## 3 New Shear Resistance Formula for the Y-Type Perfobond Rib Shear Connector
### Current Shear Resistance Formula
Equation (1) is the latest formula [17], which considers various design variables such as concrete compressive strength, the number of Y-ribs, shapes of a Y-rib, and diameters of transverse rebar:  
\[Q_{n}=11,500f_{ck}{}^{0.3}S_{rib}+R_{n}f_{ck}{}^{0.3}\Big{(}700 nA_{tr}{}^{0.75}+ 2,600(n-2)S_{rib}\Big{)} \tag{1}\]  
where, the \(Q_{n}\) (N) represents the shear resistance of the n-rib Y-type perfobond rib shear connector, \(S_{rib}=t(w/80)^{0.95}(h^{\prime}/120)^{0.95}(d/40)^{0.3}\) is the rib shape factor, \(h^{\prime}=h+0.5d\), \(R_{n}=1/(n-1)^{0.12}\) is the reduction factor, \(w\) (mm) is Y-rib's width, \(h\) (mm) is Y-rib's height, \(t\) (mm) is Y-rib's thickness, \(f_{ck}\) (MPa) is concrete strength, \(d\) is a dow \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \(n^{1,2}\) & \(t^{3}\) & \(w^{3}\) & \(h^{3}\) & \(d_{r}{}^{2}\) & \(f_{y}^{3}\) & \(f_{yr}{}^{2}\) & \(f_{ck}{}^{3}\) & \(P_{n}\) & **Average** & \\ \cline{2-13}  & (ribs) & (mm) & (mm) & (mm) & (mm) & (MPa) & (MPa) & (MPa) & (kN) & (kN) & **Reference** \\ \hline
2R-1 & \(-1\) & 2 & 10 & 80 & 80 & 16 & 235 & 400 & 43.8 & 947.6 & 941.8 & [19] \\  & \(-2\) & & & & & & & & & 959.2 & & \\  & \(-3\) & & & & & & & & & 918.6 & & \\
2R-2 & \(-1\) & 2 & 10 & 80 & 100 & 16 & 235 & 400 & 43.8 & 991.8 & 1010.5 & [19] \\  & \(-2\) & & & & & & & & & 1018.8 & & \\  & \(-3\) & & & & & & & & & 1020.8 & & \\
2R-3 & \(-1\) & 2 & 10 & 80 & 120 & 16 & 235 & 400 & 43.8 & 1052.0 & 1041.6 & [19] \\  & \(-2\) & & & & & & & & & 1031.8 & & \\  & \(-3\) & & & & & & & & & 1040.8 & & \\
2R-4 & \(-1\) & 2 & 10 & 100 & 100 & 16 & 235 & 400 & 43.8 & 1123.2 & 1156.3 & [19] \\  & \(-2\) & & & & & & & & & & 1191.2 & \\  & \(-3\) & & & & & & & & & & 1154.6 & & \\
2R-5 & \(-1\) & 2 & 10 & 120 & 100 & 16 & 235 & 400 & 43.8 & 1314.6 & 1288.1 & [19] \\  & \(-2\) & & & & & & & & & 1254.8 & & \\  & \(-3\) & & & & & & & & & 1294.8 & & \\
2R-6 & \(-1\) & 2 & 10 & 140 & 100 & 16 & 235 & 400 & 43.8 & 1343.4 & 1375.5 & [19] \\  & \(-2\) & & & & & & & & & & 1437.4 & & \\  & \(-3\) & & & & & & & & & 1345.6 & & \\
2R-7 & \(-1\) & 2 & 10 & 100 & 120 & 16 & 235 & 400 & 43.8 & 1228.4 & 1217.8 & [17] \\  & \(-2\) & & & & & & & & & & 1174.8 & & \\  & \(-3\) & & & & & & & & & 1250.2 & & \\
2R-8 & \(-1\) & 2 & 10 & 120 & 120 & 16 & 235 & 400 & 43.8 & 1254.4 & 1312.2 & [17] \\  & \(-2\) & & & & & & & & & & 1334.8 & & \\
2R-9 & \(-1\) & 2 & 10 & 140 & 120 & 16 & 235 & 400 & 43.8 & 1346.7 & 1372.3 & [17] \\  & \(-2\) & & & & & & & & & & 1407.0 & & \\  & \(-3\) & & & & & & & & & & 1363.3 & & \\
6R-1 & \(-1\) & 6 & 10 & 80 & 100 & 16 & 235 & 400 & 43.8 & 2478.9 & 2366.9 & [17] \\  & \(-2\) & & & & & & & & & & 2263.9 & & \\  & \(-3\) & & & & & & & & & & 2358.0 & & \\
2R-FEA & 2 & 10 & 80 & 100 & 16 & 235 & 400 & 40 & 1185.4 &
\begin{tabular}{c} FEM \\ model \\ \end{tabular} & [17] \\
4R-FEA & 4 & 10 & 80 & 100 & 16 & 235 & 400 & 40 & 1805.7 &
\begin{tabular}{c} FEM \\ model \\ \end{tabular} & [17] \\
6R-FEA & 6 & 10 & 80 & 100 & 16 & 235 & 400 & 40 & 2352.0 &
\begin{tabular}{c} FEM \\ model \\ \end{tabular} & [17] \\
8R-FEA & 8 & 10 & 80 & 100 & 16 & 235 & 400 & 40 & 2884.4 &
\begin{tabular}{c} FEM \\ model \\ \end{tabular} & [17] \\
10R-FEA & 10 & 10 & 80 & 100 & 16 & 235 & 400 & 40 & 3411.0 &
\begin{tabular}{c} FEM \\ model \\ \end{tabular} & [17] \\ \hline \hline \end{tabular}  
\end{table} 
Table 5: \(Cont.\)(mm\({}^{2}\)) is a cross-sectional area of a transverse rebar, and \(n\) is the number of Y-ribs (or transverse rebars). Equation (1) is designed to represent 3 main contributions, that is, the first term is for the end-bearing resistance, the second term is for the resistance by the transverse rebars, and the third term is for the resistance by Y-ribs. Because the first term provides the end bearing resistance due to the first one pair of Y-ribs located at the fronts of multi-ribs in the direction of slip, the third term contains \"\(-\)2\" to reduce the total number of Y-ribs.