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Table 2: Models for predicting ultimate shear strength steel fibre reinforced concrete beams without stirrups

PRINCIPLE MAJOR PARAMETERS APPLICABLE FOR
AUTHOR REMARKS
FOLLOWED CONSIDERED DEEP BEAM
Narayan and Validated for an a/d ratio range
Darwish et al. (1987) [11] Analytical V f , L/D, τ bf , f c , ρ, a/d Yes between 2 to 3.5
Validated for an a/d ratio range
Li et al. (1992) [40] Empirical a/d, ρ, f t , f f , V f , L/D Yes
between 1 to 4.25
Aoude et al. (2012) [16] Analytical τ uf , f c , V f , L/D Yes Validated for an a/d ratio around 3
Validated for rectangular beams
Mansur et al. (1986) [20] Analytical a/d, ρ, f c , f tu Yes with no shear reinforcement for
an a/d ratio range between 2 to 4.4
V f , L/D, a/d, τ bf , 14 parameters
Mansur and Ong Softened truss representing concrete stress-strain Yes Validated for an a/d ratio range
et al. (1991) [21] model behavior in tension, compression and between 0.29 to 1.71
bond stress.
Semi-empirical Validated for an a/d ratio range
[25]
Dang et al. (2021) a/d, ρ, f c , V f , L/D, τ bf , Yes
formula between 0.9 to 2.5
Validated for an a/d ratio range
[30]
Arslan et al. (2017) Empirical a/d, ρ, f c , V f , L/D Yes
between 2.5 to 3.5
Validated for an a/d ratio range
Kwak et al. (2002) [31] Empirical a/d, ρ, f t , f c , V f , L/D, d f Yes between 2 to 4; Also, validated for
139 data received from literature
Cho and Kim Plastic theory Yes Validated for an a/d ratio range
et al. (2003) [28] a/d, ρ, f t , f c , V f between 0.4 to 2
Analytical and Validated for an a/d ratio range
Khuntia et al. (1999) [32] a/d, ρ, V f , L/D, f c Yes
empirical between 0.46 to 4.5
Validated for an a/d ratio range
Imam et al. (1997) [35] Analytical a/d, ρ, V f , L/D Yes
between 1.75 to 4.5
Validated for an a/d ratio range
Slater et al. (2012) [36] Empirical a/d, ρ, f c , V f , L/D, d f Yes
between 0.47 to 6
Campione et al. Softened strut-and- a/d, ρ, f c , V f , L/D Yes Validated for an a/d ratio range
(2012) [37] tie macro model between 0.56 to 1.11
Moradi, and Esfahani Strut-and-tie method Yes Validated for deep beams with
et al. (2017) [38] a/d, ρ, f c , V f , w/L, τ bf opening
Mihaylov1 and Two-parameter Validated for an a/d ratio range
Rajapakse et al. (2021) [39] kinematic theory a/d, ρ, f c , V f , w/L, τ bf , L/D, Yes between 0.31 to 1.85
Validated for an a/d ratio range
Ashour et al. (1992) [41] Empirical a/d, ρ, V f , L/D, τ bf Yes
between 1 to 6
Validated for an a/d ratio range
Dinh et al. (2011) [42] Analytical a/d, ρ, f t , f c , V f Yes
between 2.5 to 4
Validated for an a/d ratio range
Yakoub et al. 2011 [43] Analytical a/d, ρ, τ uf , f c , V f , L/D Yes
between 1.0 to 5
Nguyen-Minh and Fracture-mechanics- Validated for an a/d ratio range
Rovnak et al. (2011) [44] based formula a/d, ρ, τ uf , f c , V f , L/D Yes between 1.0 to 6
Validated for an a/d ratio range
Kara (2013) [45] Empirical a/d, ρ, f c , V f , L/D Yes
between 2.5 to 4.91
Validated for an a/d ratio range
[46]
Arslan et al. (2014) Analytical a/d, ρ, f c , V f , L/D Yes
between 2.5 to 5
Direct tension force Validated for an a/d ratio range
[47]
Lee et al. (2017) a/d, ρ, f c , V f , L/D, τ bf Yes
transfer model between 2.5 to 6
a/d-shear span to depth ratio; f t -split tensile strength of FRC; f f -flexural strength of FRC; f tu -residual stress of a direct tension test on FRC coupon;
V f -Volume fraction; L/D-Aspect ratio of fibre; τ bf -average fiber matrix interfacial bond strength; τ uf -ultimate bond strength of fibre; d f -bond factor;f c -
cylindrical compressive strength of fibre concrete; w-crack width

16 THE INDIAN CONCRETE JOURNAL | FEBRUARY 2026