EXPERIMENTAL INVESTIGATION ON PARALLEL-TO-GRAIN WOOD-TO-WOOD JOINTS WITH SELF-TAPPING SCREWS Marco Ballerini 1 ABSTRACT: The paper presents the main outcomes of an experimental research performed on parallel-to-grain woodto-wood joints made with self-tapping screws in single shear. Screws have a nominal diameter of 12 mm and have been investigated with and without washers. Joints with 8 mm dowels (obtained from the shank of the self-tapping screws) have been also investigated for comparison purpose. Specimens have been designed to fail according to failure modes of the European Yield Model that don’t correspond to a uniform stress distribution in wood elements. In detail the failure modes taken into consideration are: rigid rotation of fasteners (mode c), development of a single plastic hinge in fasteners in the point-side wood elements (mode d) or in the head-side wood elements (mode e), development of two plastic hinges in fasteners (mode f). In designing, the strength increase due to the “rope effect” has been taken into account. After testing, specimens have been processed to determine the actual failure modes of fasteners, their plastic rotations and the maximum embedding deformations close to shear planes. The main results, in terms of strengths, actual failure modes and plastic deformations, are compared for the four different failure modes and for the three investigated fasteners: the 12 mm self-tapping screws with washers, without washers and the 8 mm dowels derived from the shank of self-tapping screws. KEYWORDS: Timber joints, Self-tapping screws, Rope effect 1 INTRODUCTION 1 Self-tapping screws are very interesting fasteners for timber engineering since characterized by widespread application potentials. Indeed, these screws have a lot of properties that make them very suitable and profitable in a wide number of situations. First of all, these fasteners are particularly attractive by the economic point of view. In fact, though characterized by higher cost per unit compared to ones of conventional screws, the lower processing needs on wooden elements lead usually to significant savings in time and overall costs. In addition, they have lower implementation costs since require only simple and safe electric gears. Finally, the lack of the requirement of predrilling allows larger tolerances in fasteners positioning in the erection site. Moreover, an important feature that makes these screws particularly apt in the restoration of old/ancient timber structures is the limited invasiveness of these fasteners and their “reversibility”: the possibility of remove the fasteners due to different reasons, like interim structural needs or the definition of a different structural solution. 1 Marco Ballerini, Department of Mechanical and Structural Engineering (DIMS), Faculty of Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy. Email: marco.ballerini@ing.unitn.it However, since self-tapping screws are quite recent in production, the little availability of experimental data on their mechanical properties and on their behaviour in full-scale joints limits an efficient use of these screws for structural purposes. Due to this reason, an experimental research on the effectiveness of self-tapping screws has been recently carried out at the University of Trento [1]. The research concerns with wood-to-wood joints loaded parallel-to-grain with different fasteners in single shear. The aim of the research is the definition of the strength of joints, with and without washers, varying some parameters like: the fasteners, the failure modes, the number of fasteners in force direction, the influence of axial force in fasteners (the “rope effect”, by means of a comparison with 8 mm dowel joints). For a more accurate analysis of the structural behaviour, specimens after testing have been sectioned in order to obtain the actual failure modes of each fastener in the joint, the location of plastic hinges, the amount of plastic rotations of fasteners, the maximum values of embedding deformations in wood elements (close to shear planes). The paper presents the main results of the experimental research. With respect to joints strength, the experimental outcomes are analysed and compared between them and with the design formulae embodied in the European design code for timber structures (Eurocode 5 – EN 19951-1: 2009, [2]). 2 BACKGROUNDS As it is well known, to evaluate the strength of wood-towood and wood-to-steel joints with cylindrical fasteners, the European standard for timber structures takes the plastic model proposed by Johansen in 1949 [3]. This model states that the number of failure mechanisms that a joint with cylindrical fasteners can shows is fixed and governed by some parameters like number of shear planes in fasteners, and thickness and position of steel plates in case of wood-to-steel joints. In between this family of possible failure mechanisms, the actual one is the one that presents the minimum strength. For instance, in case of wood-to-wood joints with fasteners in single shear – the joints investigated in this research – the possible failure mechanisms are the 6 ones reported in Figure 1. To each failure mode the Eurocode 5, on the basis of the Johansen’s model, assigns the following characteristic strengths: f h,1,k t1 d f h,1,k t1 d " ! + 2! 2 1+ " + " 2 + ! 3" 2 ! ! 1+ " 1+ ! $# 1,05 1,05 1,15 ) f h,1,k t1 d (2 + ! ) f h,1,k t2 d (1+ 2! ) 2! 1+ ! ( ) ( )%'& + Fax,R,k 4 t2 t1 t1 t2 t1 t2 t1 mode a t1 t2 mode d f h,2,k t2 d ( t1 t1 t2 mode b t1 t1 t2 mode e mode c t1 t1 t2 t1 mode f Figure 1 – Failure modes of wood-to-wood joints with cylindrical fasteners in single shear " % F M y,Rk $ 2! 1+ ! + 4 ! 2 + ! ' + ax,R,k ! ! 2 $ ' 4 f t d h,1,k 1 # & " % M y,Rk F $ 2! 2 1+ ! + 4 ! 1+ 2! ! ! ' + ax,R,k 2 $ ' 4 f h,1,k t2 d # & F 2 M y,Rk f h,1,k d + ax,R,k 4 ( ( ) ( ) ) ( ) In above equations, β is the ratio between the embedding strengths of timber elements (fh,2,k/fh,1,k), θ is the ratio between the lengths of fasteners in the timber elements (t2/t1), d is the fastener diameter, My,Rk is its plastic moment. The term Fax,Rk/4 represents the strength increase due to the so called “rope effect”: namely the effect of the axial force in fasteners in line with the load direction (this effect can occur only in failure modes in which fasteners rotate as rigid bodies or as a consequence of the development of plastic hinges). Previous parameters are well defined in case of traditional cylindrical fasteners. However, in case of self-tapping screws same fundamental parameters are not easy to define (see Figure 2). This is the case of the diameter – where three values are of relevance: the nominal diameter (that corresponds to the outer diameter of the threaded part), the diameter of the core of the threads, the diameter of the shank – and of the yielding moment of the screw – in this case at least two yielding moments are of relevance: one for the shank and one for the threaded part of the screw. Moreover, also the embedding strength of self-tapping screws needs to be newly investigated due to the influence of different diameters in the same screw, to the different shape of threads, to the different interface situations along the screw (the threaded part and the shank part of the screw in a wood hole generated by the larger nominal diameter). Figure 2 – A modern self-tapping screw, general view and detailed view of cutter in point. 3 THE EXPERIMENTAL PROGRAMME To supply to the lack of data on the mechanical behaviour of joints with self-tapping screws, an experimental investigation on wood-to-wood joints with fasteners in single shear has been designed. The main aim of the research is to exploit the influence on the strength of some relevant parameters. The parameters taken into account are: 1) the fasteners – self tapping screws with a nominal diameter of 12 mm with and without washers are the main object of the research; however, for comparison purpose, joints with 8 mm dowels (derived from the shank parts of screws) have been investigated; 2) failure modes – the 4 failure mechanisms associated with the rotation of the fasteners as a rigid body or as a consequence of the development of one or more plastic hinges in each fastener (modes c to f, see Figure 1) have been taken into account; 3) the “rope effect” – indirectly, by means of the comparison the values of plastic moments experimentally determined in [4]: with the strength increase observed in joints with fasteners characterised by different withdrawal strength; 4) the effective number “nef” – specimens with 2 and with 4 fasteners on each side elements (respectively with 1 and 2 fasteners aligned with the load direction) have been investigated. In order to collect some relevant data, the samples have been processed after tests execution. The main aims of this part of the research are: collect the actual failure mechanism achieved by fasteners in the investigated joints; collect the magnitude of the plastic rotations in fasteners and the location of plastic hinges; collect the magnitude of maximum plastic deformation in the wood (close to shear planes) due to embedding stresses. M y,R,core = 90900 Nmm (cov = 3.78 %) (2) M y,R,shank = 123100 Nmm (cov = 0.17 %) On the basis of previous results, the design of timber elements to get the desired failure mechanisms has been carried out. The design outcomes are summarized in Table 1. For each joint configuration 3 samples have been manufactured to have a minimum statistical base. As a consequence, considering the 4 failure modes, the 3 type of fasteners, and the 2 fasteners patterns in joints, a total number of 72 samples have been investigated. 3.1 SPECIMENS DESIGN 4 TEST RESULTS Samples have been designed in symmetrical configuration and for compressive loads in direction parallel to the grain (see Figure 3). Fasteners used in joints were 12 mm Würth Ecofast-Assy self-tapping screws supplied by the manufacturer. Timber elements were made of spruce (picea abies) with a density ranging between 350 and 535 kg/m3. The experimental research was carried out according to provisions of EN 26891 [5]. Tests were considered ended at a maximum joints displacement of 15 mm. The study was performed by means of a servo-controlled hydraulic actuator; the load and the joint slips were recorded continuously. The test setup is shown in Figure 4. With respect to the embedding strengths, a limited investigation has been specifically designed to obtain the strength values both for the threaded parts of screws (inserted in wood without predrilling) and for the shank parts (inserted in the holes produced by threaded parts). With reference, as provided in Eurocode 5, to the core diameter of screws threaded parts increased by 10% (dcore = 7.1 mm) and to that of the shank (dshank = 8 mm), the investigation has provided the following results: f h,0,threads = 0,0733 ! ! The tests results of those of measurements on processed samples are collected in Figures 5 ÷ 9 and in Table 2. Figure 5 shows the average load-slip curves of different joints. The reported loads are normalized to the number of fasteners. From Figure 5 it can be observed that joints strength generally decreases moving from joints with screws and washers, to ones with screws only, and to those with dowels. (1) f h,0,shank = 0,0608 ! ! Concerning the plastic moments of screws My,R (for the threaded part and for the shank), reference was made to 4 fasteners on each side Figure 4 – Test set-up. 2 fasteners on each side Figure 3 – Geometry of specimens with 4 and 2 fasteners on each side in single shear. Table 1 – Main geometrical parameters of joints and screws (mm). Failure modes c d e f b t1 = s1 t2 s2 140 50 50 90 90 50 90 50 90 100 190 100 190 a1 120 a2 l screw l thread 60 100 140 140 180 60 80 80 100 depends significantly by the activated failure modes (modes c and d are the only ones that require the rotation of screws heads) but also by the density of the wooden elements (the same samples with 2 screws on each side, characterised by a significantly lower density of wooden elements, had not shown this tendency). In samples designed to fail in mode c, the splitting of side elements have been very moderate; this reflected in a very limited drop in strength of these joints if compared with the strength of same joints with 2 fasteners on each side. On the contrary, the samples designed to fail in mode d have shown an abrupt collapse consequently to the Load on each fastener (kN) Load on each fastener (kN) Load on each fastener (kN) Load on each fastener (kN) However, some deviations in samples with 2 fasteners on each side and designed to fail in mode e and with samples with 4 fasteners in each side and designed to fail in modes c and d have been noticed. With respect to samples designed to fail in mode e, a strength of joints with screws and washers very close to that of joints with only screws is apparent. No supporting elements have been found to explain this lower strength. Conversely, the behaviour of samples designed to fail in modes c and d can be easily explained by the fact that a tendency of screws heads to induce longitudinal cracks in side timber elements have been recorded. This tendency Slip (mm) Slip (mm) Figure 5 – Average load-slip curves of specimens with 2 and 4 fasteners for each shear plane. complete splitting of side elements well before the maximum displacement. Finally, Figure 5 shows clearly the different behaviour of samples with dowels with respect to those with screws. The behaviour of joints with dowel can be quite well described by an elasto-plastic behaviour with no hardening. On the other side, joints with screws are almost always characterised by a significant hardening. Failure mode c Pictures in Figure 6 show the actual failure mechanisms of samples. From pictures it is evident that all joints with dowels fail according to respective design failure modes. Conversely, it does not happen for all the joints with screws or with screws and washers. In these joints, the design failure modes e and f have been regularly observed, but the design failure modes c and d have been found replaced by modes e and f. This is due to screws heads and to washers that prevent (to a different extent) the development of those collapse mechanisms that require the free rotation of fasteners ends. The qualitative considerations exposed are presented in Table 2. The data of Table 2 show clearly both the influence of the density of wood elements and of the end-restraint degree of different fasteners on the observed failure modes. sample CAB-02 sample CAC-01 sample CBD-02 sample CBB-01 sample CBC-03 sample CCD-01 sample CCB-02 sample CCC-03 sample CDD-02 sample CDB-03 sample CDC-03 Failure mode f Failure mode e Failure mode d sample CAD-03 Figure 6 – Observed failure modes in specimens with 4 fasteners for each shear. Table 2 – Design failure loads c d e f 3 Samples’ densities (kg/m ), failure loads (kN) – normalized to number of fasteners – with coefficients of variation, observed failure modes in fasteners (if different to design ones). Type of fasteners Dowels Screws Screws with washers Dowels Screws Screws with washers Dowels Screws Screws with washers Dowels Screws Screws with washers average density 376 395 487 386 384 386 394 401 436 377 410 473 2 fasteners on each side observed Fu (CV) failure modes 4.76 (0.01) 8.30 (0.07) 8.91 (0.06) 5.57 (0.03) 8.29 (0.08) 10.30 (0.09) 6.21 (0.12) 7.40 (0.14) 7.20 (0.02) 7.02 (0.01) 10.79 (0.04) 13.42 (0.25) It seems of relevance to stress out that the restraint degree offered by washers appears more effective to that offered by screws heads since it has not disadvantages. On the contrary, screws with countersunk heads tend to develop more easily brittle failures. The use of washers appears therefore important in order to avoid the premature splitting of side wooden elements in modes c and d. The normalized failure loads of joints are illustrated in Figure 7 for the different fasteners and for the different design and the observed failure modes. In the Figure, boxes are associated to the different design failure modes, symbols are associated to the different observed failure modes, type of fasteners are ordered along the x axis. Data related to joints with 2 fasteners on each side are plotted on the left side of the vertical line associated to each type of fastener while data of samples with 4 fasteners on each side are plotted on the right side. From Figure 7 it can be noticed that normalized strengths rise greatly from dowel joints to screw joints and also from screw joints to those with screws and washers. However, the latter increase is less pronounced. It suggests that treads are more effective in developing axial forces in screws, at the base of the “rope effect”, than washers. Driving the attention to joints with same fasteners, the following comments can be derived: • dowel joints show a moderate and gradual normalized strength increase with design/observed failure modes: about 5, 6 and 7 kN on each dowel (modes d and e have approximately the same strength). No substantial difference can be detected from the strength of joints with 2 and 4 dowels on each side; • screw joints show a higher normalized strength than that of dowel joints. The normalized strength is about of 8 kN for samples designed to fail in modes c, d and e, while it is of about 10.5 kN for mode f. The strength of joints designed to fail in mode d and with 4 screws on each side are significantly lower than those of samples with only 2 screws on each side but 25 % e 100 % e 38 % f average density 489 475 461 460 471 446 436 451 477 444 445 445 4 fasteners on each side observed Fu (CV) failure modes 5.62 (0.20) 7.22 (0.01) 7.51 (0.07) 6.58 (0.08) 6.73 (0.08) 10.44 (0.13) 5.46 (0.03) 7.58 (0.04) 8.52 (0.08) 7.30 (0.07) 9.57 (0.15) 10.98 (0.06) 25 % 70 % 100 % 17 % Splitting 100 % e e e c f 33 % c this is due to the already mentioned premature brittle collapse due to splitting; • screw with washer joints are the ones with higher strength. Samples designed to fail in modes c and d, due to the rotation restriction offered by washers to screws heads, failed respectively according to modes e and f. Consequently, normalized strengths of joints with design failure modes c and d are respectively equals to those of modes e and f: 8 and 11 kN. The data collected on processed samples are summarized in Figures 8 and 9 with the same illustration technique of Figure 7. In Figure 8 the average values of plastic rotations in fasteners of each sample are presented. For all kind of fasteners, the average plastic rotations recorded for failure modes d, e and f, range in between 4 to 16°. On average, failure mode d is the one with the lowest values while the e failure mode is the one with the highest values. With reference to failure mode c, some plastic hinges have been recorded in some fasteners in spite of the fact that the failure model does not require the development of any plastic hinge. In case of joints with screws and with dowels the average plastic rotations are very small: less than 4°. In case of joints with screws and washers the average plastic rotations are very large (between 8 and 16°) but, as already mentioned, these joints fail according to failure mode e. The recorded plastic rotations are in good agreement with those predicted in [6] for a density of wood elements ranging between 360 to 550 kg/m3. These plastic rotations are correlated to yielding moments of fasteners equal to 0.82÷0.86 the maximum bending moment (achieved for plastic rotations of about 50°). Figure 9 shows the values of average embedding deformations recorded close to joints shear planes. These plastic deformations range between 3 and 7 mm with a prevalence of values around 5 mm. Such value is the same set by EN 383 [7] for the experimental evaluation of the embedding strength of wood loaded by cylindrical fasteners. Figure 7 – Values of failure loads (normalized to number of fasteners) of specimens with 2 fasteners on each side (on the left of the reference line) and of 4 fasteners (on the right of the reference line) vs. design and observed failure modes. Figure 8 – Recorded plastic rotations in fasteners vs. design and observed failure modes. Figure 9 – Recorded maximum embedding deformations in wood elements vs. design and observed failure modes. 5 ANALYSIS AND COMPARISON To assess the effects of the investigated parameters, the tests results have been compared with the strengths predicted by the Johansen’s model. Such strengths are provided by the last 4 formulae of the set of equations reported in § 2. The equations have been assumed without the numerical coefficients and without the terms related to “rope effect”. For the fasteners yielding moments, the 80% of the values reported in (2) have been assumed to take into account of the average plastic rotations of fasteners recorded (see comments to Figure 8). Concerning the embedding strength of timber elements, values reported in (1) were used. The results of the comparison are illustrated in Figure 10 and in Figure 11 as a function of the average density of the samples. In latter Figure, the results are presented according to fastener type and to observed failure modes. From both Figures it is immediately evident that experimental strengths shown by dowelled joints are correctly predicted by Johansen’s model. On the other side, the screwed connections with or without washers are obviously underestimated by the model since it does not take into account the “rope effect”. For these fasteners, form Figure 10 a different strength increase can be detected for failure modes c and e and for failure modes d and f. Indeed, while samples related to modes c and e show an average strength greater of about 40-50% the ones predicted by Johansen’s model, samples related to failure modes d and f have a larger average strength: about 50-100% the ones of Johansen’s model. There are some exceptions to the described behaviour. The first one is related to the large resistance shown by the screwed joints designed to fail in mode c if compared to analogous samples with 4 screws. The second exception concerns the screwed joints designed to fail in mode d and with 4 screws on each side, which look very weak due to the splitting failure of side elements. Figure 11 does not show a marked influence of the average density of samples on the strength values with Figure 10 – Comparison between recorded failure loads and the original Johansen formulae that don’t consider the reduction in strength due to multiple fasteners in line (neff) and the increase in strength due to the “rope effect”. Figure 11 – Comparison between recorded failure loads and the Johansen formulae vs. density of wood elements (lighter markers refer to specimens with 2 fasteners). the only exception of the data of screwed joints. To the author, this influence seems only apparent since these data encompass the wake strength of samples that fail due to splitting (characterized by a density of 460-480 kg/m3) and the exceptional resistant samples with 2 screws designed to fail in mode c (characterized by a density of 380-420 kg/m3). As regards the efficiency of fasteners aligned in load direction (neff/n), from both Figures can be seen that samples with 2 fasteners on each side (in lighter marks in Figure 11) usually have a resistance greater than those with 4 fasteners (in darker marks). The higher strength is contained unless the already mentioned exceptions. For a numerical appraisal, the average strength of all test configurations are reported in Table 3. The data seem to confirm the remark previously advanced about the strength of joints failed in modes c and e and those of joints failed in modes d and f. With respect to the efficiency of the number of fasteners, ratios neff/n computed for samples failed in modes c and e generally show a reduction in strength of about 20% for dowelled joints and of 10% for screwed joints. The same ratios for joints failed in modes d and f show a reduction of about 7% with a lesser influence of fasteners type. These values are quite different from those proposed by Eurocode 5 that are more dependent by fastener diameters (they give a reduction of only 3% for the 8 mm dowels and of about 13% for the 12 mm screws). However, a more important matter is that the efficiency seems to be influenced by the failure mode. Table 3 – Dowels Screws Screws with washers (2) (3) Finally, the joints strengths have been compared with those proposed by Eurocode 5 taking into account the opposite effects of the “rope effect” and of the number of fasteners aligned in the force direction. The comparison is shown in Figure 12. From the graph it can be noticed a quite good overall estimation of the joints strengths: the maximum overestimation is of about 15-20% and the maximum underestimation of about 55%. Looking in more detail the results it can be observed: • concerning the dowelled joints, strengths are correctly predicted for samples failed in mode c and generally underestimated (of about 10%) for the samples failed according to the other modes; • with reference to joints with screws, strengths are generally underestimated. The underestimation is due to the limited value of the “rope effect” that is credited to screws head. The maximum underestimation is for failure mode f; • for joints with screws and washers, strengths are well estimated for samples failed in modes d and f while they seems slightly overestimated in case of failure modes c and e. Ratios of average Fu / FJ for all joint configurations. Type of fastener (1) Table 4 reports the strength increases of screwed joints with respect to those of dowelled joints once the effect of the number of fasteners in line with the force is taken into account (neff/n). The strength increase can be associated to the “rope effect”. From the Table an evident influence of failure modes on strength increase is detectable. The “rope effect” can be evaluated of about 45% for failure modes c and e, and of about 85% for failure modes d and f. number of fasteners on each side 4 2 4/2 neff /n 4 2 4/2 neff /n 4 2 4/2 neff /n Fu / FJ ratios vs. the design failure modes and the observed ones (in parenthesis) c e d f 0.82 0.86 0.93 0.98 1.03 1.08 0.99 1.05 0.80 0.80 0.94 0.93 0.80 0.93 1.25 1.30 1.15 1.71 1.75 1.43 1.66 1.85 0.71 (1) 0.91 0.69 (2) 0.93 0.91 0.93 1.31 (e) 1.44 1.71 (f) 1.80 1.49 (e) 1.31 1.83 (f) 1.85 0.88 1.10 (3) 0.93 0.97 0.88 0.95 value don’t taken into account in computing neff/n due to the too much higher failure loads of specimens with 2 fasteners; value don’t taken into account in computing neff/n due to splitting occurred in specimens with 4 fasteners; value don’t taken into account in computing neff/n due to the too much lower failure loads of specimens with 2 fasteners. Table 4 – Experimental strength increase in joints with screws and screws with washers. Fu / [(neff /n) FJ ] Screws Screws with washers (1) c 1.56 1.45 (e) Design failure modes and the observed ones (in parenthesis) e d 1.42 1.46 (1) 1.43 1.84 (f) value afflicted by the splitting of specimens with 4 fasteners. f 1.86 1.90 Figure 12 – Comparison between recorded failure loads and the ones predicted by Eurocode 5 taking into account both neff and the “rope effect”. 6 CONCLUSIONS The research has focused on the experimental determination of the strength of wood-to-wood joints with self-tapping screws in single shear. To this end, a parametric study that takes into account different parameters has been carried out. The research allows deriving the following conclusions: • joints with screws and washers have a higher strength of those with screws without washers which in turn are more resistant than those with dowels; • the strength increase is essentially due to the “rope effect” which can take place only if fasteners are effectively bounded; • washers, providing a rotational constraint to fasteners ends, prevent the origin of failure modes that requires this degree of freedom (modes c and d); • screws heads tend to behave as washers, however are less efficient and consequently cause higher local stresses in wood. Screws with countersunk heads used in joints designed to fail in modes c and d can lead to premature collapses for splitting of timber elements. For these failure modes, the use of washers is strongly recommended; • test results, although with some conflicting data, have allowed the estimation of the strength increase to the “rope effect” and the strength reduction due to the number of fasteners aligned in the direction of the force; • the values derived are not excessively far from those established by the European standard for timber structures which are generally more conservative. • a better appraisal of the actual strength of joints with self-tapping screws can be based on the classical set of equations assuming more appropriate values of basic parameters (yielding moment and embedding strength). ACKNOWLEDGEMENT The author wishes to thank the company Würth Srl of Egna (BZ), the company Heco Italia Srl of Romano d'Ezzelino (VI) and the company Rotho Blaas Srl of Cortaccia (BZ) that kindly provided the fasteners used in the research. REFERENCES [1] [2] [3] [4] [5] [6] [7] F. Asson: Experimental investigation on wood-towood joints with self-tapping screws (in Italian). Thesis, University of Trento, Italy, 2009. EN 1995-1-1 – Eurocode 5: Design of timber structures. Part 1-1: General – Common rules and rules for buildings. CEN, European Committee for Standardization, 2009. Johansen K. W.: Theory of timber connections. International Association of Bridge and Structural Engineering, Publication No. 9:249-262, 1949. C. Montresor: Determination of plastic moments of self-tapping screws for joints in timber structures (in Italian). Thesis, University of Trento, Italy, 2008. EN 26891 – Timber structures. Joints made with mechanical fasteners. General principles for the determination of strength and deformation characteristics. CEN, European Committee for Standardization, 1991. M. Ballerini, and C. Montresor: Mechanical characterisation of joints with self-tapping screws for reversible structural refurbishment works (in Italian). In Consolidamento delle strutture in legno, pages 129–163, Hevelius Edizioni, Naples, Italy, 2009. EN 383 – Timber structures. Test methods. Determination of embedding strength and foundation values for dowel type fasteners. CEN, European Committee for Standardization, 2007.