## 1 Introduction  
In recent decades, there has been significant growth in the development of renewable and environmentally sustainable building materials, spurred by the imperative to address the impacts of climate change. The building sector is a significant consumer of primary energy, contributing significantly to the release of substantial amounts of carbon dioxide (CO\({}_{2}\)) into the atmosphere [1, 2]. In this context, wood and wood-based products have attracted great interest in architecture and civil engineering because of their renewable resource potential when sustainably managed [3], their savings in primary energy and CO\({}_{2}\) emissions during the manufacturing process [1, 4], and the added value they bring to buildings. Furthermore, among the main structural building materials, wood is the only one composed of substantial amounts of carbon captured from the atmosphere during the tree growth process (around 50% of its dry weight) [5]. Currently, most structural timber products are made from softwoods, but in recent years, there has been growing interest in the use of hardwoods for structural purposes. The reasons for this are multiple and may be due, among others, to the under-use of aged hardwood forests and the high mechanical properties compared to softwoods [6, 7]. In this respect, _Fagus sylvatica_ L., or European beech, is one of the most important and widespread hardwood species in Europe (from southern Scandinavia to northern Sicilyand from northwestern Turkey to northwestern Spain), with an average height of about 30-40 m. [8; 9]. The large beech reserves available in European forests have aroused the interest of the scientific community. Several investigations have been carried out on this material for structural purposes, both on solid wood in terms of determining its elastic constants [10; 11; 12; 13], mechanical properties [14; 15; 16], or fracture behaviour [17; 18], as well as on structural products made of beech such as gullam [19] or laminated veneer lumber (LVL) [20]. European beech also offers good strength and stiffness compared to softwoods, which makes it an excellent choice for the design of timber structures, especially in the assessment of high-performance scenarios, such as connections with fasteners or large span elements, allowing for a reduction in the cross-section of the main members. Mechanical connections with steel dowel-type fasteners are among the most widely used connections in timber structures [21; 22; 23] because of their simplicity of manufacture and assembly and the possibility of being designed to have a ductile connection failure. However, there are certain situations where brittle failure of the timber member may occur at load levels below the bearing capacity for desirable ductile behaviour, especially in designs with connections loaded at an angle to grain where tension stresses perpendicular to the grain are induced, for which timber inherently exhibits relatively low strength and stiffness. This brittle splitting failure is, therefore, one of the most critical in timber structures and deserves particular concern in design. Eurocode 5 [24] includes the so-called European Yielding Model (EYM) originally formulated by [PERSON] [25], which is used to predict the load carrying capacity of dowel-type connections subjected to shear force. This model always considers the plastic behaviour of timber and also the possible plastic behaviour of the dowel depending on the failure mode of the connection. However, this model can dangerously overestimate the ultimate load in connections if splitting failure occurs. Concerning the prediction of the splitting capacity of connections loaded at an angle to the grain, Eurocode 5 provides a relatively simple relationship developed theoretically by [PERSON] and [PERSON] [26; 27] following an energetic approach in the framework of linear elastic fracture mechanics (LEFM).