final pp comparative investigation on shear strength prediction models for sfrc memberst

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

Objective of the thesis

2

Introduction

3

Fig.Beam failure modes (from ACI-ASCE Committee 426, 1973)

Types of Failure In Beam

4

Behavior of beam in Shear

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

5

Type of steel fibers

Fig.Types of steel fibres (Dinh,2010)

6

Steel Fibrous Reinforced Concrete (SFRC)

Enhance shear resistance and ductility in reinforced

concrete beams.

Enhance post-cracking strength of concrete.

Uniform cracking distribution.

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

8

'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

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

10

Ashour(1992)

)()711.2( 3/13 , MPaFfv ad

cu

)(25.0167.0 , MPafFev cu

5.2/ dafor

5.2/ dafor

11

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.

12

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

13

Kwak et al.(2002)

bdvadfeV bspfcn ]8.0)(7.3[

3/13/2

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)

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

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

17

0.00 3.50 7.00 10.50 14.001

2

3

4

5

6

R² = 0.18531952511524


She

ar sp

an to

dep

th r

atio

, a/d

fig, Effect of (a/d) ratio on experimental shear strength

18

0.00 3.50 7.00 10.50 14.000

1

2

3

4

5

R² = 0.136871841865802


Flex

ural

rein

forc

emen

t rati

o, (%

)

Fig. : Effect of flexural reinforcement ratio on experimental shear strength

19

0.00 3.50 7.00 10.50 14.000

20

40

60

80

100

120R² = 0.305084806704983


Com

pres

sive

stre

ngth

, f'c

(MPa

)

Fig. Effect of compressive strength on experimental shear strength

20

0.00 3.50 7.00 10.50 14.0050

60

70

80

90

100

R² = 0.0111846107432376


Aspe

ct ra

tio, L

f/Df

Fig. : Effect of aspect ratio on experimental shear strength

21

0.00 3.50 7.00 10.50 14.000.0

0.5

1.0

1.5

2.0

R² = 0.0348750434322361


Vol

ume

frac

tion,

Vf (

%)

Fig. : Effect of volume fraction of steel fibers on experimental shear strength

22

Analytical investigation

23

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

24

0.00 3.50 7.00 10.50 14.000.00

3.50

7.00

10.50

14.00Swamy (1985)

Mansur (1986)

Lim (1987)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


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

25

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)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


Dinh (2011)

Jain & Singh (2013)


Exp

erim

ent s

hear

stre

ngth

(MPa

)

Fig. Proposed shear strength values by Narayanan and Darwish (1987) versus Experimental shear strength

26

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)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


Dinh (2011)

Jain & Singh (2013)


Exp

erim

ent s

hear

stre

ngth

(MPa

)

Fig. : Proposed shear strength values by Khuntia et al. (1999) versus Experimental shear strength

27

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)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


Dinh (2011)


Exp

erim

ent s

hear

stre

ngth

(MPa

)

Fig.: Proposed shear strength values by Kwak et al. (2002) versus Experimental shear strength

28

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)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


Dinh (2011)


Exp

erim

ent s

hear

stre

ngth

(MPa

)

Fig. : Proposed shear strength values by Dinh et al. (2011) versus Experimental shear strength

29

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)


Li (1992)

Schantz (1993)

Swamy (1993)

Tan (1993)

Imam et al. (1998)


Noghabai (2000)

Kwak (2002)

Rosenbusch (2002)

Cucchiara (2004)


Dinh (2011)


Exp

erim

ent s

hear

stre

ngth

(MPa

)

Fig. : Proposed shear strength values by Ashour et al. (1992) versus Experimental shear strength

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

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

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

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34

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36

Thank You

39

Steel fibres as minimum shear reinforcement

Normalized shear stress at failure versus fiber volume fraction.(Adopted from Parra-Montesinos et al. 2006)

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