## 3 Results
### Mechanical Properties
#### 3.1.3 Modulus of Rupture
The interaction between the radial position and density was a significant factor in pine (\(p<0.01\)) but not in spruce. The RMSE values were lower in pine than in spruce. As in the case of the MOE, most of the random variation was on the stand level (69.0%) for spruce and on the residual level for pine (55.3%). Table 11 shows the fixed coefficients of the models for the MOR. The effect of density was positive for the MOR. The sole fixed coefficient of the dummy factor of the sapwood position was negative in pine. However, because of the observed positive interaction between sapwood and density, the density indicated an increase in the MOR, and the effect of density on sapwood was larger than on heartwood. In spruce, the top logs had a lower MOR than the butt logs or middle logs. The only significant effect of fire damage was observed in pine, where the burned wood had a lower MOR than the wood from the reference trees. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Norway Spruce**} & \multicolumn{4}{c}{**Scots Pine**} \\ \hline
**Source** & **F** & **df1** & **df2** & **Sig.** & **F** & **df1** & **df2** & **Sig.** \\ \hline Fire damage class & 0.981 & 2 & 120 & 0.378 & 3.593 & 2 & 118 & 0.031 \\ Height class & 4.478 & 2 & 120 & 0.013 & 0.649 & 2 & 118 & 0.525 \\ Radial position & 0.028 & 1 & 120 & 0.867 & 20.600 & 1 & 118 & \textless{}0.001 \\ Air-dry density & 18.419 & 1 & 120 & \textless{}0.001 & 81.054 & 1 & 118 & \textless{}0.001 \\ Radial position * air-dry density & 0.399 & 1 & 120 & 0.529 & 31.767 & 1 & 118 & \textless{}0.001 \\ \hline
**Random effect** & **Variance** & \multicolumn{4}{c}{**Variance**} \\ \hline Stand & 215.127 & \multicolumn{4}{c}{} & 53.704 & \multicolumn{4}{c}{} \\ Tree & 0.000 & \multicolumn{4}{c}{} & 22.311 & \multicolumn{4}{c}{} \\ Residual & 96.850 & \multicolumn{4}{c}{} & 94.116 & \multicolumn{4}{c}{} \\ \hline
**Fitting statistics** & \multicolumn{4}{c}{} \\ \hline R\({}^{2}\) & 42.8\% & \multicolumn{4}{c}{} 67.1\% \\ Bias & -5.76 & \multicolumn{4}{c}{} 0.86 (1.0\%) \\  & (-8.1\%) & \multicolumn{4}{c}{} \\ RMSE & 14.0 \multicolumn{4}{c}{} & 11.6 (13.3\%) \\  & (19.8\%) & \multicolumn{4}{c}{} \\ \hline \hline \end{tabular} \({}^{*}\) refers to interaction.  
\end{table} 
Table 10: Fixed effects in the linear mixed model (Equation (9)) for the modulus of rupture (MOR) and the variation in random effects. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Norway Spruce**} & \multicolumn{4}{c}{**Scots Pine**} \\ \hline
**Wood Material** & **Butt Log** & **Middle Log** & **Top Log** & **Butt Log** & **Middle Log** & **Top Log** \\ \hline Sapwood, heavily burned side & 74.3 (13.5) & 75.2 (11.8) & 62.4 (13.5) & 104.2 (19.6) & 81.2 (11.6) & 81.2 (9.8) \\ Sapwood, slightly burned side & 75.3 (12.3) & 77.1 (7.8) & 62.8 (7.5) & 108.3 (19.1) & 82.9 (11.8) & 81.9 (17.5) \\ Heartwood, burned trees & 51.7 (10.6) & 58.7 (9.3) & – & 84.4 (12.5) & 82.6 (9.0) & – \\ Sapwood, reference trees & 86.4 (16.9) & 77.2 (12.8) & 77.5 (14.8) & 92.8 (20.7) & 83.8 (18.7) & 71.8 (15.5) \\ Heartwood, reference trees & 77.3 (20.5) & 77.4 (12.8) & – & 67.2 (16.8) & 72.1 (13.9) & 67.3 (13.2) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Modulus of rupture (MOR) by species, damage class, radial position, and log type (MPa). Values are presented as means, with the standard deviation in parentheses.