# 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  
The residual shear strength may decrease with repeated loads and is expected to have a relation with the total cumulated energy dissipation. Table 20 summarizes the total energy dissipations with the residual shear strengths. The experimental results are plotted in Figure 14 and it is found that the relation of the residual shear strength and total energy dissipation shows a linear decreasing except two specimens (SD400-D16-3R, SD400-D19-3R in the bold dashed circle), which are found to reserve high residual shear strengths even after high energy dissipations. The reliability of steel-concrete composite structure can be affected by the casting conditions, materials, etc. Therefore, the exception of the two results in the regression process to evaluate the reduction trend of the residual shear strength may contribute as a conservative part. Based on the regression analysis in Figure 14, the following Equation (2) is proposed as a nominal residual strength factor after repeated loads (\(\gamma_{r,E,n}\)) for Y-type perfobond rib shear connectors:  
\[\gamma_{r,E,n}=1.00-2\times 10^{-5}n_{L}E \tag{2}\]  
where \(\gamma_{r,E,n}\) is the nominal residual strength factor after repeated loads, \(n_{L}\) is the number of repeated loads, and \(E\) is the dissipated energy per 1 cycle of repeated load, which should be adopted tentatively from the mean values in Table 19 depending on the intensity of repeated loads. Therefore, the nominal residual shear strength (\(P_{u,r,n}\)) (Equation (3)) is calculated from both the nominal residual strength factor (Equation (2)) and the nominal ultimate shear strength (Equation (4)) [25]:  
\[P_{u,r,n}=\gamma_{r,E,n}P_{u,n} \tag{3}\]  
Figure 13: Cyclic energy dissipations on the log-normal probability paper. (**a**) 785 and (**b**) 1010 kN. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load (kN)** & **Mean (kN-mm)** & **COV** & **Distribution** \\ \hline
785 & 25.89 & 0.696 & Log-normal \\
1010 & 47.44 & 0.666 & Log-normal \\
1235 & 92.85 * & 0.636 * & Log-normal \\
1460 & 129.49 * & 0.606 * & Log-normal \\ \hline \hline \end{tabular}  
* Revised.  
\end{table} 
Table 19: Probabilistic models of energy dissipation per repeated load. in which  
\[P_{u,n}=n_{r}^{0.67}\bigg{(}970d_{r}f_{yr}^{0.2}+4240\sqrt{f_{y}}\bigg{(}\frac{t}{1 0}\bigg{)}\bigg{(}\frac{w}{80}\bigg{)}^{0.95}\bigg{(}\frac{h}{100}\bigg{)}^{0.45} \bigg{)}f_{ck}^{0.3} \tag{4}\]  
where \(P_{u,r,n}\) is the nominal residual shear strength, \(\gamma_{r,E,n}\) is the nominal residual strength factor, \(P_{u,n}\) is the nominal shear strength, \(n_{r}\) is the number of Y-ribs, \(d_{r}\) is the diameter of the transverse rebars, \(f_{yr}\) is the yield strength of the transverse rebars, \(f_{y}\) is the yield strength of the Y-ribs, \(t\), \(w\), \(h\) are the thickness, width, and height of the Y-ribs, respectively, and \(f_{ck}\) is the concrete compressive strength. The probabilistic characteristics of the residual shear strength (\(P_{u,r}\)) were investigated with the probabilistic characteristics of the residual shear strength factor and the ultimate shear strength. The variation of the residual shear strength from the nominal value was treated as a bias factor (\(B_{\gamma}\)) from the nominal residual strength factor (\(\gamma_{r,E,n}\)) and the bias factors were plotted on various probability papers referred to in [PERSON] et al. (2015) as shown in Figure 15. The probabilistic models of bias factors are summarized in Table 21 and the Type-I Gumbel distribution was selected.