## 3 Results and Discussion
### DCLT's Bending Stiffness Comparison between the Methods  
Considering all the assessed methods in this study, Figure 14 shows the final apparent bending stiffness results of each method for comparison. All the methods confirmed that decreasing the angle of the grain orientation in the inner layers of the panels increases the bending stiffness. This is due to the fact that by decreasing the inner lamina grain orientation, these layers will no longer be stressed under shear perpendicular to the grain but parallel to the grain (which is higher than shear perpendicular to the grain), which means the specimen then shows a higher bending stiffness. As the plots indicate, the  
Figure 13: Load–deflection curves of DCLT \(\pm\)\(\alpha\) samples from FEM simulations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **EI\({}_{\text{App}}\)** \\ **(N-mm\({}^{2}\times 10^{11}\))** \\ \end{tabular} } & \multicolumn{4}{c}{**Grain Orientation**} \\ \cline{2-6}  & **10\({}^{\circ}\)** & **20\({}^{\circ}\)** & **40\({}^{\circ}\)** & **70\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline Handbook Values & 1.94 & 1.85 & 1.65 & 1.53 & 1.46 \\ \hline MoE of the Layers & 2.32 & 2.18 & 1.96 & 1.81 & 1.72 \\ \hline \% Increase to CLT & 33\% & 26\% & 13\% & 6\% & – \\ \hline \hline \end{tabular}
\end{table}
Table 5: Bending stiffness properties for different grain orientations obtained from FEM simulations.  
highest values for all the grain orientations of DCLT panels and the CLT panel are from the results of FEM modeling using the measured MoE of the boards. This FEM result is very similar to the experimental results from four-point bending tests due to higher and more accurate elastic constant values as (or for) the material properties input. An obvious observation is that using the measured MoE of the layers provides more accurate models than using the reference MoE from the Wood Handbook when used in either numerical or theoretical modeling. The results from the theory ([PERSON]'s formula in shear analogy) under-predict the apparent bending stiffness The results from these experiments show approximately 50% higher values of apparent bending stiffness compared to the theoretical values from the Hankinson/shear analogy approach with the published USDA Wood Handbook reference values, which makes this method of prediction a conservative model requiring further investigations to provide a more accurate analytical model.  
This study is also in agreement with the previous literature on DCLT's structural advantages compared to conventional CLT. The current study shows an increase of 14% for the apparent bending stiffness from CLT to DCLT \(\pm\) 40\({}^{\circ}\), which is very similar to results from four-point bending tests on DCLT \(\pm\) 45\({}^{\circ}\) panels conducted by [PERSON] et al. [4], which showed an increase of 15% in the EI\({}_{\text{app}}\) from CLT. However, the apparent bending stiffness increases from CLT to 30\({}^{\circ}\) (174%), 45\({}^{\circ}\) (112%), and 60\({}^{\circ}\) (61%) in [PERSON] et al. [5]'s study, which was conducted using a short-span three-point bending test, which appears to be significantly different from what might be concluded to be the testing fixture and its application for measuring the shear stiffness rather than bending stiffness.