direction :Ar (1 + 1 / 2 )
s⋅t

( 11)

Specimen
N4-CA30
N4-TA30
N4-DA30
N4-CA60
N4-TA60
N4-DA60
N4-CA30x2
N4-DA30x2
N4-CC06
N4-TC06
N4-DC06

Table 4 Comparison of analytical and test results
Analyzed
Data for analysis
Ratio of test to
maximum shear
analysisρ(%) sm(mm) stress (MPa)
0.301
20.0
2.20
1.11
0.522
15.0
3.21
1.01
0.514
14.8
3.09
1.13
0.603
16.7
3.41
0.84
1.045
14.8
4.24
0.95
1.030
16.0
4.22
0.96
0.603
12.1
3.41
1.00
1.029
12.1
4.21
1.44
0.308
100.0
2.20
1.03
0.534
20.0
4.34
0.58
0.526
18.2
4.60
0.59

Analyzed
failure pattern
RuptureCompression
RuptureCompression
Compression
Compression
Compression
Compression
RuptureRuptureRupture4.2 COMPARISON OF ANALYTICAL AND TEST RESULTS
The results of analysis are summarized in Table 4. Analyzed maximum shear stresses
show a good correlation with test results especially for aramid specimens. The average ofmaximum stress ratio of test results to analytical values is 1.06 and 0.73 for specimens
reinforced by aramid and carbon fiber, respectively. The analyzed failure patterns also
correspond to test results. Fig. 11 shows comparisons of shear stress - shear strain curves
between analytical and test curves. Though the reducing portion of curves is obtained byanalysis, observation of this portion is not possible in the test program because of oil jackloading. It is considered that other portions are almost similar between analytical and test
curves. However, the test curves of specimens reinforced with carbon fiber do not fit theanalysis.
5
N4-CA30

Shear stress τ (MPa)Shear stress τ (MPa)

5
4
3

Test

2
Analysis

1
0

0

10

20

30
-3

Shear strain γ (x10 )N4-TA60

Test

4

Analysis

3
2
1
0

0

10

20

30

Shear strain γ (x10-3)

Fig. 11 Analyzed shear stress - shear strain curves

5 CONCLUSIONS

To investigate the fundamental behavior of fiber-mesh reinforced plates, pure shear test
and analysis are carried out. The conclusions are summarized as follows.
(1) Two failure processes, compression failure and rupture of fiber, are observed and can beaccurately predicted from the analysis.
(2) Measured fiber strains correspond with the directions of fiber in regard to applied load
direction.
(3) Maximum shear stresses from analysis show a good correlation with measured values
for the aramid fiber meshes.
(4) The shear stress - strain curves from testing agree with the analytical curves for thearamid fibers. Shear behavior of fiber-mesh reinforced panels can be predicted by the
analysis based on the modified compression-field theory.

ACKNOWLEDGEMENT

This research is conducted under the Research Project on FRP-Hybrid Structures(Chairman : Prof. Y. Matsuzaki, Science University of Tokyo) organized in the Associationof Architectural Research Promotion. The authors gratefully acknowledge the members of
the project for their kind support.

REFERENCES[1] Vecchio, F. J. and Collins, M. P., "The Modified Compression-Field Theory for
Reinforced Concrete Elements Subjected to Shear," ACI Journal, March-April, 1986,
pp.219-231[2] Muguruma, H. and Morita, S., "Fundamental Study on Bond between Steel andConcrete," Journal of AIJ, No. 131, January, 1967, pp.1-8 (in Japanese)

APPENDIX
Ar : sectional area of reinforcement
E c : elastic modulus of concrete
E r : elastic modulus of reinforcementf c : compressive strength of concretef c1 : principal tensile stress of concretef c 2 : principal comp. stress of concretef c 2 max : max. effective strength of f c
f cr : crack strength of concretef r : average stress of reinforcementf rcr : tensile stress of reinf. at a crack
f ru : ultimate strength of reinforcementn : elastic modulus ratio = E r / E c
Prcr : tensile force of reinf. at a crack
Prm : average tensile force of reinf.

-NOTATIONs : spacing of reinforcement
sm : average spacing of cracks
sby : slip of reinforcement at τ byt : thickness of panel
γ xy : shear strain

ε 1 : principal tensile strain
ε 2 : principal compressive strain
ε c : strain of concrete at f c
ε cr : strain of concrete at f cr
ε y : strain in y-direction

ρ : reinforcement ratio
τ by : bond stress per 1mm at sby
τ xy : shear stress