1. بسم الله الرحمن الرحيم
صدق الله العظيم

2. PERFORMANCE OF STEEL FIBERS REINFORCED CONCRETE DEEP BEAMS
BENHA UNIVERSITY
FACULTY OF ENGINEERING AT SHOUBRA
جامعـــــه بنــــهــــــا
كلـــــيـــــه الـهـــنـــدســـه بشـــــبــــرا
Ph.D. Research on
PERFORMANCE OF STEEL FIBERS REINFORCED CONCRETE DEEP BEAMS
Presented by
Eng. Ahmed Abd El-Aziz Abd El-Hay El-Barbary
( M.Sc., Structural Engineering, Cairo University, 2006)
Supervision Committee
Prof. AHMED A. MAHMOUD Dr. FOUAD B. A. BESHARA
Professor of R.C. structures Associate professor
Civil Engineering Department Civil Engineering Department
Faculty of Engineering, Shoubra Faculty of Engineering, Shoubra

3. Contents
1. Research Background. 2. Objectives of Current Research. 3. Description of Experimental Program. 4. Experimental Results of the Tested Beams. 5. Finite Element Predilections of the Tested Beams. 6. Strut-and-Tie Modeling of HSSFRC Deep Beams. 7. Conclusions.

4. Deep Beam receive a single load
1- Research Background
1.1. Function of Deep Beams: Deep beams are structural elements having a depth comparable to the span length, and are used as load distribution elements such as transfer girders in high rise buildings, bent caps in bridge, pile caps in foundations.
Deep Beam receive a single load
Bridge Bent Cap

5. 1.2. Code Definitions for Deep Beams:
Egyptian Code (ECCS) defines the deep beam as:
Le/d < 1.25 for Single Span
American Code (ACI) defines the deep beam as:
Le/h < 4 for Single Span
CIRIA Guide of the U.K defines the deep beam as:
Le/h < 2 for Single Span

6. 1.3. Earlier Researches on Non-Fibrous Deep Beams:
Researcher
Year
Concrete Type
Variables
Mansur, M. A.
1991
Normal
fc ',a/d, ρv
Warwick, W. B.,
1993
High Strength
fc ',a/d, ρv, ρh
Tan K. H.,
1995
a/d, le
1997
ρv, ρh
Foster, S.J.,
1998
Oh, J.K.,
2001
a/d, ρv, ρh, ρs
Aguilar, G.,
2002
fc ', ρv, ρh
Rigotti, M.,
a/d, ρv, ρh
Tan, K. H.,
2003
Opening Location
Russo, G.,
2005
Mahmoud, A. A.,
2007
a/d, ρs and Opening Location
Abolfazl A.,
2011
fc ',a/d, ρs
Hawraz K.,
2013
Opening Size and Location
Alsaeq, H. M.,

7. 1.3. Earlier Researches on Non-Fibrous Deep Beams (Cont.):
Test results showed that:
1. The a/d ratio has a significant influence on the ultimate strength.
The concrete compressive strength fc’ had a significant effect on the ultimate shear strength.
For deep beams with (a/d 1.13), the horizontal web steel is more efficient than the vertical web steel of the same steel ratio.

8. 1.4. Earlier Researches on Fibrous Deep Beams:
Swamy, R. N.
1981
Normal
fc ',a/d, ρs, Vf
Narayanan, R.
1988
High Strength
fc ',a/d, ρv, ρh, Vf
Mansur, M. A.
1991
fc ',a/d, ρv, Vf
Yousef , A. M.
2003
Kumar, S. K.
2007
Jansson, A.
2011
Campione, G.
2012
fc ',a/d, Vf, lf /ff
Patel,V. R.
Minelli, F.
2013
Test results showed that:
The inclusion of fibers increase strength, ductility, and toughness.
2. The aspect ratio lf /ff has a significant influence on the ultimate strength.
The inclusion of fibers can be replaced by the web reinforcement in beams.
4. Steel fibers reduce the deflection and
increase the ductility of deep beams.

9. 1.5. Previous Analytical Studies for Deep Beams:
Strut-and-Tie Models
Researcher
Year
Analytical Model
Schlaich, J.,
1986
Strut and Tie Model
Mau, S. T.,
1987
Truss Models
Rogowsky, D. M.,
Hsu, T. C.,
1988
Softened Truss Model
Warwick, W. B.,
1993
Belarbi, A.,
1995
MacGregor, J. M.,
2011
Finite Element Studies
Researcher
Year
Computer Software
Rigotti, M.,
2002
ADINA
Foster, S. J.,
2003
ANSYS
Salamy, M. R.,
DIANA
2006
Ammar, Y. A.,
2009
Enem, J. I.,
2012
Patil, S. S.,
2013
Mohamed, A. R.,
2014

10. 2- Objectives of Current Research
Very few experimental and analytical studies were performed on HSSFRC deep beams.
An experimental and theoretical research program was conducted on HSSFRC deep beams in order to:
To study of the response characteristics under monotonic static loading such as
loading carrying capacity, stiffness, deflection, ductility, cracking patterns, and
failure modes.
2. To study the effect of the main following parameters:
– Fiber contents (Vf) – Shear Span-to-Depth Ratio (a/d)
– Fiber aspect ratios (lf/ff) – VL & HL Shear RFT Ratios (ρv ) & (ρh )
To modified failure criteria and constitutive relations are needed to be implemented
in standard program such as ANSYS for nonlinear analysis steel fibers deep beams.
To develop a strut-and-tie model as analysis and design tool for HSSFRC deep
beams with comprehensive verifications and parametric studies.

11. 3. Description of Experimental Work
Specimen of type (A) (a/d = 0.4)
Specimen of type (B) (a/d = 0.8)
Specimen of type (C) (a/d = 1.0)

12. Specimen (H3)
Specimen (V3)

13. 3. Description of Experimental Work (cont.)
Beam
No.
Width
(b) mm
Height
(h)
Shear
Span (a)
Span (Le) mm
a/d
Vf % lf ff Sv rv
(%) Sh rh A0
120
500
200
700
0.44
0.00 75
1.12 A1
0.50 80 A2
1.00 60 A3 B0
365
900
0.81 B1 B2 B3 C0
450
1000 C1 C2 H1 50
1.68 H2
100
0.84 H3 V1 V2 V3

14. 3. Description of Experimental Work (Cont
3. Description of Experimental Work (Cont.) Typical Test Setup and Instrumentation for all Tested Beams

15. 4. Experimental Results for Deep Beam 4
4. Experimental Results for Deep Beam 4.1 Behavior of Non-Fibrous and Fibrous Deep Beam
Beam (C0)
Without Fibers
Beam (C0)
With Fibers

16. 4.2 Modes of Failure and Cracking Patterns
Shear Compression Failure
Beam (A2)
Beam (A3)
Spalling of
Concrete
cover kN
300 kN

17. 4.2 Modes of Failure and Cracking Patterns (cont.)
Crushing of Strut Failure
Beam (C2)
Beam (V3)
Spalling
of parts
Between inclined
cracks kN kN

18. 4.2 Modes of Failure and Cracking Patterns (cont.)
Daigonal Splitting Failure
Beam (C1)
Beam (V2) kN kN

19. ** Comparison between Diagonal Cracking Load and Ultimate Load
4.3 Load-Deflection Response
4.3.1 Effect of Fiber Volume Content (Vf)
a/d = 0.44
lf /ff = 80 f f f f f
** Comparison between Diagonal Cracking Load and Ultimate Load
a/d = 0.44
lf /ff = 80
a/d = 0.81
lf /ff = 80

20. ** Comparison between Diagonal Cracking Load and Ultimate Load
4.3.2 Effect of Fiber Aspect Ratio (lf / ff)
a/d = 0.44
Vf = 1.0
a/d = 0.81
Vf = 1.0
** Comparison between Diagonal Cracking Load and Ultimate Load
a/d = 0.81
Vf = 1.0
a/d = 0.44
Vf = 1.0

21. ** Comparison between Diagonal Cracking Load and Ultimate Load
4.3.3 Effect of Shear Span-to-Depth Ratio (a/ d)
Vf = 1.0
lf/ff = 80
Vf = 0.5
lf/ff = 80
** Comparison between Diagonal Cracking Load and Ultimate Load
Vf = 0.5
lf/ff = 80
Vf = 1.0
lf/ff = 80

22. ** Comparison between Diagonal Cracking Load and Ultimate Load
4.3.4 Effect of Web Reinforcement Ratios (rv & rh)
** Comparison between Diagonal Cracking Load and Ultimate Load

23. 4.4 Load-Longitudinal Steel Strain Response
4.4.1 Effect of Fiber Volume Content (Vf) f f f f f f
4.4.2 Effect of Fiber Aspect Ratio (lf / ff)

24. 4.4.3 Effect of Shear Span-to-Depth Ratio (a/ d)
Vf = 0.5
lf/ff = 80
Vf = 1.0
lf/ff = 80

25. 5. Finite Element Analysis using (ANSYS) Program
Typical Idealization of the Beams
for Concrete Element (Solid65)
Typical Idealization of the Beams
for Steel Element (Link8)
The effect of steel fiber on failure surface
Offering high confinement which increases the strength of concrete.

26. 5.1 Stress-Strain Model for Fibrous Concrete in Compression and Tension
Simplified compressive uniaxial
stress- strain curve for concrete
Tension Stiffening Model
tf = ftf / Eci
ftf = ft ( Nf 1/ p ff lf Nf )
Nf = ho (4 Vf / p ff 2 )
am = pc / ftf
etu = 6.tf

27. 5.2 Finite Element Predictions for Tested Beams by (ANSYS)
At 25% of Pu
At 50 % of Pu
At 85 % of Pu
Beam (A2)
Shear Compression Failure
Beam (B2)
Crushing of Strut Failure
Beam (C2)
Diagonal-Splitting failure

28. 5.3 Finite Element Predictions Vs Experimental Results:
Load-Deflection Response
Beam (B2)
Beam (A1)
Beam (C1)
Beam (H3)

29. 5.3 Finite Element Predictions Vs Experimental Results (cont.):
Load-Longitudinal Steel Strain Response
Beam (A2)
Beam (B3)
Beam (C2)
Beam (V2)

30. 6. Modified Strut-and-Tie Modeling of HSSFRC Deep Beams 6
6. Modified Strut-and-Tie Modeling of HSSFRC Deep Beams 6.1 Geometrical Properties MSTM
MSTM consists of:
Horizontal Prismatic Strut BC with compression force (Fu,BC)
Diagonal Tapered Struts AB and DC with compression forces (Fu,AB),(Fu,CD)
Composite Tie AD with tension force (Fu,AD)

31. 6.1 Geometrical Properties MSTM (cont.)
6.2 Derivation of Internal Forces
& 25o < q < 85o
Astr2t = b. wst = b. (ws cosθ + lb sinθ)
Astr1= b. ws
Act= b. wct
Astr2b = b. wsb = b. (wct cosθ + lb sinθ)

32. 6.3 Main Assumptions and Modifications
Top strut is always prismatic, and the diagonal struts are tapered shape.
Improvement in compression strength of concrete due to fiber inclusion
fcuf = fcu( F)
3) Tensile resistance in composite tie is due to tension of main steel reinforcement and
post-cracking strength of steel fiber.
Tct = fy . As + pc . (Aseff – As)
4) The strut efficiency factor (sf ) and nodal zone stress condition factor (nf ) of fibrous
concrete are instead of strut efficiency factor (s) and nodal zone stress condition
factor (n) of normal concrete.
sf = s F
nf = n F

33. Increase (ws) and (wct) Check on dimension (wct) of Nodal zone [A]
Start
Increase (ws) and (wct)
Assume Vu
Internal
Forces
Calculations
Checks of
Stresses in
Diagonal Struts
And
Nodal
zones No
Check Stress in the Diagonal Strut (AB)
Fu,AB < FallDS
Yes No
Check on dimension (wct) of Nodal zone [A]
wct req < wct
Yes

34. Check on dimension (ws) of Nodal zone [B]
Yes No
Check on dimension (ws) of Nodal zone [B]
ws req < ws
Yes
Calculations
of shear
carrying
capacity
(Vu)
Accuracy
Check No
Check on accuracy to be less than 0.01
(assumed Vu - capacity Vu) / capacity Vu < 0.01
Yes
End

35. Average value of (Pu Exp /Pu MSTM)=1.20
7.5 Ultimate Strength Predictions by the Modified STM
No. of Specimens = 79
No. of Sources = 6
Average value of (Pu Exp /Pu MSTM)=1.20
STDEV = 0.08

36. 7.6 Ultimate Strength Predictions by the STM of ECCS and ACI Design Codes
No. of Specimens = 79
Average value of (Pu Exp /Pu STM (ACI) )=1.36
STDEV = 0.09
No. of Specimens = 79
Average value of (Pu Exp /Pu STM (ECCS) )=1.43
STDEV = 0.09

37. Conclusions

38. a) Conclusive points from the experimental results
1. The inclusion of steel fibers affect on the mode of failure to be changes form sudden
brittle failure mode such as (Shear-Compression failure , Crushing of Strut) to less
brittle (ductile) mode, such as Diagonal- Splitting failure mode.
2. The increase in fiber volume content (Vf) or fiber aspect ratio (lf /f) leads to an
increase in ultimate load Pu(EXP), shear cracking load (Pcrs) and displacement
ductility (fu) while it reduces the ultimate deflection (∆u ).
Such as For fiber content (Vf) = 1%, the average increase in (Pu(EXP)), (Pcrs), (fu) was
21%, 50%, 35% respectively. The mean reduction in (∆u) was 25%.
3. The increase in shear span to depth (a/d) ratio leads to an increase in Pu(EXP), (Pcrs)
while it reduces the (fu) and (∆u ).
For Example, The change of (a/d) ratio from 1.00 to 0.44 increases (Pu(EXP)) by 70%,
rises (Pcrs) by 25%,while reduces (fu) by 56% and decreases (∆u) by 61%.
4. The increase of web reinforcement improves (Pu(EXP)), and (fu), while decrease in
ultimate deflection (∆u).
5. The horizontal web reinforcement is more efficient in shear capacity than the vertical
web reinforcement.

39. b) Conclusive points from (FE) and Modified Strut-and-Tie (MSTM) Models
1. The predicted values for loading and deflection at ultimate and first cracking
levels result from the nonlinear Finite Element (FE) analysis using ANSYS
program show a good agreement with the experimental results due to the
modifications in material properties in both compression and tension.
2. The ratio between ultimate load capacity for the experimental tests and the (FE)
analysis (Pu(EXP) / Pu(FE)) is Also, the ratio (Pcrs / Pu) for the experimental tests
and the (FE) analysis is 1.12.
3. Comparison of the predictions of the modified (MSTM) with 79 test results indicates
that the model generally performs well in predicting the ultimate load carrying
capacities for HSSFRC deep beams. The ratio between the experimental strength to
the predicted strength using MSTM (Pu(EXP) / Pu(MSTM))) is 1.21, with a standard
deviation of
4. The predictions of STM of the Egyptian Code (ECCS) code and the American
code (ACI) are more conservative than the (MSTM). The overall average value of
(Pu(EXP) / Pu(ACI)) and (Pu(EXP) / Pu (ECCS)) are (1.36 and 1.43%), respectively, with
overall standard deviation as (0.09).

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THANK YOU
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