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Study of various analytical models for prediction of shear
strength of SFRC beams.
Shear strength predictions using various models available
in literature.
comparative study of various models
Objective of the thesis
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Introduction
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Fig.Beam failure modes (from ACI-ASCE Committee 426, 1973)
Types of Failure In Beam
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Behavior of beam in Shear
Fig.Typical example of Shear tension failure of reinforced concrete beam. (Nilson 2005)
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Type of steel fibers
Fig.Types of steel fibres (Dinh,2010)
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Steel Fibrous Reinforced Concrete (SFRC)
Enhance shear resistance and ductility in reinforced
concrete beams.
Enhance post-cracking strength of concrete.
Uniform cracking distribution.
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Shear strength prediction models
bdadkfVu ct
41
7
Sharma (1986)
Where,
k = 2/3,
fct - Split cylinder strength of
SFRC
a - Shear span.
d - Effective depth of beam
'0.79 ( )ct cf f MPa
If fct is unknown, then
Fig. a/d, Shear span to depth ratio
f’c - crushing strength of concrete
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'0.16 17.2 tn ucVdV f bdM
maxMM d a dV V
0.41tu F
,
τ -the fiber-matrix bond strength was taken to be 4.15
σtu - the post-cracking tensile strength.
Mansur et al. (1986)
F-Fiber factor
max / 22
MM a for a dV V
max / 2MM d for a dV V
Where
ff
f VDL
F
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e = 1.0 for a/d > 2.8 and e = 2.8d/a when a/d ≤ 2.8;
fspfc=computed value of spited cylinder strength of fiber concrete
9
MPavadfevu bspfc
8024.0
FCBF
ff cuspfc
20
vb - fiber pullout strength
Narayanan & Darwish (1987)
B= 0.7 C = 1
fcu= cube compressive strength
where
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Ashour(1992)
)()711.2( 3/13 , MPaFfv ad
cu
)(25.0167.0 , MPafFev cu
5.2/ dafor
5.2/ dafor
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Khuntia et al. (1999)
0.167 0.25 'n cV e F f bd
Where,
e = 1.0 for a/d > 2.5 and
e = 2.5d/a when a/d ≤ 2.5.
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Dinh et al.(2011)
n cc FRCV V V
Where,
c- Depth of compression zone
1 3 10.85k k
(σt )avg - the average tensile stress of SFRC
Where, β1 = 0.85 for fc’ ≤ 27.6 MPa and
β1 = 0.65 for fc’≥ 55.1 MPa,
yScc fAV 13.0
)(cot)()( ancdbV avgtFRC
bfkkfA
cc
ys,
31
)()0075.0*(*5.1*8.0)( 4/1 MPaV favgt
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Kwak et al.(2002)
bdvadfeV bspfcn ]8.0)(7.3[
3/13/2
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BEAM DATA TAKEN FROM FOLLOWING INVESTIGATORS
• Swamy (1985)• Mansur (1986)• Lim (1987)• Ashour et al. (1989)• Li (1992)• Schantz (1993)• Swamy (1993)• Tan (1993)• Imam et al. (1998)• Casanov and Rossi (1999)• Noghabai (2000)• Kwak (2002)• Rosenbusch (2002)• Cucchiara (2004)• Parra-Montesinos (2006)• Dinh (2011)• Jain & singh (2013)
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Table A-1 : Details of beams from various investigators
Investigator Beam ID
b (mm)
h (mm) d (mm) a/d ρ
(%)fy
(MPa)Fiber type
Lf (mm)
Df (mm) Lf/Df Vf
(%)f'c
(MPa)vu(exp.)
(MPa)
Swamy (1985) B52 175 250 210 4.5 4.00 415 C 50 0.5 100 .4 35.5 2.16
B53 175 250 210 4.5 4.00 415 C 50 0.5 100 .8 37.4 3.1
B54 175 250 210 4.5 4.00 415 C 50 0.5 100 1.2 39.8 3.13
B55 175 250 210 4.5 3.05 415 C 50 0.5 100 .8 38.2 3.21
B56 175 250 210 4.5 1.95 415 C 50 0.5 100 .8 41.8 2.62
B63R 175 250 210 4.5 1.95 415 C 50 0.5 100 .8 35.1 2.05
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0.00 3.50 7.00 10.50 14.00150
250
350
450
550
650
R² = 0.0311011370249685
Experimental shear strength, MPa
Ove
rall
dept
h ,h
(mm
)
Fig. Effect of depth of beam on experimental shear strength
Effect of various parameters on shear strength of SFRC
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0.00 3.50 7.00 10.50 14.001
2
3
4
5
6
R² = 0.18531952511524
Experimental shear strength, MPa
She
ar sp
an to
dep
th r
atio
, a/d
fig, Effect of (a/d) ratio on experimental shear strength
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0.00 3.50 7.00 10.50 14.000
1
2
3
4
5
R² = 0.136871841865802
Experimental shear strength, MPa
Flex
ural
rein
forc
emen
t rati
o, (%
)
Fig. : Effect of flexural reinforcement ratio on experimental shear strength
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0.00 3.50 7.00 10.50 14.000
20
40
60
80
100
120R² = 0.305084806704983
Experimental shear strength, MPa
Com
pres
sive
stre
ngth
, f'c
(MPa
)
Fig. Effect of compressive strength on experimental shear strength
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0.00 3.50 7.00 10.50 14.0050
60
70
80
90
100
R² = 0.0111846107432376
Experimental shear strength, MPa
Aspe
ct ra
tio, L
f/Df
Fig. : Effect of aspect ratio on experimental shear strength
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0.00 3.50 7.00 10.50 14.000.0
0.5
1.0
1.5
2.0
R² = 0.0348750434322361
Experimental shear strength, MPa
Vol
ume
frac
tion,
Vf (
%)
Fig. : Effect of volume fraction of steel fibers on experimental shear strength
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Analytical investigation
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GRAPHICAL REPRESENTATION
0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00Sharma (1986) Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig. : Proposed shear strength values by Sharma (1986) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)
Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Masur et al. (1986)
Fig. Proposed shear strength values by Mansur et al. (1986) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00
Narayanan & Darwish (1987) Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)
Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig. Proposed shear strength values by Narayanan and Darwish (1987) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00
Khuntia et al. (1999)Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)
Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig. : Proposed shear strength values by Khuntia et al. (1999) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00
Kwak et al. (2002) Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig.: Proposed shear strength values by Kwak et al. (2002) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00
Dinh et al. (2011)Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig. : Proposed shear strength values by Dinh et al. (2011) versus Experimental shear strength
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0.00 3.50 7.00 10.50 14.000.00
3.50
7.00
10.50
14.00
Ashour et al. (1992)Swamy (1985)
Mansur (1986)
Lim (1987)
Ashour et al. (1989)
Li (1992)
Schantz (1993)
Swamy (1993)
Tan (1993)
Imam et al. (1998)
Casanov and Rossi (1999)
Noghabai (2000)
Kwak (2002)
Rosenbusch (2002)
Cucchiara (2004)
Parra-Montesinos (2006)
Dinh (2011)
Jain & Singh (2013)Proposed shear strength (MPa)
Exp
erim
ent s
hear
stre
ngth
(MPa
)
Fig. : Proposed shear strength values by Ashour et al. (1992) versus Experimental shear strength
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Table A-2 : Shear strength predictions using available models in literature
Investigator Beam ID vu(exp.) (MPa)
vu(the.)/vu(exp.)
Sharma (1986)
Mansur et. al. (1986)
Narayanan & Darwish
(1987)
Ashour et. al.(1992)
Khuntia et. al.(1999)
Kwak et al. (2002)
Dinh et al.(2011)
Swamy (1985) B52 2.16 1.00 0.90 0.96 0.87 0.67 1.01 1.18
B53 3.1 0.71 0.86 0.86 0.76 0.63 0.88 0.86
B54 3.13 0.73 1.10 1.04 0.90 0.79 1.03 0.88
B55 3.21 0.70 0.82 0.78 0.67 0.61 0.80 0.75
B56 2.62 0.89 1.01 0.91 0.72 0.78 0.91 0.81
B63R 2.05 1.05 1.19 1.11 0.89 0.92 1.11 1.00
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Investigators MV SD COV
Proposed shear
strength/ Experiment
shear strength
Sharma (1986) 0.92 0.29 31.58
Mansur et al. (1986) 0.89 0.31 35.25
Narayanan & Darwish (1987) 0.97 0.24 24.62
Ashour et al.(1992) 0.93 0.29 30.96
Khuntia et al.(1999) 0.73 0.21 29.11
Kwak et al. (2002) 1.11 0.26 23.63
Dinh et al.(2011) 0.89 0.30 33.63
Comparison of predictions
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It is concluded that the proposed model of Narayanan &
Darwish (1987) is in good agreement with the test results. It
provides better results than seven different predictions, when
compared with test data for beams without stirrups.
CONCLUSION
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•Khuntia, M., Stojadinovic, B., and Goel, S. C. (1999), “Shear Strength of Normal and High-Strength Fiber Reinforced Concrete Beams
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•9. Narayanan, R., and Darwish, I. Y. S. (1987), "Use of Steel Fibers as Shear Reinforcement." ACI Structural Journal, 84(3), 216-227.
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Thank You
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Steel fibres as minimum shear reinforcement
Normalized shear stress at failure versus fiber volume fraction.(Adopted from Parra-Montesinos et al. 2006)
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parameter Effect Investigator
d [Kani 1967] shear stress at failure decreases with an increase in the member depth
Ashour et al. 1992 and Swamy et al. 1993
It is generally concluded that a higher ratio of tensile reinforcement results in a higher shear stress at failure because of increased dowel action and a deeper compression zone
Vf Adebar et al. [1997]
concluded with at low fibre volumes, the increase in shear strength was proportional to the amount of fibre, but the rate of increase was reduced at higher fibre volumes.
[Kwak et al. 2002].
Generally, an increase in SFRC compressive strength leads to an increase in beam shear strength
a/d Ashour et al. [1992]
observed that the beam shear strength increases rapidly when the shear span-to-effective depth ratio is less than 2.0.
,cf