Alterations to the bending mechanical properties of Pinus sylvestris timber according to flatwise and edgewise directions and knot position in the cross-section

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Introduction
Various authors have investigated the mechanical properties of scots pine (Pinus sylvestris L.) timber through bending tests in order to know the modulus of elasticity (MOE) and the modulus of rupture (MOR) (Arriaga et al. 2012, Krzosek et al. 2021, Ranta-Maunus et al. 2011).Bending tests have been complemented with different non-destructive testing (NDT) techniques, including the vibration test (Arriaga et al. 2012, Hassan et al. 2013, Villasante et al. 2019).In this way, the stiffness and bending strength could be easily predicted.Some studies on conifers have attempted to improve the prediction of mechanical properties made with NDT by adding different variables related to the features of sawn timber.Ranta- Maunus et al. (2011) in scots pine (Pinus sylvestris L.) and Simic et al. (2019) in sitka spruce (Picea sitchensis ((Bong.)Carr.) studied the influence of density.Guntekin et al. (2013) in calabrian pine (Pinus brutia Ten.) and Martins et al. (2017) in cluster pine (Pinus pinaster Aiton) studied the relationship between rate of growth and mechanical properties.Arriaga et al. (2007) studied the influence of wanes in scots pine (Pinus sylvestris L.), and Arriaga et al. (2014) the effect of the slope of grain in radiata pine (Pinus radiata D. Don).Knottiness is one of the features with an important influence on the mechanical properties.This relationship has been studied in different works using scots pine (Pinus sylvestris L.).Conde García et al. (2007) used measurement of the relative diameter of the maximum knots on the face and on the edge.They verified that the inclusion of a knottiness variable improved MOE and MOR predictions made using models based exclusively on ultrasound speed.Hautamäki et al. (2014) found that MOR prediction from the MOE improved if the knot area ratio (KAR) was included in the model.Likewise, they found that MOE prediction on the basis of density improved when including KAR in the model.Arriaga et al. (2012) andVillasante et al. (2019) also used a similar measure of knottiness, the concentrated knot diameter ratio (CKDR).In both cases, the authors observed that adding the CKDR improved the prediction of MOR based on the longitudinal resonant frequency.Some works have studied the influence of the position of knots along the piece.Baillères et al. (2012), in four-point bending tests using radiata pine (Pinus radiata D. Don), found that only the knots situated between the internal loading points had a significant contribution in the prediction of MOR.Wright et al. (2019), in tests with loblolly pine (Pinus taeda L.), found that the best MOE prediction was obtained when including only the knots that were within 85 % of the span and that the best MOR prediction was obtained with the knots located in 65 % of the span.
In contrast, very few works have studied the influence of the position of knots in the cross-section (tension or compression zones).In these cases, the margin knot area ratio (MKAR) was used, which is included in BS 4978 (2017).The margin zone used was a quarter of the width in the upper and lower margins.Lam et al. (2005), in tests made with douglas fir (Pseudotsuga menziesii (Mirb.),found that the MKAR could be used to establish grades for Canadian Douglas fir timber.Algin (2019) performed a multivariate optimisation on machine graded scaffold boards from sitka (Picea sitchensis, (Bong.)Carr.) including the KAR and MKAR simultaneously.In order to predict the mechanical characteristics of norway spruce (Picea abies (L.) H. Karst.),Lukacevic et al. (2015) constructed linear multivariate models that included some knot position measurements in the crosssection.Guindos and Guaita (2014) performed a theoretical simulation based on the characteristics of scots pine (Pinus sylvestris L.) timber to determine the influence of knot type and size, as well as its position in the cross-section.Their theoretical models indicated that the highest MOR decrease was due to the presence of margin knots (the knots most distant from the centre of the cross-section).
As wood is a heterogenous and anisotropic material, the choice of the tension side in the bending test can have a significant effect on the mechanical properties.This is important when comparisons are made of results obtained by machine grading performed with a continuous lumber tester with those obtained through conventional bending tests.In the first case the samples are normally bent flatwise, whereas in the second the bending is commonly performed in edgewise direction.For this reason, it is of fundamental importance to know the relationship between the results of the tests in the two directions.Despite this, only very few works have studied this relationship.Some authors have found a high correlation between the MOE values calculated via bending in edgewise and flatwise directions.These include Kim et al. (2010) in southern pine (R 2 = 0,69), Baillères et al. (2012) in radiata pine (Pinus radiata D. Don) (R 2 = 0,70), Yang et al. (2015) in different conifers (R 2 = 0,85) and Pošta et al. (2016) in norway spruce (Picea abies (L.) H. Karst.)(R 2 = 0,88).Baillères et al. (2012) obtained a weak relationship (R 2 = 0,41) for the multiple linear regression with the MOE in flatwise direction and knottiness to predict the MOR in edgewise direction.
The aims of the present study were (1) to analyse the mechanical properties obtained via edgewise and flatwise bending tests in samples of scots pine (Pinus sylvestris L.), and (2) to verify whether the variables that take into account knot position in the cross-section can improve prediction of the mechanical bending properties calculated in both directions.Grading of scots pine (Pinus sylvestris L.) timber from the Montsec mountains (Spain) was not an objective of this work.

Materials
The study was carried out using 57 samples of scots pine (Pinus sylvestris L.) with a size of 70 x 100 x 2000 mm 3 obtained from the province of Lerida (NE Spain).The pieces were selected randomly from a batch of unclassified timber at a local sawmill.Each sample was marked with a number.Each of the four sides was marked with a letter, A and C for the edges and B and D for the faces (Figure 1).The wood was stored for 10 months in the interior of a test laboratory until reaching constant weight (maximum difference of ± 0,1 % between weightings made with a time interval of 6 h) in accordance with EN 408:2011+A1 (2012).The same standard was used to measure each sample to obtain the density.The slope of grain and the rate of growth of each sample were measured in accordance with the procedure outlined in EN 1309EN -3 (2018)).

Bending tests
The samples were subjected to a non-destructive four-point bending test using a 50-kN universal testing machine (Cohiner, Spain) to know the global MOE in accordance with EN 408:2011+A1 (2012).The test was performed four times, placing the loading heads on each of the four sides of the sample (Figure 1) to obtain four positional global MOE values (MOEA, MOEB, MOEC, MOED).On the basis of these values, the mean MOE values in edgewise direction (MOEedge, from MOEA and MOEC) and in flatwise direction (MOEflat from MOEB and MOED) were obtained.For this test, a linear displacement transducer with spring (AEP Transducers, Italy) was used situated on the lower part of the piece.The distance between supports (1800 mm) was the same for the tests in edgewise and flatwise direction, and so the length-to-depth ratio was 18 and 25,7, respectively.The MOE was calculated with Equation 1 (EN 408:2011+A1 2012) using the stress-strain curve in the loading area between 10 % and 40 % of the estimated ultimate bending strength.It was verified that the linear regression presented an R 2 value above 0,99 for all the samples.(1) Where MOE is the modulus of elasticity, L is the distance between supports, a is the distance between the loading heads, b and h are the width and the depth of the sample, w is the increase in deformation, F is the increase in force and G is the shear modulus.As allowed in EN 408:2011+A1 (2012), the shear effect was ignored taking a value G equal to infinity.
Test with other values of G were made in Equation 1 to analyse the influence of the shear effect on MOEedge and MOEflat.Firstly, 650 MPa was used as also permitted in EN 408:2011+A1 (2012).A value of G equal to the MOE divided by 16 was also considered (EN 338 2016).A value of G equal to the MOE divided by 17 was then used, as proposed by Brancheriau et al. (2002).Finally, a value of G was calculated to make both MOE values (MOEedge and MOEflat) equal.These three values of G were obtained by iterative calculation.
The samples were also subjected to a destructive four-point bending test in edgewise direction to determine the MOR in accordance with EN 408:2011+A1 (2012).In this case, a different displacement transducer (Burster, Germany) was used situated on the mid-point of the side subjected to tension.The loading heads were always positioned on side A (Figure 1) until rupture to obtain the MORA.In this test, another global MOE value was also obtained (MOEAR).The MOEA and MOEAR values should be identical but may present slight differences as two different displacement transducers were used and the wood was repositioned between both bending tests (destructive and non-destructive).The MOEAR was used as reference to analyse MOE variability according to the side on which the test was performed.

Knottiness
Two different criteria were followed to measure knottiness (Appendix 1).In the first approach, the width of each knot was measured in the direction perpendicular to the length of the piece in accordance with Annex A of EN 1309-3 (2018).Two variables were obtained from this measurement, knottot when the sum of all the knots of the sample was included, and knot1/3 when only the knots situated in the central third of the sample were included.The second approach used (Figure 1) was based on the knot area ratio (KAR) that indicates the proportion of the complete cross-section occupied by knots (Walker 1993).The margin knot area ratio (MKAR), that indicates the proportion of the margin cross-section occupied by knots, was used to determine the influence of the position of the knots with respect to the direction of the load.The MKAR allowed variables of positional knottiness to be obtained.
The MKAR1/4 (BS 4978 2017) was measured, using as margin the outer quarter of the cross-section's width.The MKAR1/8 was also measured, using as margin the outer eighth of the cross-section's width.
The MKAR (Figure 1) were measured considering the direction of the bending test (edgewise or flatwise).In addition, it was also considered if the margin area was subjected to tension or compression.In this way, a total of 12 different MKAR-based measures of positional knottiness were obtained (Appendix 1).

Statistical analyses
The prediction was studied through simple linear regression (SLR) of the MOEAR and MORA on the basis of each of the 12 variables of knottiness (Appendix 1) and the four positional MOE (MOEA, MOEB, MOEC, and MOED).This first calculation allowed selection of the knottiness variables with the best predictive capacity.Attempts were then made to improve the predictive capacity of the SLR models using multiple linear regression (MLR) models of two variables.These models comprised a positional MOE and a knottiness variable.
The root-mean-square error (RMSE) was used instead of the coefficient of determination (R 2 ), commonly used in most previous studies, to assess the goodness-of-fit of the different models.This decision was adopted because it is more important to know the precision of the values generated by a model (RMSE) than to quantify the variability (R 2 ) of the predicted values (Alexander et al. 2015, Mansfield et al. 2007).Nonetheless, the R 2 value was also calculated to enable a comparison of the results obtained with those of other authors.
The models obtained from the whole dataset can be affected by overfitting because they are also fitted to the noise of the sample.For small datasets, the K-fold cross-validation can help avoid overfitting (Lever et al. 2016).In the present study, the 10-fold cross-validation method (Faydi et al. 2017, Hashim et al. 2016, Villasante et al. 2019) was used to calculate the RMSE of each model.The samples were randomly split into 10 groups of folds, using each group to validate the model generated with the remaining 9.This procedure was repeated 5 times to obtain 50 RMSE values for each model.
WEKA 3.6 software (Waikato University 2014) was used to carry out this process.For the purposes of comparison with other studies, the 10-fold cross-validation was not applied in the calculation of R 2 .
The non-parametric Kruskal-Wallis test was used to compare the RMSE values of each model.If statistically significant differences between the RMSE were found, a post hoc analysis was carried out using Dunn's test with Bonferroni adjustment.The Kruskal-Wallis test and post hoc analysis were performed with R 3.6.1 software (R Core Team 2019).In all cases, the level of significance was 0,05.

Results and discussion
MC, slope of grain, rate of growth and density of the samples are shown in Table 1.The differences in MC between samples were small.Pith was observed in just 12 % of samples.MOE, MOR and knottiness values observed in the samples are shown in Table 2.The mean MOE values obtained for the different sides ranged between 7600 and 7900 MPa.These values were slightly lower than those observed by other authors in scots pine (Pinus sylvestris L.) (Arriaga et al. 2012, Krzosek et al. 2021, Ranta-Maunus et al. 2011).This can be attributed to the fact that in the present study unclassified structural timber was used.
In the case of the MOR a mean value of 40,0 MPa was obtained, similar to that obtained in other studies with scots pine (Pinus sylvestris L.) in Spain (Arriaga et al. 2012, Villasante et al. 2019).As for knottiness, a mean KAR value of 0,24 was obtained with high coefficient of variation (CV) values.

Comparison of MOEflat and MOEedge
The MOEflat value was 2,6 % higher than the MOEedge value (Table 3).This difference can be attributed to the shear effect.When the deformation is measured over the entire length of the beam (global MOE), deformations due to shear are included in the total measured deformation (Boström 1999).In consequence, for both MOEflat and MOEedge, in reality an apparent value was obtained that underestimated the true MOE value.The shear effect increases as the length-to-depth ratio decreases (Timoshenko 1938), which explains how MOEflat was higher than MOEedge (length-to-depth ratio of 25,7 and 18, respectively).The shear effect is especially important in wood because the MOE/G ratio is particularly high in comparison with an isotropic elastic material (Brancheriau et al. 2002).These results coincide with those of Kim et al. (2010) who, in three pine species of Korea, also found that MOEflat was higher than MOEedge (between 1,3 % and 6,1 %).These authors used a length-to-depth ratio in flatwise direction between 23 % and 45 % higher than in edgewise direction.This length-todepth ratio value was similar to that of the present study (25,7 %), which explains the similar relationships between the MOE values.However, Boström (1994) and Steffen et al. (1997) obtained the opposite result in norway spruce (Picea abies (L.) H. Karst.), with MOEflat between 20 % and 40 % lower than MOEedge.This discrepancy can be put down to two reasons.Firstly, these authors used different spans for the different bending directions, and so the length-to-depth ratio in flatwise direction was up to 30 % lower than in edgewise direction.With this arrangement, the shear effect caused an increase in the underestimation of the MOE in flatwise direction.Secondly, these authors used a four-point bending test in edgewise direction and a three-point bending test in flatwise direction.Brancheriau et al. (2002) found that a three-point bending test underestimates by about 19 % the MOE value in relation to a four-point loading test.
The differences detected between MOEflat and MOEedge should be considered when the pieces are classified by bending tests in flatwise direction and are subsequently installed in the structure in edgewise direction.Currently, classification is commonly made on the basis of flatwise direction tests because less loading is required to deform the pieces, as is the case of continuous lumber testers.
The MOEedge and MOEflat results with the different tested G values are shown in Table 3.When the shear effect is ignored (G = ∞) higher differences between both MOE are found.The value of 650 MPa proposed in EN 408:2011+A1 (2012) decreased the differences, but does not seem to be an appropriate value as it is a generic value for any MOE value and any species of softwood.Lower differences between MOEedge and MOEflat were observed with a G equal to the MOE divided by 16 (EN 338 2016) and divided by 17 (Brancheriau et al. 2002).The differences between MOEedge and MOEflat disappeared for a G value equal to the MOE divided by 18,2.All indications are that the differences between the MOEedge and MOEflat values were due to shear effect differences caused by modifications to the length-to-depth ratio.In addition to this effect, other authors found that some features could influence in the relationship between MOEedge and MOEflat, such as knots and the slope of grain (Guindos and Ortiz 2013).To confirm the shear effect, it would be advisable to carry out tests with samples of other species and different length-to-depth ratios.

Selection of knottiness variables for MOE and MOR prediction
The predictive capacity of mechanical characteristics on the basis of knottiness variables is shown in As for the MORA, the lowest RMSE values were obtained with MKAR1/8AC.This shows that the knots situated in the tension and compressions margins are those which have the highest influence on rupture because this is where the highest bending stress values are found.
R 2 values obtained in the prediction of the MORA on the basis of knottiness variables were higher than those obtained in the MOEAR prediction (Table 4), which concurs with the observations of other authors in scots pine (Pinus sylvestris L.) (Conde García et al. 2007, Šilinskas et al. 2020) and in other pine species (Conde García et al. 2007, França et al. 2019, Wright et al. 2019).Only in one study was the opposite trend observed (Hautamäki et al. 2013, Hautamäki et al. 2014).

Linear regression to predict the MOE
Table 5 shows the predictive capacity of the MOEAR (reference MOE) obtained on the basis of the four positional MOE (MOEA, MOEB, MOEC, MOED).With respect to the differences between the four sides, MOEA was the best MOEAR predictor, which was expected as, although the sample was repositioned, the loading heads were positioned on the same side.MOEB and MOED, both carried out in flatwise direction, obtained the worst prediction result, almost doubling the RMSE obtained with MOEA.The explanation for this difference is that the test taken as reference (MOEAR) corresponds to the edgewise direction.
It was also observed that adding a knottiness variable to any of the positional MOE did not improve MOEAR prediction, and so the multivariable models offered no advantage.França et al. (2020)

Figure 1 :
Figure 1: Knottiness measures based on the KAR: (a) Cross-section, edgewise direction, (b) Crosssection, flatwise direction, (c) example of MKAR1/4, proportion of the margin cross-section (h/4) occupied by knots when the sample was tested in edgewise direction (loading heads on A), (d) RMSE calculated with the mean value of the 50 RMSE values (10-fold cross-validation, 5 repetitions); R 2 calculated with the whole dataset.Lowest RMSE values shown in bold.
in southern pine and Wright et al. (2019) in loblolly pine (Pinus taeda L.) also found that introducing a knottiness variable in an MLR together with the dynamic MOE did not improve the prediction of the static MOE.Table 5: RMSE of the linear regression to predict MOEAR.MOE in MPa, knot1/3, and knottot in mm RMSE calculated with the mean value of the 50 RMSE values (10-fold cross-validation, 5 repetitions) The same letter indicates there are no statistically significant differences (Kruskal-Wallis test, post hoc Dunn's test with Bonferroni adjustment) 1 RMSE increase with respect to the model with the lowest error

Table 1 :
Characteristics of the samples.

Table 2 :
Summary of the study variables.

Table 3 :
MOEflat and MOEedge according to different G values.

Table 4 .
In the MOEAR prediction, the lowest RMSE value was obtained with knot1/3 and knottot, the two knot variables based onEN 1309EN  -3 (2018)).These knot measures achieved better predictions than the local measures associated to KAR.The explanation for this is that the MOE values the global behaviour of the piece.The knot1/3 variable obtained the lowest RMSE value because the highest bending moment values in the four-point bending test are given in the central third of the piece.

Table 4 :
Simple linear regression based on knottiness to predict MOEAR and MORA.