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Table 6 Existing shear strength models.

From: Shear Tests for Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) Beams with Shear Reinforcement

Authors

Shear strength models

Sharma (1986)

\( v_{u} = kf_{t}^{\prime} \left({d/a} \right)^{0.25} \)

where k = 2/3; a/d is the shear span-to-depth ratio; f t  = 0.17√f cf , if the tensile strength is unknown, and f cf is the concrete cylinder compressive strength

Narayanan et al. (1987)

\( v_{u} = e\left[{0.24f_{spfc} + 80\rho \frac{d}{a}} \right] + v_{b} \)

where f spfc is the computed split-cylinder strength of fiber concrete (= f cuf /(20 − √F) + 0.7 + 1.0√F); ρ is the longitudinal reinforcement ratio; F is the fiber factor (=(L f /D f )V f d f ; e is the arch action factor, 1.0 for a/d > 2.8 and 2.8d/a for a/d ≤ 2.8; f cuf is the cube strength of fiber concrete; V f is the fiber volume fraction; d f is a bond factor, 0.5 for round fibers, 0.75 for crimped fibers, and 1.0 for indented fibers; v b is equal to the equations of 0.41τF, and τ is the average fiber matrix interfacial bond stress, taken as 4.15 MPa

Ashour et al. (1992)

For a/d ≥ 2.5 \( v_{u} = \left({2.11\sqrt[3]{{f_{cf}}} + 7F} \right)\left({\rho \frac{d}{a}} \right)^{1/3} \)

Kwak et al. (2002)

\( v_{u} = 3.7ef_{spfc}^{2/3} \left({\rho \frac{d}{a}} \right)^{1/3} + 0.8v_{b} \)

where e is the arch action factor, 1 for a/d > 3.4, and 3.4d/a for a/d ≤ 3.4