# Shear Resistance Assessment of the Y-Type Perfobond Rib Shear Connector under Repeated Loadings
## 5 Residual Shear Strength Design Procedure under Repeated Loads
### Design Residual Shear Strength under the Repeated Loads Based on the Actual Shear Strength
#### 5.2.1 Residual Shear Strength Due to the Repeated Loads
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Load Type**} & \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Total Energy Dissipation** (kN-mm)**} & \multirow{2}{*}{**Residual Shear Strength (A)**} & \multicolumn{2}{c}{**Nominal Residual Shear Strength on Regression Line (B)**} & \multirow{2}{*}{**Ratio (A/B)**} & \multirow{2}{*}{**Note**} \\ \hline
1 & SD400-D16-IR & 2137.6 & 0.959 & 0.963 & 1.001 \\ \hline
2 & SD400-D16-2R & 3000.3 & 0.954 & 0.946 & 1.015 \\ \hline
3 & SD500-D16-1R & 3231.0 & 0.933 & 0.941 & 0.997 \\  & SD400-D19-1R & 3031.5 & 0.935 & 0.945 & 0.995 \\  & SD500-D19-1R & 4481.5 & 0.917 & 0.916 & 1.008 \\ \hline
4 & SD400-D16-3R & 4061.6 & 0.982 & 0.977 & - & Excluded \\  & SD500-D16-2R & 1444.0 & 0.981 & 0.969 & 1.010 \\  & SD400-D19-2R & 1848.1 & 0.975 & 0.977 & 1.013 \\  & SD500-D19-2R & 1423.9 & 0.970 & 0.949 & 0.998 \\ \hline
5 & SD500-D16-3R & 2819.6 & 0.971 & 0.957 & 1.029 \\  & SD400-D19-3R & 3882.8 & 0.979 & 0.963 & - & Excluded \\  & SD500-D22-1R & 2423.1 & 0.953 & 0.946 & 1.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Comparison of dissipated energy and residual shear strength. Figure 14: Distribution of residual shear strength and energy dissipation. The probabilistic characteristics of the ultimate shear strength of the fresh shear connectors without any preceding loads (\(P_{u}\)) suggested by [PERSON] et al. (2016):  
\[P_{u}=B_{Pu}P_{u,n} \tag{5}\]  
where \(P_{u}\) is the ultimate shear strength, \(B_{Pu}\) is the bias factor of the shear strength. The mean value of the bias factor for the shear resistance formula (\(P_{u}\)) was found to be 1.129 and COV was 0.127, as shown in Table 22 ([PERSON] et al., 2016). The probabilistic characteristics of the residual shear strength due to the repeated loads (\(P_{u,r}\)) were calculated by Monte-Carlo simulation by combining the bias factors of the shear strength and probabilistic characteristics of the residual shear strength. Table 23 shows the results by the number of repeated loads (\(n_{L}\)) with 25, 50, and 100 times. Figure 16 shows the simulation results plotted on the normal papers and it is found that the fitness does not match well to the normal PDF when the total energy dissipation amount becomes large. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **PDF** & **Mean** & **COV** & **Correlation Coefficient** \\ \hline Residual shear strength & Normal & 1.0067 & 0.0117 & 0.9529 \\ \hline Log-normal & 1.0067 & 0.0117 & 0.9542 \\ \hline Type-I & 1.0075 & 0.0128 & 0.9802 \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Bias factor (\(B_{7}\)) models of nominal residual strength factor. Figure 15: Bias factors of the nominal residual shear strength factor on PDF probability paper. (**a**) Normal, (**b**) Log-normal and (**c**) Type-I. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Repeated Loads (\(n_{L}\))** & **Type** & **785 kN** & **1010 kN** & **1235 kN** & **1460 kN** \\ \hline
25 & Mean & 1.123 & 1.111 & 1.084 & 1.064 \\  & COV & 0.128 & 0.129 & 0.131 & 0.135 \\ \hline
50 & Mean & 1.108 & 1.084 & 1.031 & 0.990 \\  & COV & 0.129 & 0.132 & 0.144 & 0.156 \\ \hline
100 & Mean & 1.030 & 0.924 & 0.843 & 1.030 \\  & COV & 0.146 & 0.193 & 0.243 & 0.146 \\ \hline \hline \end{tabular}
\end{table} 
Table 23: Residual shear strength (normalized) after the repeated loads (\(P_{u,r}\)).