# Modelling tensile mechanical properties of oak timber
from fibre orientation scanning for strength grading
purpose

Guillaume Pot, Joffrey Viguier, Benoît Besseau, Jean-Denis Lanvin, Didier Reuling

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Guillaume Pot, Joffrey Viguier, Benoît Besseau, Jean-Denis Lanvin, Didier Reuling. Modelling tensile mechanical properties of oak timber from fibre orientation scanning for strength grading purpose. Hardwood conference, May 2024, Sopron, Hungary. hal-05336637

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# Modelling tensile mechanical properties of oak timber from fibre orientation scanning for strength grading purpose

POT Guillaume¹, VIGUIER Joffrey¹, BESSEAU Benoit², LANVIN Jean-Denis³, REULING Didier³

¹ Arts et Metiers Institute of Technology, LaboMaP, HESAM Université, F-71250 Cluny, France.

² Ducerf Groupe, Le Bourg, 71120 Vendenesse-lès-Charolles, France.

³ FCBA, Allée de Boutaut BP227, 33028 Bordeaux, France.

E-mail: guillaume.pot@ensam.eu; joffrey.viguier@ensam.eu; benoit.besseau@ducerf.com; jean-denis.lanvin@fcba.fr; didier.reuling@fcba.fr

**Keywords:** strength grading machine, slope of grain, grain angle

## ABSTRACT

Structural sawn timber must be graded to guarantee its mechanical characteristics in accordance with the European standards (EN 14081 parts 1-4). While these standards allow the strength grading of oak sawn timber, the technique typically used - visual grading by operators - is insufficient in producing viable material yields. As such, it remains a significant cause of material yield loss for oak timber. The objective of the present study is to assess the performance of a grading method based on fibre orientation scanning on a large sample of oak, fully representative of the French forest resource and the various cross-sections used in the industry. For this purpose, over 900 oak sawn timber boards were tested under tensile stress. A new method of interpolation of the measurement of fibre orientation on boards surface has been proposed and the mechanical model based on it allowed for predicting tensile strength with a coefficient of determination R²=0.49. This prediction level is sufficient to highly improve the grading yields compared to visual grading, and thus allow the usage of a strength grading machine for oak timber.

## INTRODUCTION

In Europe, the timber construction market is dominated by softwoods, and this is also true in France, where production of softwood structural timber is well below demand. In terms of surface area, the French forest is made up of almost 75 % hardwoods, and oak in particular accounts for almost 25% of the surface area of the French forest. There is no problem finding outlets for the best quality oak, which is used in the cooperage and furniture industries. On the other hand, oak of secondary quality, with a high flexuosity, a small diameter and generally too many knots are only used as firewood. Consequently, the main objective of this work is to propose a means of grading that will enable this secondary-grade oak resource to be used for structural purposes.

To be used as structural member, sawn timber must be graded to guarantee its mechanical characteristics in accordance with the European standard EN 14081-1 (2016). While this standard allows the strength grading of oak sawn timber, the technique typically used - visual grading by operators - is insufficient in producing viable material yields (Lanvin and Reuling 2012). As such, it remains a significant cause of material yield loss for oak timber. In Europe, despite that the current standard EN 14081-2 (2018) permit it, no approved machine for grading oak exists yet.

Fibre orientation measurement is a technique included in many industrial scanning machines. It consists in lines of laser dots projected at each board surface from which the fibre orientation is extracted thanks to the scattering of the light of the laser dot in fibres direction (phenomenon called the tracheid effect). Several publications have demonstrated the potential of using fibre orientation scanning in models to predict mechanical properties, in particular for softwoods (Olsson et al. 2013; Viguier et al. 2015; Viguier et al. 2017). Faydi (2017) and Olsson et al. (2018) dealt with the case of small cross-section sawn oak with good success, but on a reduced number of samples and under bending loading only. Rais et al. (2021) used the same measurement to predict the mechanical properties of beech in tension and Briggert et al. (2020) for Norway spruce.

The objective of this study is to propose and assess the performance of a method based on laser light scattering and mechanical modelling to predict the tensile mechanical properties of second quality oak sawn boards. It is aimed to enable to certify strength grading machines based in this principle.
# MATERIALS AND METHODS

## Sampling

Sampling was conducted following the guidelines of standard EN 14081-2 (2018). This standard requires obtaining the settings of a new grading machine from a sample of at least 900 boards, divided into four sub-samples. The sample must also include boards that are representative of the range of sizes, quality, and surface finish to be graded in actual production.

A total of 89 trees were selected for sampling from four different geographic regions: Bourgogne, Auvergne, Franche-Comté and Rhône-Alpes. All selected trees met either quality class C (approximately 45 %) or D (approximately 55 %) according to standard EN 1316-1 (2012), which can be described as secondary quality wood. A total of 924 oak boards were sampled, divided into eight different sections. The boards were planed in a factory to thicknesses varying from 21 to 35 mm and depth varying from 70 to 140 mm. The lengths were chosen according to the cross-section in order to be able to carry out the destructive tensile test according to EN 408+A1 (2012) and EN 384+A2 (2022) standards. In particular, the free test length should include the weakest assumed cross-section, i.e. the expected failure position, this is why the initial length of the boards was chosen to be greater than the required length to facilitate the positioning of the weakest section between the grips. Table 1 shows the distribution of the different boards by section and region of origin, the length between the grips used for different cross-sections and the initial length of the board.

<table><caption>Table 1: Number by region, length and distance between grips for each board cross-section</caption><thead><tr><th></th><th>70x21<br>[mm²]</th><th>85x21<br>[mm²]</th><th>105x21<br>[mm²]</th><th>140x21<br>[mm²]</th><th>105x28<br>[mm²]</th><th>105x35<br>[mm²]</th><th>140x28<br>[mm²]</th><th>140x35<br>[mm²]</th><th>Total</th></tr></thead><tbody><tr><td>Bourgogne</td><td>31</td><td>40</td><td>53</td><td>19</td><td>33</td><td>17</td><td>25</td><td>18</td><td>236</td></tr><tr><td>Auvergne</td><td>0</td><td>33</td><td>118</td><td>75</td><td>32</td><td>0</td><td>19</td><td>5</td><td>282</td></tr><tr><td>Franche-Comté</td><td>69</td><td>50</td><td>30</td><td>17</td><td>0</td><td>0</td><td>5</td><td>0</td><td>171</td></tr><tr><td>Rhône-Alpes</td><td>17</td><td>48</td><td>10</td><td>27</td><td>38</td><td>48</td><td>20</td><td>27</td><td>235</td></tr><tr><td>Total</td><td>117</td><td>171</td><td>211</td><td>138</td><td>103</td><td>65</td><td>68</td><td>50</td><td>924</td></tr><tr><td>Average length [m]</td><td>2.2</td><td>2.7</td><td>3.1</td><td>3.7</td><td>3.3</td><td>3.2</td><td>3.7</td><td>3.7</td><td></td></tr><tr><td>Distance between<br>grips [m]</td><td>0.63</td><td>0.76</td><td>0.95</td><td>1.26</td><td>0.95</td><td>0.95</td><td>1.26</td><td>1.26</td><td></td></tr></tbody></table>

## Physical and mechanical properties measurements

Clear wood density of each board was, in accordance with EN 408+A1 (2012), determined using a specimen free of knots cut out as near as possible to the fracture zone. These specimens were also used to determine the moisture content in accordance with EN 13183-1 (2002), by oven-drying. The density, $\rho$ was then, in accordance with EN 384+A2 (2022) adjusted regarding its moisture content following Eq. 1.

$$ \rho_{12\%} = \rho(1 - 0.005(u - u_{ref})) \qquad (1) $$

Where $u$ is the moisture content of the board and $u_{ref}$ taken equal to 12%.

The tensile strength and modulus of elasticity (MoE) of each board has been determined by a destructive tensile test. The tests were carried out to obtain a free test length of at least nine times the largest dimension of the cross-section, as required by EN 408+A1 standard (2012), with the weakest possible zone between the grips, as stated in EN 384+A2 (2022).

The tensile strength of each board $f_{t,0}$ was calculated using Eq. 2.

$$ f_{t,0} = \frac{F_{max}}{b \times h} \qquad (2) $$

where $F_{max}$ is the maximum applied tensile force, and $b$ and $h$ are the smaller and the larger cross-section dimensions, respectively. Because of the size effects existing in wood material, the tensile strength was corrected from the effect of the depth $h$ by using Eq. 3:

$$ f_{t,0,h} = \frac{f_{t,0}}{k_h} \qquad (3) $$
Where $k_h$ is calculated according to Eq. 4:

$$k_h = \begin{cases} \min\left\{\left(\frac{150}{h}\right)^{0.2}, \frac{1.3}{1} \right. & \text{if } h < 150 \text{ mm} \\ 1 & \text{if } h \ge 150 \text{ mm} \end{cases} \quad (4)$$

Eq. 3 and Eq. 4 are proposed in EN 384+A2 (2022) standard, and apply if the characteristic density is lower than or equal to 700 kg/m³, which is the case in the present work, therefore these equations was applied to every board. As a result, the experimentally determined tensile strength was reduced for boards with a width smaller than 150 mm and not adjusted if larger than 150 mm. The tensile MOE $E_{t,0}$ was calculated by using Eq. 5.

$$E_{t,0} = \frac{l_1 (F_2 - F_1)}{b \times h (w_2 - w_1)} \quad (5)$$

Where $F_2 - F_1$ is an increment of load on the straight-line portion of the load deformation curve, and $w_2 - w_1$ the increment of deformation corresponding to this increment of load. The deformation are measured over a length of 5h (noted $l_1$ in Eq. 5) using an extensometer. Finally, $E_{t,0}$ is adjusted in accordance with EN 384+A2 (2022) using Eq. 6.

$$E_{t,0,12\%} = E_{t,0} (1 + 0.01(u - u_{ref})) \quad (6)$$

## Non-destructive measurements

An industrial scanner was used to analyze the boards. By conveying the boards longitudinally, this scanner provides different images of the four long faces of the boards, as well as local density and local orientation of the fibers. The principle of board scanning is presented in Figure 1 and thoroughly described in a dataper dealing with Douglas-fir (Longuetaud et al. 2022).

<figure><img src="image_2.png" /><figcaption>Figure 1: Illustration of board scanning with side view on the top of the figure, and top view on the bottom of the figure, corresponding to left and top faces of the board, respectively. In the detail view, dashed lines represent a line of pixels which is recorded by the cameras while the board is conveyed longitudinally, and the greyed area with dotted line contour represents the region of interest used in the camera to treat ellipses information. From (Longuetaud et al. 2022)</figcaption></figure>
In the present study, only the fibre orientation measurement has been used and will therefore be described more in detail. To determine the orientation of the fibres on the surface of the boards, the tracheid effect was utilised, as described by (Nyström 2003; Simonaho et al. 2004). This method takes advantage of the anisotropic light-scattering properties of wood. When a laser point is directed at the surface of the wood, the light observed resembles the shape of an ellipse. The ellipse's major axis aligns with the wood's fiber direction, specifically its projection onto the board's surface. Laser points diffracted from a single point are projected onto each face of the board, spaced approximately 4 mm apart. The image within the region of interest containing the elliptic pattern, as shown in detailed view in figure 1, is binarized to detect the contours of the ellipses. The contours of each binarized ellipse is then approximated using an ellipse equation, with parameters optimised in the least squares sense.

At this stage, the fibres orientation is only known in the plane of the face on which the elliptical laser scattering images were recorded. Recent work has proposed various models and estimates of fibre orientation within a sawn timber based on observable data on its external surfaces. In their grading models for mechanical strength, Olsson et al. (2013) and Olsson et al. (2018) assigned to discretized parts of board volume the fiber orientation values measured on the faces. To model the fiber orientation of a sawn timber, Lukacevic et al. (2019) used a scanner to determine the position and size of the knots to use them as input data for a model based on the Rankine-Foley model (Foley 2003). Therefore, they did not use fibre orientation measurements as a starting point. Rais et al. (2021) proceeded by interpolating the plane angles measured on the faces and edges and then calculating the angle in space using the product of the angles in each of the two planes.

In the present study, a different method is proposed, firstly described in (Besseau 2021). Figure 2 shows a wood volume element whose average fibre orientation is represented by the vector $\vec{u}_{Fiber}$. The projection of this vector in the plane $(\vec{x}, \vec{y})$ is denoted $\vec{u}_{xy}$ and that in the plane $(\vec{x}, \vec{z})$ is denoted $\vec{v}_{xz}$. The angles formed by these vectors and the board main direction $\vec{x}$ are denoted $\alpha_{xy}$ and $\beta_{xz}$, respectively. They correspond to the angles that can be measured at the surface of the boards by a scanner. The orientation in space of a fibre element is given by the angle $\gamma_{xyz}$ between $\vec{u}_{Fiber}$ and the normal vector $\vec{n}$, here conflated with the direction $\vec{x}$.

<figure><img src="image_3.png" /><figcaption>Figure 2: Definition of fibre orientation within a wood volume. From (Besseau 2021)</figcaption></figure>

Following this representation, the lengths b and c can be expressed using Eq. 7 and Eq. 8:

$$b = a \times \tan(\alpha_{xy}) \qquad (7)$$

$$c = a \times \tan(\beta_{xz}) \qquad (8)$$

and $\gamma_{xyz}$ can be calculated using Eq. 9, Eq.10 and Eq. 11.
$$ \vec{u}_{Fibre} \cdot \vec{x} = \|\vec{u}_{Fibre}\| \cdot \|\vec{x}\| \cdot \cos(\gamma_{xyz}) \quad (9) $$

$$ \cos(\gamma_{xyz}) = \frac{\vec{u}_{Fibre} \cdot \vec{x}}{\|\vec{u}_{Fibre}\| \cdot \|\vec{x}\|} = \frac{a}{\sqrt{a^2+b^2+c^2}} \quad (10) $$

$$ \gamma_{xyz} = \arccos\left(\frac{1}{\sqrt{1+\tan^2(\alpha_{xy})+\tan^2(\beta_{xz})}}\right) \quad (11) $$

Finally, the angle $\gamma_{xyz}$ can be expressed only as a function of the angles $\alpha_{xy}$ and $\beta_{xz}$, which are plane angles. However, the measurements of $\alpha_{xy}$ on the faces of the boards and $\beta_{xz}$ on the edges of the boards using tracheid effect described previously do not allow directly the calculation of $\gamma_{xyz}$ in the wood volume. In order to obtain the missing values, it was decided to discretise the board into a 1x1x1 mm³ cube and to perform a linear interpolation. Thus, $\alpha_{xy}$ is obtained by linear interpolation in the thickness of the boards from measurements taken on both sides of the boards and similarly $\beta_{xz}$ is obtained by linear interpolation in the width of the boards.

## Mechanical modelling and IPs calculation

Clear wood should be considered as an orthotropic material in a LTR-coordinate system where L is the longitudinal direction of the fibres, T the tangential direction, and R is the radial direction. In this study clear wood has been considered to have a transverse isotropic behaviour, in which tangential and radial properties are the same since no data were available to differentiate and locate T- and R- directions. As a result, the compliance matrix [S] of clear wood is presented in Eq 12.

$$ [S] = \begin{bmatrix} \frac{1}{E_0} & -\frac{\nu_{TRL}}{E_{90}} & 0 \\ -\frac{\nu_{LTR}}{E_0} & \frac{1}{E_{90}} & 0 \\ 0 & 0 & \frac{1}{G_{LTR}} \end{bmatrix} \quad (12) $$

Young's modulus in the fiber direction (and corresponding to $E_0$ in Eq. 6) has been chosen equal to 14,620 MPa, in accordance with experimental tensile tests. $E_{90}$, the modulus of elasticity in the direction orthogonal to the local fibre direction in this transverse isotropic model was calculated as the average of the orthotropic ratios $E_T/E_L$ and $E_R/E_L$ from Kretschmann (2010). $G_{LTR}$ the shear modulus in the transverse isotropic plane was similarly calculated as the average of the orthotropic ratios $G_{LT}/E_L$ and $G_{LR}/E_L$ from Kretschmann (2010). Finally, $\nu_{LTR}$ the Poisson's ratio in the transverse isotropic model, was taken equal to the average of the orthotropic Poisson's ratios $\nu_{LT}$ and $\nu_{LR}$ from (Kretschmann 2010), which is 0.4. For each element of the grid of interpolated angles $\gamma_{xyz}$, the material compliance matrix [S] was rotated according to $\gamma_{xyz}$ by application of Eq. 13 to obtain the local compliance matrix in the specimen system of axes $(\vec{x},\vec{y},\vec{z})$ [S'] for each $(x, y, z)$ location.

$$ [S'] = [T_{\gamma}^{-1}] [S] [T_{\gamma}] = \begin{bmatrix} S'_{11} & S'_{12} & S'_{16} \\ S'_{12} & S'_{22} & S'_{26} \\ S'_{16} & S'_{26} & S'_{66} \end{bmatrix} \quad (13) $$

with $T_\gamma$ the transfer matrix, from the local fiber coordinate system to the global specimen coordinate system, dependent on the fiber orientation $\gamma_{xyz}$ obtained locally (abbreviated $\gamma$ in the following). $E_x$, the MoE in the main, lengthwise direction of the specimen $(\vec{x})$, is therefore calculated as the inverse of the first coefficient of the compliance matrix [S'] using Eq. 14.

$$ E_x(x, y, z) = \frac{1}{S'_{11}} = \frac{1}{\frac{1}{E_{90}}\sin^4(\gamma) + \frac{1}{E_0}\cos^4(\gamma) + \left(\frac{1}{G_{LTR}} - 2\frac{\nu_{LTR}}{E_0}\right)\sin^2(\gamma)\cos^2(\gamma)} \quad (14) $$
The average longitudinal boards stiffness can be calculated according to Beam Theory (BT) for each position x of the board by integrating over the surface of the cross-sectional area of the plank using Eq. 15.

$$E_{a,BT}(x) = \frac{\iint_{b \times h} E_x dy dz}{b \times h} \qquad (15)$$

The longitudinal displacement can be obtained using Eq. 16.

$$u_{x,l,BT}(x) = \int_{0}^{x} \frac{\sigma}{E_{a,BT}(\xi)} d\xi \qquad (16)$$

The calculation was performed by numerical integration with $d\xi = 1$ mm and $\sigma$ the input axial stress has been set arbitrarily to 1 MPa.

Finally, an "apparent MoE" was computed from these displacements. It can be seen as the MoE that would be observed if a mechanical test could be done within a short portion of the beam, of length $\delta$. Thus, this apparent axial MoE is calculated using Eq. 17. In this study this portion has been set to 90 mm as this length has been successfully applied on numerous previous study dealing with calculation of IPs for strength grading purpose (Olsson and Oscarsson 2017; Olsson et al. 2018; Briggert et al. 2020).

$$E_{a,app,90,BT}(x) = \sigma \frac{90}{u_{x,l,BT}(x+\frac{90}{2})-u_{x,l,BT}(x-\frac{90}{2})} \qquad (17)$$

Two different IPs were finally computed from this apparent MoE profile:

- the first one related to $f_{t,0,h}$ and noted $E_{a,app,90,BT,min}$ taken as the minimum of $E_{a,app,90,BT}(x)$ within the portion of the board which is between the grips in the tensile test. The assumption here is that the tensile strength is correlated to the minimum of the apparent MoE as suggested in several publications about strength grading of timber.

- the second one related to $E_{t,0,12\%}$ and noted $E_{a,l,BT}$ which is nothing more than a particular case of apparent MoE, calculated with computed displacement over the central area of the specimen over a distance of 5h. The calculation is described in Eq. 18.

$$E_{a,l,BT} = \sigma \frac{5h}{u_{x,l,BT}(x_{l,center} + 2.5h) - u_{x,l,BT}(x_{l,center} - 2.5h)} \qquad (18)$$

# RESULTS AND DISCUSSIONS

## Physical and mechanical properties measurements

In Table 2, some descriptive statistics of corrected tensile strength ($f_{t,0,h}$), corrected tensile MoE ($E_{t,0,12\%}$), corrected clear wood density ($\rho_{12\%}$), and moisture content (u) are presented. The average moisture content of the tested boards was 9.5 %, with minimum and maximum values of 7.4 % and 12.2 % respectively. Only 21 boards had a moisture content of less than 8 %, the minimum limit to apply moisture content correction defined in EN 384+A2 (2022). Nevertheless, the same correction of density and MoE stated in EN 384+A2 (2022) was applied considering the fact that they were very close to this limit. The mechanical properties can be found rather low but it has to be kept in mind that the boards were produced from only second quality oak (grade C or D as stated in the sampling part). Nevertheless, a non-negligible proportion of boards meets the requirements for structural use.

Figure 3 shows the distribution and relationship between $\rho_{12\%}$, $E_{t,0,12\%}$ and $f_{t,0,h}$. It appears that there is no correlation between density and tensile strength (coefficient of determination $R^2 = 0$) and only a small correlation between density and tensile MoE ($R^2 = 0.02$). This result can be surprising since for coniferous species, such relationships exists. Indeed, (Briggert et al. 2020) reported $R^2$ of 0.23 between density and tensile strength and 0.53 between density and tensile MoE for Norway spruce. However, the results are in accordance with previous finding on European oak in bending (Olsson et al. 2018), and on beech in tension (Rais et al. 2021). The presence of singularities such as rather large knots and their associated strong grain angle variation for oak are of higher influence on the mechanical properties than
the density. A R² of 0.42 is observed between $E_{t,0,12\%}$ and $f_{t,0,h}$ supporting the hypothesis that the stiffness of boards can somehow be related to its strength. In (Olsson et al. 2018) a R² between MoE and bending strength was found equal to 0.53.

<table><caption>Table 2: Descriptive statistics for physical and mechanical properties measured</caption><thead><tr><th></th><th>u [%]</th><th>ρ<sub>12%</sub><br>[kg/m3]</th><th>E<sub>t,0,12%</sub><br>[MPa]</th><th>f<sub>t,0,h</sub><br>[MPa]</th></tr></thead><tbody><tr><td>Mean</td><td>9.5</td><td>724.1</td><td>9,820</td><td>27.0</td></tr><tr><td>Std</td><td>0.7</td><td>65.4</td><td>2,780</td><td>14.4</td></tr><tr><td>Minimum</td><td>7.4</td><td>550.5</td><td>1,510</td><td>2.3</td></tr><tr><td>Maximum</td><td>12.2</td><td>964.5</td><td>18,210</td><td>79.7</td></tr><tr><td>5%<br>percentile</td><td>8.2</td><td>621.0</td><td>4,720</td><td>7.3</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Figure 3: Distribution and relationship between physical and mechanical properties measured</figcaption></figure>

## Mechanical behaviour prediction

Figure 4. shows the relationship between the computed IPs and their corresponding mechanical properties. The R² between $E_{a,l,BT}$ and $E_{t,0,12\%}$ is equal to 0.45 and the prediction gives slightly lower modulus of elasticity than the reality. The R² between the tensile strength $f_{t,0,h}$ and $E_{a,app,90,BT,min}$ appears to be higher, being equal to 0.49. Similar results were observed on Norway spruce by Briggert et al. (2020), with R² = 0.51 between $f_{t,0,h}$ and $E_{a,90,nom}$, an IP also obtained from fibre orientation data with a very similar modelling method (comparisons are made and discussed in (Pot et al. 2024)). Such level of R² is also consistent to what is obtained under bending loading, as a value of 0.56 was obtained in (Olsson et al. 2018) on a much smaller batch of boards comprising only one cross-section. The performance of the predictions can seem rather low compared to what can be obtained on coniferous species but would be sufficient for commercial grading of oak obtained from secondary quality logs.
<figure><img src="image_5.png" /><figcaption>**Figure 4:** Linear relationship between computed IPs based on grain angle measurement and beam theory modelling and their corresponding mechanical properties in tension</figcaption></figure>

## CONCLUSIONS

The results confirm results that was observed in bending, global density is not correlated to the MoE and the tensile strength. This was explained by the fact that knots and fibre distortion around knots in oak boards often affect the entire cross section, resulting in very low local stiffness and low strength. This is not captured by a measure of a global density of a board.

A new method of interpolation of the measurement of fibre orientation on boards surface has been proposed and IPs based on these data alone gives a rather good prediction of tensile strength and MoE with a coefficient of determination equal to 0.49 and 0.45, respectively. This performance is good enough for commercial grading of oaks board and should lead to higher yield than using visual grading. Improvement are expected through a better interpolation of the fibre orientation within the volume of the board and/or by improving the way wood is modelled.

This work could also contribute to the development of engineered wood products made of oak (Glulam of CLT). Applying these methodologies to the production of finger-jointed lamellas is already an ongoing work and gives satisfactory results (Soh Mbou et al. 2024).

Finally, the results presented show that mechanical properties of a large proportion of oak boards obtained from second quality logs can be suitable for structural use. In particular the data presented in this work can also contribute to the development of hardwood tensile classes, which is needed since the tensile classes in (EN 338 2016) currently exist for softwoods only.

## ACKNOWLEDGEMENTS

This work was supported by the French Environment and Energy Management Agency (ADEME) through the funding of the GRAINE 2019 TreCEffiQuaS project (convention 2003C006).

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