# Parametric Study of Three Types of Timber Connections with Metal Fasteners Using Eurocode 5
## 3 Simplified Equations in Designed Timber Connections  
The yield strength, the embedment strength, and the withdrawal strength of the fastener must be considered to determine the characteristic load-carrying capacity of the dowelled connections [18]. Theoretical models were developed to define the characteristic values of the connection load-carrying capacity, based on the material properties and the dimensions of the connection [20; 21]. Eurocode 5 part 1-1 [18] provides simplified equations for calculating the load-carrying capacity of single-shear and double-shear plane in different connection types. In double-shear plane connections, the resistance of each shear plane must be determined. The basic prerequisite for the calculation is the symmetrical arrangement of the connection [18]. For the dimensioning of timber connections under double shear, it is intended to determine the main dimensions (width, height, thickness of the wood elements and steel plate, minimum spacing and edge/end distances between the dowels and the wooden plate). The number of dowels is an important parameter in the connection design with the arrangement by rows and columns [3; 5; 6; 7]. Connections are verified to satisfy double shear, considering several potential failure modes. This will depend on the length of penetration of the dowel into elements, the strength to localized crushing, the dowel diameter, and the characteristic yield moment of the fastener. During this study, different parameters are considered for the three studied connections: tensile applied load \(F_{d}\), dowel diameter \(d\), the wooden board thickness \(t_{1}\) (smaller thickness of the wood side member or the penetration depth), \(t_{2}\) (thickness of the wood middle member) and the steel plate thickness \(t_{s}\). To calculate the dimension of each connection type, the load was considered as parallel to the grain direction, [24; 25]. The present study compares the performance of the three different types of connections, depending on the different variables, and based on the work previously started by the authors [25; 26; 27; 28]. The following equations are considered for connection for double-shear, where the dowel diameter must be greater than 6 mm and less than 30 mm. According to Eurocode 5, part 1-1 [18], the design tensile strength along the grain \(f_{t,0,d}\), must be equal or greater than the design tensile stress along the grain \(\sigma_{t,0,d}\). The tensile strength \(f_{t,0,d}\), defined by Equation (1), represents a reduced value of its characteristic value along the wood grain \(f_{t,0,k}\), due to the application of two safety factors: the modification factor for load duration and moisture content \(k_{mod}\), considered equal to 0.6 for permanent load action, and the partial factor for material property \(\gamma_{M}\) equal to 1.25 according to Eurocode 5 part 1-1 [18]. \[f_{t,0,d}=\frac{f_{t,0,k}\,k_{mod}}{\gamma_{M}} \tag{1}\]  
Considering \(A_{s}\) the cross-section of the member, the design tensile stress along the grain \(\sigma_{t,0,d}\) is calculated using Equation (2), Eurocode 5, part 1-1 [18]. \[\sigma_{t,0,d}=\frac{F_{d}}{A_{s}} \tag{2}\]  
For symmetrical connections in double shear, the characteristic load-carrying capacity per shear plane and fastener \(F_{v,Rk}\), is obtained according with Eurocode 5 part 1-1 [18]. These equations are based on a theory developed by [PERSON] in 1949 [10; 24; 29]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mechanical Properties** & **GL20H** & **GL24H** & **GL32H** \\ \hline Average parallel-to-grain tensile & & & \\ strength, \(f_{t,0,k}\), N/mm\({}^{2}\) & 16 & 19.2 & 25.6 \\ \hline Young’s Modulus, \(E\), N/mm\({}^{2}\) & 8400 & 11,500 & 14,200 \\ \hline Density, \(\rho_{k}\), kg/m\({}^{3}\) & 370 & 420 & 480 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties for glulam at approximately 12% moisture content [9; 20; 21]. [PERSON] was the first to describe the mechanical behavior of this type of connections [30].