# Numerical Investigation on Novel Shear Connectors in Prefabricated Composite Beams
## 4 FEA Results
### Influence Factors of Load Capacity  
Table 5 lists the orthogonal testing results. The ultimate load capacity of the modeling results due to different factors is listed in the table, represented by \(y_{i}\). Figure 11: Uniaxial material constitutions. Figure 10: Uniaxial material constitutions. (**a**) Concrete damage and (**b**) stud failure. Next, \(T_{11}\) is calculated in the determined sequence. Here, the three tests corresponding to \"1\" adopt only the first level of factor \(D\) and three levels of factors \(L\) and \(f_{c}\) in each test. The summation and average values of the three tests are obtained as shown in Equations (3) and (4). \[T_{11}=y_{1}+y_{2}+y_{3} \tag{3}\]  
\[\overline{T_{11}}=T_{11}/3 \tag{4}\]  
The three tests corresponding to \"2\" adopt only the second level of factor \(D\) and three levels of factors \(L\) and \(f_{c}\) in each test. The summation and average values of the three tests are obtained as shown in Equations (5) and (6). \[T_{12}=y_{4}+y_{5}+y_{6} \tag{5}\]  
\[\overline{T_{12}}=T_{12}/3 \tag{6}\]  
The three tests corresponding to \"3\" adopt only the third level of factor \(D\), and three levels of factors \(L\) and \(f_{c}\) in each test. The summation and average values of the three tests are obtained as shown in Equations (7) and (8). \[T_{13}=y_{7}+y_{8}+y_{9} \tag{7}\]  
\[\overline{T_{13}}=T_{13}/3 \tag{8}\]  
From the above, we can see that the difference among \(\overline{T_{i1}}\), \(\overline{T_{i2}}\), \(\overline{T_{i3}}\) (the same as the difference among \(T_{11}\), \(T_{12}\), \(T_{13}\)) only reflects the difference among the three levels of factor \(D\). The reason lies in the fact that, in the three tests with different level combinations, the level of factor \(D\) is the only varied factor. Therefore, by comparing the three average values, the optimum level of factor \(D\) is obtained. We can see from the above data, that the third level of factor \(D\) is the best one. We call this comparison method \"general comparison\", \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{4}{*}{**Models**} & \multirow{2}{*}{\begin{tabular}{c} **Stud** \\ **Diameter** \\ \end{tabular} } & \begin{tabular}{c} **Lateral Space** \\ **of Steel Plate** \\ \end{tabular} & \begin{tabular}{c} **Concrete** \\ **Strength** \\ \end{tabular} & \begin{tabular}{c} **Random** \\ **Factor** \\ \end{tabular} & \begin{tabular}{c} **Ultimate** \\ **Strength** \\ \end{tabular} \\ \cline{2-7}  & \multicolumn{2}{c}{\(D\) **(mm)**} & \(L\) **(mm)** & \(f_{c}\) **(Mpa)** & & \(P_{\textbf{u}}\) **(kN)** \\ \cline{2-7}  & \
\begin{tabular}{c} **Sequence** \\ **Number** \\ \end{tabular} & **1** & **2** & **3** & **4** & \(y_{i}\) \\ \hline HS-M1 & 1 & 13.00 & 20.00 & 50.00 & 1.00 & 69.34 \\ HS-M2 & 2 & 13.00 & 40.00 & 60.00 & 2.00 & 71.93 \\ HS-M3 & 3 & 13.00 & 60.00 & 70.00 & 3.00 & 71.90 \\ HS-M4 & 4 & 16.00 & 20.00 & 60.00 & 3.00 & 101.47 \\ HS-M5 & 5 & 16.00 & 40.00 & 70.00 & 1.00 & 101.44 \\ HS-M6 & 6 & 16.00 & 60.00 & 50.00 & 2.00 & 98.62 \\ HS-M7 & 7 & 19.00 & 20.00 & 70.00 & 2.00 & 125.27 \\ HS-M8 & 8 & 19.00 & 40.00 & 50.00 & 3.00 & 131.65 \\ HS-M9 & 9 & 19.00 & 60.00 & 60.00 & 1.00 & 132.42 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} \(T_{i1}\) \\ \(T_{i2}\) \\ \end{tabular} } & \(T_{i1}\) & 213.17 & 296.08 & 299.60 & 303.19 & \\ \cline{1-1} \cline{2-7}  & \(T_{i2}\) & 301.53 & 305.02 & 305.82 & 295.81 & \\ \cline{1-1} \cline{2-7}  & \(T_{i3}\) & 389.34 & 302.94 & 298.61 & 305.03 & \\ \cline{1-1} \cline{2-7}  & \(\overline{T_{i1}}\) & 71.06 & 98.69 & 99.87 & 101.06 & \\ \cline{1-1} \cline{2-7}  & \(\overline{T_{i2}}\) & 100.51 & 101.67 & 101.94 & 98.60 & \\ \cline{1-1} \cline{2-7}  & \(\overline{T_{i3}}\) & 129.78 & 100.98 & 99.54 & 101.68 & \\ \cline{1-1} \cline{2-7}  & \(R\) & 58.72 & 2.98 & 2.4 & 3.08 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis calculation results of the numerical orthogonal models. which is determined by the orthogonality of the orthogonal list.