## 5 Finite Element Analyses of Specimens Using UTW Connector
### FE Modelling  
The FE model is created in ABAQUS software. Solid element C3D8R is used for the FE model. All the self-drilling screws are not modelled because they are sound in the test and tie the U-shape connector and the SHS members tightly during the whole testing. In order to model the interaction between the U-shape connector and the SHS members caused by the screws, a ring-shaped surface shown in Figure 20 is created on both the U-shape connector and the SHS members at the screw region. The two red surfaces are tied together in the FE modelling whereas hard contact with normal and tangential behavior is defined at other physical contact areas (blue surfaces in Figure 20) of the U-shape connector and SHS members. Because a surface cannot be defined as contact and tie interactions simultaneously in ABAQUS software, it has to create an untreated region (green surfaces in Figure 20) between the tied and contacted regions. Untreated surfaces in Figure 20 mean no contact or tie is defined between the two of them. Figure 21 shows a completed mesh model of a K-joint using the UTW connector and mesh density is increased for the connector.  
Boundary conditions of the FE models are shown in Figure 22a,b. As shown in Figure 22a, for the FE models used for investigating the effect of chord stress ratio \(n\), one end of the chord is fixed, and the other end is constrained only in X- and Y-directions so that axial force can be applied in Z-direction. For the free end of two braces, only axial displacement is allowed. For other FE models, two ends of the chord are fixed (no axial force applied to the chord), and also only axial displacement is allowed for the free end of two braces as shown in Figure 22b. A general static analysis has been run for each FE model in this study. For the brace axial loading, it is applied using the 'Risk' method in ABAQUS software.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Group** \\ **No.** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Specimen** \\ **No.** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Thickness of** \\ **the Connector** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Ultimate Bearing** \\ **Capacity** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **The Average** \\ **(kN)** \\ \end{tabular} } \\ \hline \multirow{3}{*}{Group 1} & UPL1 & 1.74 & 43.40 & \multirow{3}{*}{42.60} \\  & UPL2 & 1.71 & 45.60 & & \\  & UPL3 & 1.75 & 38.90 & \\ \hline \multirow{3}{*}{Group 2} & UPU1 & 1.75 & 37.10 & \multirow{3}{*}{39.90} \\  & UPU2 & 1.73 & 42.70 & & \\  & UPU3 & 1.73 & 39.90 & & \\ \hline \multirow{3}{*}{Group 3} & ULW1 & 1.75 & 44.80 & \multirow{3}{*}{42.40} \\  & ULW2 & 1.77 & 40.00 & & \\  & ULW3 & 1.76 & 42.40 & & \\ \hline \multirow{3}{*}{Group 4} & UTW1 & 1.75 & 43.20 & \multirow{3}{*}{44.50} \\  & UTW2 & 1.75 & 45.60 & & \\ \cline{1-1}  & UTW3 & 1.74 & 44.60 & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Ultimate bearing capacity of each specimen.  
Figure 21: Mesh model of typical K-joint specimens using the UTW connector.  
Figure 22: Boundary conditions of FE models.  
Figure 20: Illustration of interactions between the connector and the SHS member.