Increased yield of finger jointed structural timber by accounting for grain orientation utilizing the tracheid effect

The engineering properties of softwood timber vary considerably not only between species, but also within single species, between origins, stands, trees, boards and within boards. For example, the bending strength of boards of Norway spruce timber from Sweden, Norway and Finland may vary between 10 MPa and 80 MPa and the corresponding variation for modulus of elasticity (MoE) is between 5 and 20 GPa (Olsson and Oscarsson 2017). The shape stability of timber (timber distortion), when subjected to changes in moisture content, varies depending on the extent of spiral grain and on the part of the log cross section the board is cut from (Ormarsson 1999). Moreover, the length of logs restricts the length of boards that can be produced, unless finger joints are applied to give longer assembled members. All this means that production of structural timber with well-defined and appropriate engineering properties, and with length set by the needs of applications rather than from the length of the logs produced, requires both accurate grading with respect to engineering properties and application of finger joints. Competitiveness on the market also requires production at low costs. The latter can partially be achieved by minimizing the waste of material when applying finger joints.

The properties of structural timber of different strength classes are defined in the European standard EN 338 (2016). In this standard, characteristic values of several strength and stiffness properties are specified, in addition to characteristic density. However, machine strength grading of timber according to the European standard EN 14081-2 (2018) concerns only requirements on three different grade determining properties, namely the bending or tensile strength, the MoE in bending or tension and the density. In addition to these requirements, there are limitations regarding geometrical imperfections and visually identified defects, as specified in EN 14081-1 (2016). The yield achieved in different strength classes thus depends both on the quality of the timber and on the accuracy of the methods/machines used for prediction of the abovementioned grade determining properties. Regarding accuracy in grading it is, in most cases, the ability to predict strength rather than density or MoE, that limits the yield and, consequently, improved grading accuracy with respect to strength leads to higher yield in high strength classes (Olsson and Oscarsson 2017).

The most accurate machine strength grading methods available on the market are based on X-ray scanning or surface laser scanning, in combination with other techniques like dynamic excitation of longitudinal modes of vibration (Bacher 2008; Hanhijärvi and Ranta-Maunus 2008; Olsson and Oscarsson 2017). These methods also give the basis for assessment of the variation of strength along each board, such that a weak part of a board may be removed in order to enable grading of the remaining parts to a high strength class.

Finger joints are applied to the production of structural timber and glulam lamellae mainly to produce long boards, but in some production lines also for the removal of weak/poor sections. Performance requirements and minimum production requirements of finger jointed solid/structural timber are given in the European standard EN 15497 (2014). Similar but not identical requirements for glulam laminations are given in EN 14080 (2013). Regarding the edgewise bending strength of finger joints, it is stated in EN 15497 that this strength shall be equal to or greater than the declared characteristic bending strength of the unjointed timber. Strength of finger joints depends on the wood properties but also on the geometry of the fingers, on the glue applied and on the skill of the manufacturer (Aicher 2003). The dependency between wood properties is such that higher clear wood MoEs, which correlate to higher strength of clear wood parallel to grain and higher shear strength, give stronger joints. These stiffness and strength properties correlate to the clear wood density and therefore it should be relatively easy to select timber that is well suited to give strong finger joints. Serrano (2000) performed finite element calculations on the influence of bond line properties and on the significance of defects in finger joints, and showed that even small defects in bond lines may have a considerable effect on the strength of a finger joint. The current situation regarding the edgewise bending strength of finger joints produced in industry in Sweden is that many manufacturers are certified to produce finger joints in structural timber strong enough for the strength class C30, some even for the class C35 (C30 and C35 refer to characteristic edgewise bending strength of 30 MPa and 35 MPa, respectively) but not for higher C-classes (Ziethén 2017). Regarding finger joints in glulam lamellae (characterised by tensile strength classes, i.e. T-classes), the tensile strength of finger joints is indeed an issue, since failure on the tension side of glulam beams loaded in bending very often occurs in finger joints (Fink et al. 2015). Frese and Blass (2009) presented a research indicating that higher characteristic tensile strength of finger joints than required at the time is necessary in order to produce glued laminated timber (GLT) that meets the strength requirements. Current requirements on characteristic strength of finger joints for different GLT strength classes are specified in EN 14080.

The standard EN 15497 gives guidance regarding the interpretation of the knot diameter that defines the required minimum distance between a knot and the finger joint, but some additional interpretation is necessary. The drawing shown in Fig. 1a is resembling a drawing in EN 15497 and shows that for a round or oval knot the diameter, d, shall be understood as the width of the knot in the transversal direction of the board. The drawing in Fig. 1b shows an arris knot, and for such a knot, the diameter shall be set to the length of the knot in the longitudinal direction of the board. This definition is thus different from how knots are generally measured in visual grading (e.g. SS 230120 2010; Thunell 1981). Figure 1c shows a drawing of a splay knot. How to interpret knot diameter in this case is not explained in EN 15497, but the interpretation herein is to measure it in the same way as an arris knot, as indicated in Fig. 1c. Thus, in all cases where a knot is visible both on the wide and on the narrow edge, the knot diameter is interpreted as the length of the knot in longitudinal board direction, even if the size of the knot in transversal direction on one or more sides is larger. If a knot is removed, the requirements are somewhat different compared to if it remains within the timber. Figure 1d illustrates the case, and corresponding alternative margin requirements, when a knot is removed (the shaded part of the board will not be used).

When a softwood surface is illuminated with concentrated light, such as laser, fibres conduct light better in the direction of the fibres than across. This is referred to as the tracheid effect (Matthews and Beech 1976; Seltman 1992; Soest et al. 1993). The shape of a dot of light, which on a surface of an isotropic material would have been circular in shape, becomes, on a softwood surface, stretched out in the direction of the fibres and the major axis of the thus stretched, elliptically shaped spot indicates the local in-plane fibre direction. Attempts to detect knots on the basis of data from tracheid effect scanning have been presented both by Briggert et al. (2016) and by Kandler et al. (2016). In both studies, light dots on the wood surfaces from a laser source were assessed both with respect to the main direction of the elliptically shaped light spots, from which the in-plane fibre directions were obtained, and with respect to the roundness of the light spots. The latter was, in both investigations, assumed to give an indication of the so-called diving angle, i.e. the angle between the local fibre direction and the investigated surface. On the basis of this, 3D fibre directions were determined locally on wood surfaces with a resolution of about 4.4 mm. A threshold was set for the angle between the determined local fibre direction and the longitudinal direction of the board such that positions on the wood surface where the determined angle exceeded a threshold of 56° (Briggert et al. 2016) were regarded as being within a knot. In both studies (Briggert et al. 2016 and Kandler et al. 2016), knots were identified on surfaces with reasonable but not excellent accuracy with respect to size and shape of knots. The reasons for the limited accuracy being (1) the limited spatial resolution of the laser dot grid and (2) the uncertainty of the relationship between the roundness of the laser dots and the assessed diving angle.

The aim of the present research is to investigate the potential yield of finger jointed machine strength graded timber. Since the accuracy regarding recognition of knots and fibre deviations, as well as how the requirements of EN 15497 are interpreted, are decisive for where finger joints may be applied, these issues are discussed in detail. More precisely, the following is included:

The investigation is limited to planed boards of Norway spruce of size 45 × 145 mm from Sweden, Norway and Finland. Other dimensions, and other species or origin, may give different results. Furthermore, results of the study are strictly valid only for structural timber, even though the results should give a relevant indication also for GLT laminations.

Sampling of the timber considered in the present research was first done to give the basis for a formal approval of a machine strength grading method described in Olsson et al. (2013) and Olsson and Oscarsson (2017), i.e. for fulfilment of requirements of initial type testing according to EN 14081-2 (2010+A1:2012), and for derivation of settings for a growth area covering Sweden, Norway and Finland. Thus, the sampling and the preparation of the timber, including drying aiming at 12% moisture content (MC), was performed in accordance with the requirements laid down in the standard. At the time, it was stated in EN 384 (2010), clause 5.2, that when assessing bending strength the critical section, i.e. the section along the board at which failure is expected to occur, shall be in a position that can be tested, that is within the loading heads in a four point bending test as described in EN 408 (2010+A1:2012). Therefore, boards having their critical section closer to one of the ends than about 6.5 times the board depth were discarded. Hence, in order to assess at least 900 pieces, required according to EN 14081-2 (2010+A1:2012), about 2100 pieces, ranging in size from 30 to 70 mm in thickness and from 70 to 245 mm in depth, were sampled at a first stage. Out of the 2100 pieces, 897 were of dimension 45 × 145 mm and these constitute the sample for the present study. This latter sample was divided into five subsamples representing timber from (1) northern Sweden, (2) mid Sweden, (3) southern Sweden, (4) Norway, and (5) Finland. The numbers of specimens included in each region are presented in Table 1.

All the boards of the sample considered herein were assessed with respect to dimensions, weight, axial resonance frequency and tracheid effect scanning, as described in Olsson and Oscarsson (2017), but as explained above not all of them were actually subjected to destructive testing in four-point bending. Dynamic MoE (E_dyn) and board density (ρ_corr), both adjusted to 12% MC were, however, determined for all the boards of the present sample and mean values, standard deviations and coefficients of variation of these properties are given in Table 2. Given in Table 2 are also the mean MC of each subsample, determined on the basis of measurements of a limited number of boards of each sub sample using a pin type MC metre. Relationships between timber properties, in terms of coefficient of determination, are reported in Olsson and Oscarsson (2017).

There are several different manufacturers of wood scanners operating on the market and scanning of sawn timber has been performed for different purposes at sawmills and in the wood working industry for more than 20 years. For the present research, an industrial scanner of make WoodEye (WoodEye 2018) was used. This machine is equipped with lasers and multi-sensor cameras, one set for each longitudinal surface of the board, for collecting data regarding the in-plane fibre directions and high-resolution three colour photographs of the scanned surfaces. In the scanner, fibre direction data is obtained by means of the tracheid effect. Figure 2 shows (a) the industrial scanner used, (b) an enlarged photograph of a small wood surface, (c) the spread of light from a dot laser when illuminating the small wood surface, the drawn black line indicating the determined in-plane component of the fibre direction, (d) an image/photograph obtained from the scanner showing a larger wood surface, and (e) the determined local in-plane component of the fibre directions over the same surface represented by small black lines. Within knots, such as the two displayed in Fig. 2d, fibres are actually directed almost perpendicular to the surface displayed. Thus, the in-plane component of the fibre direction is very small in such areas and laser light spots become almost circular in shape. As a result, the determined in-plane component of the fibre directions are uncertain within the knot areas marked by shadowed fields in Fig. 2e.

Data corresponding to what is displayed for one wood surface in Fig. 2d, e can be collected by a scanner for all four sides and for the full length of a wooden board when scanned at a speed as high as 450 m/min, which is a common operation speed in industry. The resolution of the fibre direction data obtained in the transverse direction of the board surfaces is 4.4 mm (resolution depends on the beam diffraction splitter installed on the dot laser source) and with a conveyor speed of 450 m/min, the same resolution is obtained in longitudinal direction. Regarding colour photographs, the data obtained consists of three colours, red, blue and green, and the resolution is as high as 0.07 mm in the transverse direction of the board and 0.8 mm in longitudinal board direction. Furthermore, by means of the scanning operation, it is also possible to determine length, thickness and depth of the investigated boards.

The machine strength grading method mentioned in Sect. 2.1, Sampling of material, was used to calculate bending MoE profiles for each board. Such profiles give the basis to decide which sections to remove by cross-cut, in order to produce finger-jointed structural timber of certain quality. In addition to data from tracheid effect scanning, the method to calculate bending MoE profiles utilizes knowledge of longitudinal resonance frequency and weight obtained by a complementary strength grading machine. In brief, the method to calculate MoE profiles comprises the following stages (for further details see Olsson et al. 2013; Olsson and Oscarsson 2017):

Figure 3 gives an illustration of the method showing (a) local fibre directions scanned on a board surface, (b) board cross-section divided into sub-areas implying that the exhibited angle φ and corresponding MoE in the longitudinal direction, E_x(x,y,z), to be valid within the volume dA × dx, (c) segment of length dx for which the edgewise bending MoE is calculated by stiffness integration over the segment’s cross-section, and (d) a bending MoE profile, each value along the graph representing the average edgewise bending MoE of the surrounding 90 mm, and the lowest value along the profile defining the IP to bending strength.

Obtained bending MoE profile, such as the one shown in Fig. 3d, indicates where along each board assessed, the calculated bending stiffness is at its lowest. This is utilized for the prediction of the strength of the board. In the present investigation, the information is utilized in simulated production of finger jointed machine strength graded structural timber.

Some other strength grading methods/machines, for example those based on X-ray technology, enable lengthwise resolution of predicted bending strength in a similar way and there are sawmills utilizing this feature of X-ray based machines to eliminate weak section and reconnect, by finger joints, the remaining parts. When this is utilized, the assembled members are assigned to higher strength classes than what would be allowed if the weak sections of the original, full-length member were not removed (Ziethén 2017).

The method developed by Briggert et al. (2016) for the detection of knots on wood surfaces on the basis of tracheid effect scanning, as briefly described in Sect. 1.3, was utilized in a first step for the detection of knots in the boards of the present sample. Then, a rectangular area, enclosing the knot surface, was determined by adding margins of 3 mm on each side of the knot in transversal direction of the board and of 5 mm on each side in longitudinal direction. Figure 4 shows photographs/images and local fibre directions, both obtained by a scanner, on four wood surfaces of a 250 mm long section of a timber member, 45 × 145 mm in size. The drawn red rectangles mark the abovementioned rectangular knot containing areas.

Within the identified rectangular areas, knots were then identified again but now on the basis of the light intensity of the images of the wood surfaces. Actually, the only image utilized, out of the three available, was the red scaled one, although the blue scaled or green scaled images could have been utilized as well. For each pixel of the image a number between 0 (very dark) and 255 (very bright) is obtained and a threshold was set below which the pixel is considered dark enough to be part of a knot. The threshold was, however, not a fixed number but adjusted in relation to the brightness of a surrounding, semi-local area in the following way: At a given longitudinal position p on a board surface, the median value, denoted m_e, of all light intensity values of a line of pixels oriented in transversal board direction was determined. Then the median value of all such median values of lines within a range of 300 mm in longitudinal board direction was determined. This median value was denoted n_p, and the dynamic threshold to be used for a pixel in the current longitudinal position, p, was calculated aswhere t_s is a fixed number, here set to 200 based on trial and error, and comparisons of results and images made with the naked eye. Thus, if the light intensity number of the pixel considered (a number between 0 and 255) is lower than t_p then this pixel/position indicates knot surface. Considering the pixels contained within an investigated rectangular area (red rectangles in Fig. 4) one or several coherent group/groups of knot indicating pixels are usually identified, although sometimes no knot indicating pixels are contained within the area. Convex hulls that encircle such coherent groups of knot indicating pixels are determined and the largest one within each rectangular area is regarded a knot. Knots identified in this way are encircled by cyan blue contours in Fig. 4. The reason to look for knots only within the rectangular areas is that this reduces the risk of mistaking, for example, dirt on the surface for a knot.

Surface (d) of Fig. 4 is located close to the pith of the log from which the piece of timber is cut (the pith is located at a distance of only 5–10 mm from this surface, outside the piece). On such surface, the borders of the knots are often hard to distinguish on the basis of surface darkness, i.e. the identification is sensitive to the threshold set by Eq. 1, and in this particular case it is quite clear that the size of the knot at the top left on this surface is underestimated. The knots to the top right and to the bottom left on surface (d) are traversing knots that are also visible as larger round knots on surface (b). Likewise, the knots to the top left and to the bottom right on surface (d) are also visible on surface (c) and (a), respectively. All the knots visible on surfaces (a–c) seem to be accurately determined. A small part of the knot visible on surface (a) is also identified on surface (b). Hence this is an example of an arris knot for which the knot diameter is calculated as the length of the knot in longitudinal direction of the board, here determined on surfaces (a), as explained in Sect. 1.2. Further comments on the results of the described knot detection procedure, of which Fig. 4 shows just an example, are given in Sect. 4 below. Finally, a knot diameter, d, is determined for each detected knot as described in Sect. 1.2 above.

To determine whether there is any pronounced grain disturbance in a certain section along the board, i.e. at a certain position in longitudinal direction, the following is considered. For the position p in longitudinal direction (position in millimetre from one end of the board), the fibre directions of the scanning grid, on all four sides and within the section p ± 5 mm, is considered. This is done for all 10 mm long sections along the board, i.e. for p = 5, 15, 25, …, L – 5 mm, where L is the length of the board. Then, each 10 mm section along the board is regarded as a section with or without pronounced grain deviation on the basis of a criterion. Four different criteria are considered herein to define a section with pronounced grain disturbance, namely the following:

The thresholds used for grain deviation in criteria (i–iv) are set based on the following considerations. A simple expression for the tensile strength as a function of fibre angle is given by Hankinson’s formula (Hankinson 1921) aswhere \(f_{t,0}\) and \(f_{t,90}\) are tensile strength along and perpendicular to the fibre direction, respectively, n is a parameter to be set empirically on the basis of experimental results and α is the fibre angle, i.e. the grain deviation. Using a relationship of \(f_{t,0} /f_{t,90} = 30\) and n = 1.7, which is representative for what has been reported in literature for Norway spruce, although different investigation have shown different results (Gustafsson 2003), a grain deviation of 8° means a reduction in tensile strength of about 50%. Correspondingly, a grain deviation of 13° means a reduction in tensile strength of about 70%. This means, of course, that grain deviation smaller than 8° may have considerable influence on the strength of finger joints but for reasons discussed in Sect. 4.2, a smaller grain deviation than 8° is neglected herein.

Detection and definition of knots and pronounced grain disturbance give the basis for the definition of the criteria concerning where along the boards finger joints may, or may not, be placed. Eight different criteria are considered herein, namely:

Of course, the length of a section where a finger joint may be applied must always be at least as long as the length of the finger joint itself. Herein the length of a finger joint is set to 30 mm. Criteria (1), (7) and (8) could, according to the author’s interpretation of EN 15497, be used in the production, whereas the other criteria cannot.

Two different cases of production of finger jointed sawn timber are simulated herein. These are

For all cases it is required that the length of utilized members are at least 500 mm long. Shorter members than this are always discarded. For both production cases (a) and (b), the principle is that a single infinitely long board, consisting of boards connected by finger joints according to one of the eight criteria defined in Sect. 3.4, is produced.

Detection of knots as described in Sect. 3.2 gives, according to visual inspection, i.e. manual inspection of results represented by images such as those displayed in Fig. 4, of a high number of boards, accurate results. This holds for the vast majority of boards and knots and the example of wood surfaces including knots shown in Fig. 4 is representative for the knot identification performed herein. However, as for the example shown in Fig. 4d, the size of surfaces of splay knots, which are common on wood surfaces close to the pith of boards, and usually brighter in colour than what other knots are, is often underestimated. Since such knot surfaces may be disregarded with respect to the knot diameter defined in Sect. 1.2 this is, however, not an issue for the applications considered in this research. For other applications, where it may be important to identify splay knots accurately, additional use can be made of the fibre directions identified on wood surfaces using the tracheid effect, since the fibre direction within splay knots coincides with the direction of the knot itself.

Even apart from splay knots, the knot detection algorithm presented herein fails in a few cases. For example, this can happen if an area that actually contains more than one knot is identified as one coherent fibre distorted area (fibre distorted areas are marked by red rectangles in Fig. 4). In such a case, two different misinterpretations can be made. One is that only the biggest knot within the fibre distorted field is identified, whereas smaller knots that are also contained within the area are erroneously disregarded, or that two or more smaller knots within the area are identified as a single large knot. However, finger joints are not seriously misplaced because of such misinterpretations.

The identification of pronounced grain disturbance, as defined in Sect. 3.3 and used in finger joint criteria (3–8), see Sect. 3.4, is even more reliable than the detection of knots. Unless the wood surface is rough or very dirty the fibre directions identified on the basis of the tracheid effect are reliable, i.e. measurement errors are negligible compared to the comparatively large fibre angles that indicate pronounced grain disturbance. Errors caused by rough or very dirty wood surfaces could lead to identification of pronounced grain disturbance where, in reality, no such disturbance would occur on the corresponding well-planed surface, but such cases have not been observed in this study. The opposite situation, that fibres are identified as straight where they are actually disturbed, can be ruled out. Thus, any incorrect identification caused by rough or very dirty wood surface would lead to errors on ‘the safe side’ with respect to where finger joints are placed. It should be noted, however, that the present study is performed on planed timber.

A small number of the boards included in the sample were probably cut from non-straight logs or from logs with considerable spiral grain. For a study on the occurrence and magnitude of spiral grain in Norway spruce, see Säll (2002). As a result, for about 3% of the boards, the inclination of fibres observed on large parts of the wood surfaces amounts to more than 6° also where the fibre orientation is not affected of knots. Therefore, fibre deviations below 8° are not considered herein as pronounced grain disturbance, even if fibre deviations of 6–8 degrees correspond to a significant reduction in strength. It can be questioned, of course, if boards with such inclination of fibres should be used at all for the production of finger jointed structural timber. However, using finger joint criterion (1), which is based solely on the distance to knots, no boards would be discarded because of general inclination of fibres and therefore, in order to make a fair comparison of the yield using different criteria, the lowest threshold employed regarding fibre deviation was set to 8°.

Figure 5 shows (a) a calculated bending MoE profile of one board where red lines indicate positions/sections where the calculated bending MoE, see Sect. 3.1, is lower than what is required for strength class C35 (Olsson and Oscarsson 2017), (b) photographs of four sides of the board where coloured horizontally drawn lines indicate longitudinal sections that would pass for class C35 (green lines), sections that would not pass as C35 (red lines), sections that contain pronounced grain disturbance according to criterion (4) (black lines), sections with a knot present within a distance in longitudinal direction shorter than 1.5 times the knot diameter (blue lines), and sections with a knot present within a distance shorter than 3 times the knot diameter (purple lines). Thus, purple lines correspond to finger joint criterion (1) and blue lines correspond to criterion (2). In the case when the knot remains in the timber, the union of blue and black lines corresponds to criterion (7), whereas in the case when the knot is removed, black lines alone correspond to criterion (7). Figure 5c shows enlarged images of a 600 mm long part of the board. The vertically drawn purple arrows indicate where the board would be cut if criterion (1) was used to remove the weak section represented by the red marked field, as is done in production cases (b) defined in Sect. 3.4, i.e. the wood between the two purple arrows would then have to be discarded. The black arrows indicate where the board would be cut if criterion (7) was used instead. In the case illustrated in Fig. 5c there is a short gap in the horizontally drawn purple line between the two purple arrows but since this gap is shorter than 30 mm, which is the assumed length of a finger joint, a finger joint cannot be placed there.

Figure 5 illustrates a typical case showing that finger joint criterion (1) gives, in general, longer continuous sections along which finger joints may not be placed, compared to what, for example, criterion (7) does. Thus, the use of criterion (1) should, in most cases, result in longer sections discarded than what the use of criterion (7) would.

Table 4 shows the calculated percentage of waste of the total volume of the timber used to simulate production of finger-jointed timber, for each of the eight different finger joint criteria defined in Sect. 3.4 and for the two different production cases defined in Sect. 3.5. It is shown both for the entire sample and separately for each sub-sample. The yield percentage of the simulated production is equal to 100% minus the percentage of waste. Focusing first on production case (a) and the entire sample of boards including all regions, and comparison of criteria (1) and (2), it is clear that a minimum distance between a knot and a finger joint of 1.5 times the knot diameter, rather than of three times the knot diameter, would reduce the waste from about 7.4 to 3.1%. However, criterion 2 is not permitted according to EN 15497, unless it is supplemented by or (if the knot is removed) replaced by a requirement of more or less straight fibres within the finger joints. Criterion (7) represents such a composite criterion and, for this, the calculated waste was 4.0%, which is 3.4% unit points lower compared to when criterion (1) is used. Note that the use of criterion (1), where only the presence of knots is taken into account, means that there is still a risk that the finger joint will contain pronounced grain disturbance. This will certainly be the case, for example, when a large knot is cut off just outside the board’s end before the board is connected to another one. For this reason, criterion (1) may, for some finger joints, give less waste than what criterion (7) does. Producers could use criterion (1), whenever it gives the least waste, and criterion (7), whenever it gives the least waste. Such a procedure is represented by criterion (8), which gives less than half of the waste compared to using criterion (1). Criterion (4), which is part of criteria (7) and (8), represents one possible interpretation of the requirement of EN 15497 regarding unacceptable fibre distortion within a finger joint. As shown by Table 4, criterion (4) on its own gave, for production case (a), slightly more waste than what criterion (2) did. The reason for this is, however, not that criterion (4) in general gives larger margins to knots than what criterion (2) does (see Fig. 4), but that criterion (2), just as criterion (1), fails to ensure straight fibres in finger joints when knots are cut off just outside a board´s end. Comparisons of results for criterion (3–6) give indications of how the percentage of waste changes due to changes of the definition of pronounced grain disturbance.

Production case (b) represents production of finger jointed structural timber of grade C35 where weak sections of boards are removed such that the remaining pieces can be utilized for production of finger jointed sawn timber of this high strength class. This means that the number of finger joints per unit length of produced timber is larger for production case (b) than what it is for production case (a). The average distance between finger joints was, for simulated production case (b) and finger joint criterion (1), 2.8 m, whereas for production case (a) and finger joint criterion (1) the average distance was 4.2 m. Hence the yield of produced timber is even more dependent on the finger joint criterion applied for production case (b) than what it is for production case (a). For example, for production case (b) the calculated waste was reduced by as much as 6.4% unit points when finger joint criterion (7), rather than criterion (1), was used.

Note that it is beyond the scope of this paper to investigate whether it is appropriate to produce strength graded sawn timber in the way as simulated by production case (b), i.e. to assign only parts of an investigated board to a certain strength class, but as explained above this actually occurs in production. Therefore, it is relevant to investigate the significance of the choice of finger joint criteria on such a production case. The results presented in Table 4 regarding the waste of production case (b) mean that the yield of timber in class C35 was, for the whole sample, 72–79%, depending on the finger joint criteria used. This shall be compared to the yield obtained when discarding all boards that do not fulfil the requirement for class C35 along the entire length, in production of finger jointed C35 timber. For the investigated sample, this would be 50–53% depending on the finger joint criteria used.

Timber of different origins and subsamples differ in quality and the percentages of waste differ between subsamples. For example, the subsample from mid Sweden gave, for production case (a) and using finger joint criteria (1) and (7), a waste of only 6.1% and 3.0%, respectively, whereas the subsample from northern Sweden gave a waste of 9.8% and 5.4%, respectively. On the other hand, for production case (b), the yield of the subsample from northern Sweden was higher than what the yield of the subsample from mid Sweden was. The explanation is that the timber from northern Sweden contained a high number of small knots leading to far-reaching restrictions on where finger joints may be placed (cf. criterion (1) in the example illustrated in Fig. 4c) and thus to considerable waste related to finger joints for connection of boards. At the same time, since the knots were small, comparatively few boards, or sections of boards of the subsample from northern Sweden needed to be discarded to meet the requirement defining the class C35. The number of boards of a single sample is relatively small, comprising between 90 boards (southern Sweden) and 294 boards (mid Sweden) and the results presented for the subsamples may not be representative for the regions they come from. Comparisons indicate, however, that the amount of waste related to finger jointing may differ considerably depending on the quality of the timber.

Table 5 shows how often application of the knot distance criteria, i.e. criteria (1–2), would imply violation of the criteria of pronounced grain disturbance, i.e. criteria (3–6). The percentage 13.8 given for production case (a) and criteria (1) and (3) in Table 5 means, for example, that 13.8% of the board ends, appropriate for finger jointing according to criterion (1), would mean violation with respect to criterion (3) if a finger joint was applied there. Results show that for production case (a), application of knot criterion (1) means violation of fibre criteria (3–5) in as much as 10–16% of the cases. Only the very, so to speak, generous fibre criterion (6) is seldomly violated applying criterion (1). For production case (b) the application of knot criterion (1) does not mean violation of fibre criteria (3–5) quite as often as it does for production case (a) but still quite often, namely in 8–14% of the cases. Application of knot criterion (2) would mean violation of the fibre criteria more than twice as often as what application of knot criterion (1) does. However, criterion (2) is not allowed to be used on its own, but only in combination with a fibre criterion.