"In the last four decades, many equations have been proposed to estimate the shear strength of Steel Fiber Reinforced Concrete (SFRC) beams. However, in terms of accuracy and uniformity of the prediction, there is considerable diversity between existing available models in literature. It is very necessary to point out the most correct model for prediction of shear strength. In this study, the shear strength prediction for SFRC beams without stirrups can be made by using seven exiting models. The predictions from seven models are compared to the test results of 185 SFRC beams without stirrups. It is found that the proposed equation by Narayanan and Darwish (1987) shows comparatively good agreement with regard to the existing test results''.

1.  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
1
Objective of the thesis

2. 2
Introduction

3. 3
Fig.Beam failure modes (from ACI-ASCE Committee 426, 1973)
Types of Failure In Beam

4. Behavior of beam in Shear
4
Fig.Typical example of Shear tension failure of reinforced
concrete beam. (Nilson 2005)

5. Type of steel fibers
5
Fig.Types of steel fibres (Dinh,2010)

6. 6
Steel Fibrous Reinforced Concrete (SFRC)
Enhance shear resistance and ductility in reinforced
concrete beams.
Enhance post-cracking strength of concrete.
Uniform cracking distribution.

7. Shear strength prediction models
bd
a
d
kfVu ct
4
1







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

8. '
0.16 17.2 tn uc
Vd
V f bd
M
 
  
    
  
8
maxMM
d a d
V 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
/ 2
2
MM a
for a d
V V
  
max
/ 2
MM
d for a d
V V
  
Where
f
f
f
V
D
L
F 

9. 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
 MPav
a
d
fevu bspfc 











 8024.0
FCB
F
f
f cu
spfc 


20
vb - fiber pullout strength
Narayanan & Darwish (1987)
B= 0.7 C = 1
fcu= cube compressive strength
where

10. Ashour(1992)
  )()711.2(
3/13 ,
MPaFfv a
d
cu 
10
  )(25.0167.0 ,
MPafFev cu 
5.2/ dafor
5.2/ dafor

11. Khuntia et al. (1999)
11
 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.

12. Dinh et al.(2011)
n cc FRCV V V 
12
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 
bfkk
fA
c
c
ys
,
31

)()0075.0*(*5.1*8.0)( 4/1
MPaVfavgt 

13. 13
Kwak et al.(2002)
bdv
a
d
feV bspfcn ]8.0)(7.3[
3/1
3/2






 

14. 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)
14

15. 15
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

16. 16
R² = 0.0311
150
250
350
450
550
650
0.00 3.50 7.00 10.50 14.00
Overalldepth,h(mm)
Experimental shear strength, MPa
Fig. Effect of depth of beam on experimental shear strength
Effect of various parameters on shear strength of SFRC

17. 17
R² = 0.1853
1
2
3
4
5
6
0.00 3.50 7.00 10.50 14.00
Shearspantodepthratio,a/d
Experimental shear strength, MPa
fig, Effect of (a/d) ratio on experimental shear strength

18. 18
R² = 0.1369
0
1
2
3
4
5
0.00 3.50 7.00 10.50 14.00
Flexuralreinforcementratio,(%)
Experimental shear strength, MPa
Fig. : Effect of flexural reinforcement ratio on experimental shear strength

19. 19
R² = 0.3051
0
20
40
60
80
100
120
0.00 3.50 7.00 10.50 14.00
Compressivestrength,f'c(MPa)
Experimental shear strength, MPa
Fig. Effect of compressive strength on experimental shear strength

20. 20
R² = 0.0112
50
60
70
80
90
100
0.00 3.50 7.00 10.50 14.00
Aspectratio,Lf/Df
Experimental shear strength, MPa
Fig. : Effect of aspect ratio on experimental shear strength

21. 21
R² = 0.0349
0.0
0.5
1.0
1.5
2.0
0.00 3.50 7.00 10.50 14.00
Volumefraction,Vf(%)
Experimental shear strength, MPa
Fig. : Effect of volume fraction of steel fibers on experimental shear strength

22. 22
Analytical investigation

23. GRAPHICAL REPRESENTATION
23
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
Sharma (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)
Fig. : Proposed shear strength values by Sharma (1986) versus Experimental shear strength

24. 24
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Masur et al. (1986)
Fig. Proposed shear strength values by Mansur et al. (1986) versus Experimental shear strength

25. 25
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Fig. Proposed shear strength values by Narayanan and Darwish (1987) versus Experimental shear strength

26. 26
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Fig. : Proposed shear strength values by Khuntia et al. (1999) versus Experimental shear strength

27. 27
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Fig.: Proposed shear strength values by Kwak et al. (2002) versus Experimental shear strength

28. 28
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Fig. : Proposed shear strength values by Dinh et al. (2011) versus Experimental shear strength

29. 29
0.00
3.50
7.00
10.50
14.00
0.00 3.50 7.00 10.50 14.00
Experimentshearstrength(MPa)
Proposed shear strength (MPa)
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)
Fig. : Proposed shear strength values by Ashour et al. (1992) versus Experimental shear strength

30. 30
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

31. 31
Investigators MV SD COV
Proposedshearstrength/Experimentshearstrength
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

32. 32
 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

33. 33
References
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Structural Journal, 89(2), 176-184.

34. 34
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Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, 285 pp.
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35. 35
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38
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36. Thank You
36

37. 37

38. 38

39. Steel fibres as minimum shear reinforcement
39
Normalized shear stress at failure versus fiber volume fraction.
(Adopted from Parra-Montesinos et al. 2006)

40. 40

41. 41
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