Table 6.

Summary of previous mechanical models in predicting RCDBs shear strength. MW stands for Matamoros and Wong's formula.

Code Standard	Formulas
ACI31817	$V_{\mathit{ACI}}=0.85{\beta }_s{f}_c^{\prime }{b}_w{w}_s\text{sin}\theta ,w_s=\left[1.8,w_t,,\ast ,\text{cos},\theta ,+,\left(w_{\mathit{tp}},+,w_{\mathit{bp}}\right),\text{sin},\theta \right]/2$
EC218	$V_{u,EU}=0.85{\beta }_s\ast f_c^{\prime }{b}_w{w}_s\text{sin}\theta ,w_s=[1.85w_t\ast \text{cos}\theta +\left(w_{\mathit{tp}},+,w_{\mathit{bp}}\right)\text{sin}\theta ]/2$
Matamoros and Wong13	$V_{M-W}=C_c{f}_c^{\prime }{b}_w{w}_s+C_{\mathit{wv}}{\rho }_v{b}_w\frac{a}{3}{f}_{\mathit{yv}}+C_{\mathit{wh}}{\rho }_h{b}_w\frac{d}{3}{f}_{\mathit{yh}},$ $C_c=0.3/\left(\frac{a}{d}\right)$, $C_{\mathit{wv}}=1$,$C_{\mathit{wh}}=3(1-a/d)$
Russo et al.14	$V_{\mathit{Russo}}=0.76\left(k,\chi ,f_c^{\prime },\text{sin},\theta ,+,0.35,\frac{a}{d},{\rho }_v,f_{\mathit{yv}},+,0.25,\text{tan},\theta ,{\rho }_h,f_{\mathit{yh}}\right)b_{w}d,\chi =0.74r^3-1.28r^2+0.22r+0.87,r=f_c^{\prime }/105$
Current study	Without web reinf.: $\frac{V_n}{b_{w}h}=1.5f_c^{\left(0.85,-,0.22,\frac{a}{d}\right)}{\rho }_l^{\left(0.29,-,\frac{a}{d},{\rho }_l\right)},\frac{a}{d}\le 2.5,{\rho }_l\le 0.1$ With web reinf.: $\frac{V_n}{b_{w}h}=\frac{29{\rho }_l+3.8{\rho }_l^{0.3}\sqrt{f_c^{\prime }}}{{\left(0.3\right)}^{{\mathrm{\Psi }}_{\mathit{vh}}}\left(\frac{a}{d}\right)+0.47},{\mathrm{\Psi }}_{\mathit{vh}}={\rho }_h\left(\frac{f_{\mathit{yh}}}{f_c^{\prime }}\right)+{\rho }_v\left(\frac{f_{\mathit{yv}}}{f_c^{\prime }}\right)$

where β_s is coefficient of strut, θ is the angle between the strut and the longitudinal axis, w_s and w_t are the widths of the strut and tie, ${\epsilon }_s$ is the tie's tensile strain, ρ_v is reinforcement ratio for VWR, and ρ_h is reinforcement ratio for HWR; the χ function is obtained for 10 ≤ fc′ ≤ 105 MPa.