# Parametric Study of Three Types of Timber Connections with Metal Fasteners Using Eurocode 5
## 4 Parametric Study of the Connections
### Numerical Simulation on S-W-S Connection (\(t_{2}\) = 27.5 mm, d = 8 and 12 mm)  
In accordance with the previous conclusion, a numerical simulation is included to verify the effect of the dowel diameter in S-W-S connections, where the number of the dowels is greater, with \(t_{2}\) equal to 27.5 mm and wood GL20H.  
This analysis is ongoing research, where the main objective is to evaluate the increase in the hole connection and its effect on the strength of the cross-section. Two numerical simulations are presented for dowels diameters equal to 8 and 12 mm.  
A numerical and structural 3D model was developed using ANSYS 2020 R2, using a solid finite element with 8 nodes and three degrees of freedom per node, with element edge equal to 2 mm. Previous mesh convergence tests were performed to minimize the computational error.  
The numerical model aims to simulate an incremental tensile load applied to the connection. To solve the problem and the convergence, [PERSON]'s method was used. Based on the geometric model and its symmetry, typical boundary conditions were applied. Due to the contact interface between wooden and steel elements, a coefficient of static friction equal to 0.3 was considered [5].  
The material properties considered are described in Section 2 of this work. The mechanical model is based on the von Mises criterion for both materials, where the stress-strain curve of steel and a stress-strain curve parallel to the grain of the wood material GL20H were introduced. The mesh model, the load carrying capacity in each connection and the stress distribution in all the involved elements are represented in Figure 5.  
The results between the two numerical models show that the stress levels to which they are subjected are different.  
In connection with a dowel diameter equal to 8 mm, the number of dowels is equal to 9 and in connection with a diameter equal to 12 mm, only 6 dowels are required.  
The model with a diameter equal to 8 mm, presents higher stresses in the steel plate and dowels.  
On the other hand, in the wooden element, the normal stresses are more homogeneous and around the holes tend to smaller is comparison with the other model. This may mean that, although the number of dowels is greater, it does not affect the level of stresses installed in the wood.  
Alternatively, in connections with larger dowel diameters, the level of stress installed around the hole in the wooden element is more pronounced and higher, which facilitates the stress concentration and the wood embedment failure mode.  
The characteristic load-carrying capacity per shear plane and fastener obtained in the numerical simulation was 2972 N for the connection with a dowel diameter equal to 8 mm, whose value calculated with Equation (6a) was equal to 2821 N.  
For the model with a dowel diameter of 12 mm, the numerical value was 5083 N and 4048 N using Equation (6a).  
Figure 5: S-W-S connection (\(t_{2}\) = 27.5 mm, d = 8 and 12 mm).  
With these conclusions, it means that the use of alternative methodologies can complement the use of simplified design calculations.