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TECHNICAL PAPER

Moradi et al. (2017) [38] demonstrated the applicability of the The three recent models considered for the comparative study
[39]
strut-and-tie method (STM) in the design of SFRC deep beams showed inconsistent results. Model by Mihaylov et al. (2021) ,
with openings by considering the contribution of SFRC in overpredicted the strength as the fibre contribution was
tension. The simplified 2-parameter kinematic model (S2PKT) overestimated. The strut-and-tie method based on model
[38]
[39]
model is an iterative method proposed by Mihaylov (2021) , by Moradi et al. (2017) , gave no enhancement in strength,
based on a kinematics-based mechanical model. The model as the yielding of tension steel governed the failure, where
includes five shear resisting mechanisms: critical loading no contribution of steel fibres could be considered. Even
zone, dowel action, aggregate interlock, transverse shear though, model by Dang et al. (2021) [25] could reasonably predict
reinforcement, and contribution due to steel fibre, V fr . The shear the strength, the rate of increase due to added fibres was
resistance may be considered as the sum of the contributions overestimated. With the limited experiments, an increase in
due to each of these mechanisms. Dang et al. (2021) proposed strength of deep beams is not significant and hence the strut-
[25]
a single semi-empirical expression to predict shear strength (V ur ) and-tie model may be adopted as per the guidelines suggested
[38]
for SFRC deep beams, including all relevant parameters, for by Moradi et al. (2017) , for a conservative strength prediction.
steel fibre volume fraction, V f ≤ 2 %. More experimental studies are recommended to establish
design guidelines for SFRC deep beams.
A sample deep beam of size 300 × 500 mm, with an effective
depth of 450 mm, shear span to depth ratio (a/d) of 1, and 6. SUMMARY AND CONCLUSIONS
concrete strength, f c ’=50 MPa, is chosen to study the SFRC
[38]
deep beam models proposed by Moradi et al. (2017) , Dang The steel fibre reinforced concrete (SFRC) beams are now being
et al. (2021) [25] and Mihaylov et al. . The percentage of main adopted in construction due to its improved strength, ductility
[39]
reinforcement considered is 0.5 %, assuming the diameter and crack control. The enhanced properties are primarily
of the rebar as 20 mm and yield stress as 500MPa. No shear attributed to the ability of SFRC to resist tensile stresses at
high strains. The fib Model code , RILEM and Eurocode 2 [10]
[6]
[7]
reinforcement is provided. Hooked steel fibre is assumed with provides guidelines for designing SFRC beams, considering
a length of fibre, l f = 36 mm, the diameter of fibre, d f = 0.6 the post peak behavior of SFRC in tension and shear strength
mm, and yield stress of 1000 MPa. The strength prediction is contribution from steel fibres. However, these design guidelines
carried out using the three models [25,38,39] and was normalized are not applicable for deep members where the load is directly
with shear strength obtained from the strut-and-tie method transmitted to the supporting member through ‘strut action’.
[8]
of ACI 318 (2019) provisions (for no fibre content). The fibre Eurocode 2 [10] provides brief guidelines to adopt strut-and-tie
[39]
contribution in the model by Mihaylov et al. (2021) was method of design. However, detailed guidelines for strut-and-tie
conservatively obtained from the expression provided by method of design for SFRC deep members is not available in
the authors for straight fibre. The ratio, V/V STM is plotted with design standards.
increasing modified fibre factor, F’(=V f ×l f /d f ) for the 3 models,
along with the collected experimental data of SFRC deep beams Deep members require heavy distributed reinforcement
(with hooked fibres) in Figure 5. primarily to control diagonal crack widths. Adopting SFRC in
deep beam can help in crack control and can result in reduction
s
Exp. ata_ ooked teel fibres Moradi et al. [38] of distributed reinforcement. This is validated in an experimental
h
d
Dang et al. [25] Mihaylov et al. [39] study, where a complete replacement of distributed
s
f
Linear (Exp. D ata_ ooked teel ibres) reinforcement gave an equivalent serviceability performance of
h
deep beams (without fibres), reinforced with minimum specified
3.5
distributed reinforcement as per AASHTO code . Further, many
[9]
3
experimental studies highlighted the increased strength and
2.5
ductility, and reduced crack widths in SFRC deep beams [25,20,30-31] .
V /V STM 2
1.5 The present study summarised the experimental details of
127 SFRC deep beams, with shear span to depth ratio of less
1
than 2 and quantified the effect of fibre factor on first diagonal
0.5
cracking load and strength. The increased strength and delayed
0
0 0.2 0.4 0.6 0.8 1 1.2 cracking load were observed with increasing fibre factor, from
F’ the plots presented, similar to the observations in literature.
Figure 5: Variation of V/V STM with respect to modified fibre factor The study showed an increase in average strength and diagonal
F’ for the proposed models superimposed with collected cracking load of about 8 and 23 %, respectively corresponding
experimental data from the literature. to a fibre factor of 1, in comparison with deep beam without
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