**1. Introduction**

Wood has been used for centuries in different buildings and structures, from residential buildings, through sacral architecture, to defensive structures for settlements and towns or complex engineered structures [1]. A large number of these structures, which have survived tens or hundreds of years, now require interventions to maintain or improve their technical condition. A key factor in their development is related to joints, which enabled building elements to be connected into a single whole and for loading to be shared between elements. Historical joints pay testimony to the highly developed techniques and craftsmanship of builders at that time [2]. It should also be noted that, to date, there are few reliable references that include detailed specifications related to forming carpentry joints [3], as their creators relied mainly on their own experience and tradition.

As a rule, the behaviour of joints has a large influence on the global outcome of the structure as a whole, especially with respect to internal forces. This is why carrying out a detailed analysis of the structure as a whole requires analyses of the behaviour of joints. A simple example serves to demonstrate the role played by correctly formed scarf and splice joints connecting construction elements. In the case of vertical loading, an element with a splice joint formed on an horizontal surface can transfer the bending moment up to a quarter of the moment transferred in a continuous beam, whereas the same joint formed on a vertical surface, with the same load, can transfer a moment of half the value of the moment transferred in the continuous beam. Analyses presented in the

literature [4] sugges<sup>t</sup> that in the case of a nibbed scarf joint, which is the most effective solution for transferring shearing stress [3], the moment that can be transferred is only one-third of the load in the continuous beam.

To a large degree, it is the technical condition of joints that shapes the ability of a structure to transfer loading, its static behaviour and deformations. Over time, carpentry joints in historic wooden structures are worn down or even completely destroyed by loading and other external factors, which can present serious danger. The damage or destruction of a joint can threaten the safety of the whole structure due to a considerable weakening of segments where elements are connected to one another. Understanding the static behaviour of joints in wooden structures allows for a detailed and comprehensive analysis of the whole system and helps in making decisions concerning corrective measures or reconstruction work, which is acceptable from the point of view of conservation doctrine [5,6].

Researchers distinguish many different types of carpentry joints in historic buildings, depending on their function and form (inter alia [7]). One group includes scarf joints and splice joints which enable a connection along the length of two elements. These were applied when the available material could not cover the whole beam length. Typically, whenever possible, the joints were applied in the least stressed sections, as the connecting elements at the point of contact could not bear a load greater than that in continuous sections [8]. Aside from extending foundation beams and capping beams in the building frames of historical structures, scarf and splice joints were used to extend roof frame elements, such as purlins or rafter beams. Until the introduction of glulam wood, this was a universal method for extending wood elements [9]. Scarf and splice carpentry joints are used today to restore historical joints or replenish material in historical elements of special value [10]. Examples of scarf and splice joints found in historical structures are presented in Figure 1.

**Figure 1.** Various forms of scarf and splice joints: (**a**) splice joint, (**b**) nibbed splice joint, (**c**) nibbed scarf joint, (**d**) tabled splice joint, (**e**) stop-splayed scarf joint ('Bolt of lightning'), (**f**) stop-splayed and tabled scarf joint with key.

The type of joint applied in a given connection is related to the function to be performed or the type of loading to be transferred. For example, a nibbed scarf joint (Figure 1c) would be used where the connection is stressed vertically and located near a support. In such a situation, the joint is responsible for transferring shear stress. In situations where tensile elements are connected, such as rafter beams, a different type of joint needs to be applied. For tensile elements, stop-splayed and tabled scarf joints with a key (Figure 1f) were used.

### **2. Stop-Splayed Scarf Joints ('Bolt of Lightning')**

Stop-splayed scarf joints (presented inter alia in [11–15] and referred to as 'Bolt of lightning', 'Trait-de-Jupiter') were widely used in historical buildings. They constituted a sophisticated type of connection along the length of elements in the form of a scarf joint. In historical structures, there are also elements connected along their whole length with a so-called stop-splayed scarf joint or a composite beam (built-up beams, composite beams with a teethed joint), described inter alia in [16–18].

Stop-splayed scarf joints ('Bolt of lightning') were used in ancient times, for example, in the Roman construction of bridges, and later, in roof beam constructions and wooden ceiling construction elements right up to the end of the 19th century. A special period of development for this method of joining beam elements was that of the Italian Renaissance, which was the time of such masters as Leon Battista Alberti (Figure 2a) [19] and Leonardo da Vinci (Figure 2b) [16]. This method of connecting elements along their length was applied especially in elements subjected to tensile and bending forces. Typically, the joints were wedged, which was supposed to help in transferring loading and to ensure a tight fitting joint. Today, they are used mainly to strengthen and repair historical structures. Examples of stop-splayed scarf joints ('Bolt of lightning') and so-called composite beams are presented below (Figures 2–4).

**Figure 2.** Sketches presenting scarf and splice joints in wooden beams (**a**) according to Leon Battista Alberti, (**b**) according to Leonardo da Vinci.

**Figure 3.** Sketch of a stop-splayed scarf joint ('Bolt of lightning') with dimensions of an actual element, drawing based on data from [11].

**Figure 4.** Examples of scarf and splice joining of wooden beams in existing buildings: (**a**) building in Italy, (**b**) building in Poland—13th century Czocha Castle in Sucha.

The few available descriptions of research concerning typical stop-splayed scarf joints ('Bolt of lightning') are presented in [16–18,20–23].

An analysis of the behaviour of a stop-splayed scarf joint subjected to tensile forces is presented in Figure 5 (drawing based on data from [20]). Different methods of strengthening the joints using timber pegs and steel pins were also analysed.

**Figure 5.** Geometry of a stop-splayed scarf joint ('Bolt of lightning').

An increase in estimated sti ffness for the joints with strengthening was noted: 41% for the joint strengthened with wooden pegs and 52% for the joint strengthened with steel pins in relation to joint without strengthening was noted. Load-deflection plots were prepared and failure modes were described. Attention was paid to the di fference in the static behaviour of the joints in relation to the material used for strengthening (wood, metal).

The results of research carried out at the University of Bath in the UK by a team consisting of Walker, Harris, Hirst and others on the static behaviour of scarf joints, inter alia stop-splayed scarf joints, which are universally found in historical buildings across England, are presented in [21]. The joints studied were under-squinted butt in halved scarf with two pegs, side-halved and bridled with two pegs, stop-splayed and tabled scarf with key and four pegs, and face-halved and bridled scarf with four pegs (Figure 6) (drawing based on data from [21]).

**Figure 6.** Scarf joints analysed in research: (**a**) under-squinted butt in halved scarf with two pegs, (**b**) side-halved and bridled with two pegs, (**c**) stop-splayed and tabled scarf with key and four pegs, (**d**) and face-halved and bridled scarf with four pegs.

Experimental testing [21] was carried out on model beams of 2.5 m in length joined by means of the joints listed above and 1.5 m continuous beams in order to compare results. The elements were subjected to a four-point vertical bending test and lateral bending test to provide for pure bending. Load-deflection plots were determined, and on the basis of a comparison of results for the di fferent joint types and also the parameters for the continuous element, it was possible to determine the performance factor describing the relationship of loading and sti ffness of the composite beam to that of the continuous beam. The stop-splayed scarf joint ('Bolt of lightning') displayed the greatest sti ffness and load-bearing (28% in relation to the continuous beam) with bending in the vertical plane.

For the case of bending of the elements joined along their length with the stop-splayed scarf joint ('Bolt of lightning'), i.e., for the so called composite beams (or built-up beams), analyses were presented by Mirabella-Roberti and Bondanelli in [16]. Based on a numerical analysis, the authors identified the most probable locations of stress concentrations, especially in the vicinity of joining planes.

Rug et al. [17,18] present principles for developing and gauging the beams described above, which have been presented in the literature up to the 1970s. Today, it is di fficult to find any principles which can provide a basis for constructing or restoring such building elements. For this reason, the University of Eberswalde in Germany carried out experimental research aimed at determining the load-bearing capacity of such elements, describing their static behaviour in terms of displacement resulting from applying loading. The research [17,18] was carried out on models constructed at a 1:1 technical scale (the dimensions adopted were the same as those in an existing rafter beam roof in a tower of a German church) and also on 1:2 scale models (Figure 7). Bending tests were carried out (in accordance with EN408), achieving an average loading at the level of approximately 57 kN; the deflection plot and flexibility modulus of the joint in the technical scale were determined in accordance with EN26891.

**Figure 7.** Model of a composite beam connected with a stop-splayed scarf joint and models used for testing of the joint itself and the element as a whole, image adapted from [17] with permission.

Sangree and Schafer [22,23] presented their research and numerical analysis carried out in Baltimore, USA on scarf joints with key found in traditional wooden constructions, e.g., in the Morgan Bridge, which was the subject of their analysis. They tested halved and tabled scarf joints and stop-splayed scarf joints with key (Figure 8 drawings based on data from [22,23]).

**Figure 8.** Models representing the geometry of scarf joints.

The joints were analysed as elements operating under complex loading conditions, i.e., tensile bending. In the case of the stop-splayed scarf joints with key [23], it was determined that the orientation of the key had the greatest influence on the static behaviour of the joint, as it causes a vertical pressure to the grain. In addition, special attention was paid to the presence of drawbolts as essential for sustaining the joint. In such cases, it was possible to obtain shear failure parallel to the grain, which made it possible to withstand higher stress levels.

The research presented to date in the literature concerning the static behaviour of carpentry joints has focused mainly on tenon and notched joints. There has been decidedly less research on joints typically subjected to bending (or bending and tensile stress or bending and compressive stress). It is worth noting that practically all researchers who have been concerned with this topic (in Germany inter alia Rug [17,18], in the UK Hirst et al. [21], and also in The Czech Republic Kunecky et al. [24–29] and Fajman et al. in [30–35]) underscore that there is a shortage of research for appropriately describing the static behaviour of such joints, and so proposing the most beneficial methods for repairing or strengthening them.

As a consequence (as part of a research project financed by the National Science Centre), experimental testing was carried out on the static behaviour of stop-splayed scarf joints subjected to bending. The goal was to determine the load-bearing capacity and stiffness of the joint subjected to testing and to determine the dependency of the type of joint and the method of sustaining it and its load-bearing capacity.
