## 4 Conclusions  
The numerical and experimental splitting capacity results for European beech (_Fagus sylvatica_ L.) beams loaded perpendicular to the grain by single- and double-dowel connections with different locations along the beam span are provided.  
The use of an additional dowel slightly increases the splitting capacity at low \(\alpha\) (\(h_{e}/h\)) values (0.32) but significantly increases it at high \(\alpha\) values (0.64), by about 50%. For the same test configuration, the larger the beam span, the higher the splitting load. For single-dowel connections, the position of the dowel along the beam span influences the splitting capacity, which is lower the closer the connection is to the supports. For double-dowel connections, the greater the distance between the dowels, the greater the splitting load, but in no case will the increased load from an additional dowel double the ultimate load of a single-dowel connection. Beams with \(l_{b}/h<2.4\) fail by splitting, and those with an \(l_{b}/h\) ratio \(\geq 2.4\) are susceptible to fail by bending, but these values are influenced by the number of dowels loaded into the connection, as beams with two dowels can transfer more load to the beam before splitting occurs. This fact favours bending as the dominant failure mode.  
A 2D finite element model was developed for each geometry in the experimental programme, using a cohesive element model and a bilinear cohesive law to reproduce the mode I and II fracture process.  
The proposed finite element model successfully replicated the behaviour of beams exhibiting purely brittle failure patterns more effectively than those displaying mixed-mode failure.  
The numerical \(P\)-\(\delta\) curves are in good agreement with the experimental ones. The proposed numerical model demonstrates its efficacy as a powerful tool for predicting the splitting capacity of timber connections with various arrangements. Moreover, it proves to be structurally safe from a design standpoint.  
Of the three design models based on fracture mechanics (including the Eurocode 5 expression), the models based on elastic and linear fracture energy generally give good load predictions for single-dowel arrangements. For two-dowel layouts, where the two dowels are considered as part of the same connection, design models that include fracture properties only in mode I provide too conservative values. The model that considers mode I and II fracture and the influence of joint width (\(l_{c}\)) predicts overestimated values for high \(l_{c}\) configurations.  
Further experimental research on the splitting behaviour considering other connection geometries and hardwood species would be desirable in order to obtain a general expression valid for all of them.  
Conceptualisation, [PERSON]-[PERSON], [PERSON] and [PERSON]; methodology, [PERSON]-R., [PERSON]-[PERSON], [PERSON], J.X. and M.F.S.F.d.M.; validation, [PERSON]-R.; formal analysis, [PERSON]-R.; investigation, [PERSON]-R., [PERSON] and [PERSON]-[PERSON]; writing--original draft preparation, [PERSON]-R.; writing--review and editing, [PERSON]-R., [PERSON]-B., [PERSON], J.X. and M.F.S.F.d.M.; visualisation, [PERSON]-R.; supervision, [PERSON]-M., J.X. and M.F.S.F.d.M.; funding acquisition, A.M.-M., J.X. and M.F.S.F.d.M. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
The original contributions presented in the study are included in the article material, further inquiries cab be directed to the corresponding author/s.  
The authors declare no conflict of interest.