## 4 Reduction Factor for the Y-Type Perfobond Rib Shear Resistance  
### Probabilistic Characteristics of the Shear Resistance  
The probabilistic characteristics of the shear resistance of Y-type perfobond rib shear connector are investigated with the proposed resistance formula, Equation (3). The proposed formula contains many uncertainty sources from the design variable as well as the formula itself. The uncertain characteristics inherent in the proposed formula and all the design variables except the concrete strength are already included in the estimation summarized in Table 16 and Figure 5, in which the experimental concrete strengths are adopted from the cylinder tests. The probabilistic characteristics are evaluated with the experimental results of 4-rib specimens, in which the sample size is 54. The experimental results of 27 2-rib specimens and 3 6-rib specimens are excluded to guarantee the homogeneous specimens. Figure 7 shows 54 experimental results plotted on a normal probability paper and two linear regression lines. One is the regression line with all 54 data and the other is the regression line with the lower 27 data. Even though two regression lines do not show the noticeable difference in Figure 7 and Table 19, the regression results (solid line in Figure 7) obtained with the lower part of the data is adopted to provide a conservative model.  
Figure 6: Comparison of numerical and calculated results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **FEA** & **Equation (3) Using \(n^{0.67}\)** & \multicolumn{3}{c}{**Equation (3) Using \(n^{0.69}\)**} \\ \hline
**Test No.** & \(P_{u}\) & \(Q_{u}\) & **Ratio** & \(Q_{u}\) & **Ratio** \\ \hline  & **(kN) (A)** & **(kN) (B)** & **(A/B)** & **(kN) (C)** & **(A/C)** \\ \hline
2R-FEA & 1185.4 & 1120.6 & 1.06 & 1136.2 & 1.04 \\
4R-FEA & 1805.7 & 1782.9 & 1.01 & 1833.0 & 0.99 \\
6R-FEA & 2352.0 & 2339.4 & 1.01 & 2424.8 & 0.97 \\
8R-FEA & 2884.4 & 2836.7 & 1.02 & 2957.2 & 0.98 \\
10R-FEA & 3411.0 & 3294.2 & 1.04 & 3449.4 & 0.99 \\ \hline \end{tabular}
\end{table}
Table 18: Biasness of the proposed formula (Equation (3)).  
The probabilistic characteristics of the shear resistance including the uncertainty of the concrete strength are simulated combining two uncertainty sources, one from the concrete strength and another from the rest part in the proposed formula (Equation (3)). The uncertainty model for the other part is the normal PDF with mean of 1.008 and COV of 0.043. The probabilistic model for the concrete strength is adopted from the previous study [25]. The basic models are summarized in Table 20. The simulation is performed through the Monte-Carlo simulation procedure. The first part of Equation (3), except \(f_{ck}\)[3, 4] is generated based on the normal PDF with a mean of 1.008 and a COV of 0.043, in which \(f_{ck}\) is assumed to be a deterministic normalized value. The \(f_{ck}\)[3, 4] part is generated based on another normal PDF with a mean of 1.120 and a COV of 0.120. Then, two parts are multiplied. The Monte-Carlo simulation results are also plotted on a normal probability paper (Figure 8) and the regression model is summarized in Table 21 with the statistical estimations. The mean and COV obtained from the linear regression on the probability paper are almost the same as those from the statistical estimation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **PDF** & **Mean** & **COV** \\ \hline Shear resistance (except \(f_{ck}\)) & Normal & 1.008 & 0.043 \\ \(f_{ck}\) & Normal & 1.120 & 0.120 \\ \hline \hline \end{tabular}
\end{table}
Table 20: Probabilistic models for Monte-Carlo simulation with the 4-rib case.  
Figure 7: Plot of experimental results on a normal PDF paper.