Table 2 Existing models for shear strength prediction of SFRC deep beams without stirrups.

Mansur et al. (1986)

$v_u=v_{\text{c}}+{\mathit{\sigma }}_{tu}\ast b\ast d,\text{where},v_{\text{c}}=\left(0.16\ast \sqrt{f_c^{\prime }}+17.2\ast \frac{\mathit{\rho }Vd}{M}\right)$

ACI code modification

V_c < (0.29($f_c^{\prime }$)^0.5)bd

Li et al. (1992)

$v_u=9.16\ast \left({\left(f_t\right)}^{\frac{2}{3}}\ast {\left(\mathit{\rho }\right)}^{\frac{1}{3}}\ast \left(\frac{d}{a}\right)\right)$

Regression analysis

a/d ≤ 2.5

Khuntia et al. (1999)

$v_u=\left(0.167\ast \left(2.5\ast \frac{\text{d}}{\text{a}}\right)+.25\ast \text{F}\right)\ast \sqrt{{{\text{f}}^{\prime }}_{\text{c}}}$

ACI code modification

a/d ≤ 2.5 0.25 ≤ ρ ≤ 2 20 ≤ $f_c^{\prime }$ ≤ 100 MPa

Ashour et al. (1992)

$v_u=\left(\frac{2.5}{\frac{\text{a}}{\text{d}}}\right)+0.41\ast \mathit{\tau }\ast F\ast \left(2.5-\frac{\text{a}}{\text{d}}\right)$

Regression analysis

a/d < 2.5

$v_u=\left(0.7\ast \sqrt{{\text{f}}_{\text{c}}^{\prime }}+7F\right)\ast \frac{d}{a}+17.2\mathit{\rho }\ast \frac{d}{a}$

ACI code modification

More accurate for HSC beams

Imam et al. (1994)

$v_u=0.7\ast \left(\frac{1}{\sqrt{1+\frac{d}{25d_a}}}\right)\ast \sqrt[3]{\mathit{\rho }}\ast \left(f_c^{i0.44}\left(1+F^{0.33}\right)+870\ast \sqrt{\frac{\mathit{\rho }}{{\left(\frac{a}{d}\right)}^5}}\right)$

Regression analysis

Maximum aggregate size

Kwak et al. (2002)

$\begin{array}{c}{v}_u=3.7\ast \left(3.4\ast \left(\frac{d}{a}\right)\ast {\left(\frac{f_c^{\prime }}{20-\sqrt{F}}+0.7+\sqrt{F}\right)}^{\frac{2}{3}}\ast {\left(\frac{\mathit{\rho }d}{a}\right)}^{\frac{1}{3}}\right)\\ +0.8\ast \left(0.41\ast \mathit{\tau }\ast F\right)\end{array}$

–

a/d ≤ 3.4

Khaloo and Kim (1997)

$v_u=\left(0.65+0.123\ast V_f+0.080\ast {\left(V_f\right)}^2-0.013\ast {\left(V_f\right)}^3\right)\ast \sqrt{{\text{f}}_{\text{c}}^{{}^{\prime }}}$

Regression analysis

l/d = 29

$v_u=0.65+0.46\ast V_f-0.080\ast {\left(V_f\right)}^2\ast \sqrt{{\text{f}}_{\text{c}}^{{}^{\prime }}}$

Regression analysis

l/d = 58

Shin et al. (1994)

$v_u=0.22\ast {\text{f}}_{\text{sp}}+217\ast \mathit{\rho }\ast \left(\frac{d}{a}\right)+0.834\ast \left(0.41\ast \mathit{\tau }\ast F\right)$

–

HSC a/d < 3

Sharma (1986)

$v_u=\frac{2}{3}\ast f_t\ast {\left(\frac{d}{a}\right)}^{\frac{1}{4}}\text{where},f_t\approx 9.5\ast \left(\sqrt{f_c^{\prime }}\right),psi$

–

–

Narayanan and Darwish (1988)

$\begin{array}{c}{v}_u=2.8\ast \frac{\text{d}}{\text{a}}\ast \left(0.24\ast \left(\frac{f_c^{\prime }}{20-\sqrt{F}}+0.7+\sqrt{F}\right)+80\ast \mathit{\rho }\ast \frac{d}{a}\right)\\ +0.41\ast \mathit{\tau }\ast F\end{array}$

Regression analysis

a/d ≤ 2.8