# Parametric Study of Three Types of Timber Connections with Metal Fasteners Using Eurocode 5
## 4 Parametric Study of the Connections
### Design Parameters
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Load & \multicolumn{2}{|c|}{Dowel} & \multicolumn{2}{|c|}{\begin{tabular}{c} Dowel \\ arrangement \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} Distances \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} Connection dimensions \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} Design \\ characteristic \\ \(a_{\text{5}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} Design \\ characteristic \\ \(a_{\text{6}}\) \\ \end{tabular} } \\ \hline kN & \multicolumn{2}{|c|}{mm} & \multicolumn{2}{|c|}{mm} & \multicolumn{2}{|c|}{mm} & \multicolumn{2}{|c|}{N/mm2} & \multicolumn{2}{|c|}{N} \\ \hline \multirow{2}{*}{Fd} & \multirow{2}{*}{d} & \multirow{2}{*}{length} & N & N & \multirow{2}{*}{\begin{tabular}{c} \(a_{\text{1}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} \(a_{\text{2}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} \(a_{\text{3},t}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} \(a_{\text{4},c}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} \(a_{\text{5}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\begin{tabular}{c} \(a_{\text{6}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{\
\begin{tabular}{c} \(a_{\text{7}}\) \\ \end{tabular} } & \multicolumn{2}{|c|}{
\begin{tabular}{c} \(a_{\text{8}}\) \\ \end{tabular} } \\ \hline \multirow{2}{*}{10} & 8 & 96 & 2 & 3 & 40 & 24 & 80 & 24 & 45 & 6 & 72 & 480 & 16.38 & 2986 \\ \cline{2-13}  & 10 & 96 & 1 & 3 & 50 & 30 & 80 & 30 & 45 & 6 & 90 & 520 & 16.38 & 3868 \\ \cline{2-13}  & 12 & 96 & 1 & 3 & 60 & 36 & 84 & 36 & 45 & 6 & 96 & 480 & 16.38 & 2986 \\ \hline \multirow{2}{*}{15} & 8 & 96 & 3 & 3 & 40 & 24 & 80 & 24 & 45 & 6 & 96 & 480 & 16.38 & 3868 \\ \cline{2-13}  & 10 & 96 & 2 & 3 & 50 & 30 & 80 & 30 & 45 & 6 & 108 & 576 & 16.38 & 4828 \\ \hline \multirow{2}{*}{20} & 8 & 96 & 3 & 3 & 40 & 24 & 80 & 24 & 45 & 6 & 96 & 480 & 16.38 & 2986 \\ \cline{2-13}  & 10 & 96 & 2 & 3 & 50 & 30 & 80 & 30 & 45 & 6 & 120 & 520 & 16.38 & 3868 \\ \cline{2-13}  & 12 & 96 & 2 & 3 & 60 & 36 & 84 & 36 & 45 & 6 & 108 & 576 & 16.38 & 4828 \\ \hline \end{tabular}
\end{table} 
Table 3: Design parameters for W-W-W connections. The number of calculated dowels were distributed in rows and columns, with 3 considered the fixed number of columns. In addition, the thickness of the wooden board \(t_{1}\) and \(t_{2}\) was chosen, [18]. For unprotected connections with side members of wood, the thickness of the members must be greater than 45 mm, in accordance with Eurocode 5 part 1-2 [30]. The thickness of the steel plate \(t_{\text{s}}\) inside the connection was considered equal to 6 mm and on the outside of the connection equal to 3 mm. A total of 81 timber connections were studied, 27 by type of connection. Tables 2-4 show  
board thicknesses \(t_{1}\) and \(t_{2}\). The failure mode associated with each design equation is also identified. The parametric study shows a linear correlation between all design parameters for each type of timber connections. This shows that the number of dowels increased for small diameters and lower strength and density of wood. In general, when using larger dowel diameters, the wood density effect is not relevant. The strength and density of wood exert a relative influence when connections have small dowel diameters. In all connections, there is a considerable increase in shear strength for higher dowel diameters, wood density and strength. But as the dowel diameter increases, the hole connection also increases, which weakens the resistance of the cross-section and allows different failure modes to occur, as reported by [12]. A wooden board thickness less than or equal to 45 mm influences the required number of dowels. For wooden thicknesses greater than 45 mm, the calculated number of dowels is not dependent on this parameter, as indicated in the design equations.