## 2 Materials and Methodology  
### Theoretical Investigations  
Initial investigations were conducted on predicting the bending stiffness of DCLT panels with different grain orientation angles and species. An analytical model was developed by applying [PERSON]'s formula in the shear analogy approach. [PERSON]'s formula (Equations (1) and (2)) was used to find the axial and shear stiffness values of the angle-ply inner layers, and the final panel stiffness (EI\({}_{\text{app}}\)) was found using the shear analogy approach (Equations (3)-(5)),  
\[E_{\alpha} =\frac{E_{0}\ \times E_{90}}{E_{0}\times\alpha\ +\ E_{90}\times\alpha} \tag{1}\] \[G_{\alpha} =\frac{G_{0}\ \times\ G_{90}}{G_{0}\times\alpha\ +\ G_{90}\times\alpha} \tag{2}\]  
where \(\alpha\) is the angle of the grain orientation of the main axis, E\({}_{\alpha}\) is the modulus of elasticity in the major strength direction of the diagonal layer, and E\({}_{0}\) and E\({}_{90}\) are the moduli of elasticity parallel and perpendicular to the grain. G\({}_{\alpha}\) is the shear modulus of the diagonal layer in the span direction, and G\({}_{0}\) and G\({}_{90}\) are the shear moduli parallel and perpendicular to the grain,  
\[EI_{eff}=\sum_{i=1}^{n}E_{i}\ \times b_{i}\ \times\frac{h_{i}^{3}}{12}+\sum_{i=1 }^{n}E_{i}\ \times A_{i}\ \times z_{i}^{2} \tag{3}\]  
where i is the individual layer of the panel, EI\({}_{\text{eff}}\) is the effective bending stiffness in the span direction, E\({}_{\text{i}}\) is the modulus of elasticity of the individual layer that can be E\({}_{0}\) for outer layers and E\({}_{\alpha}\) for inner layers, b\({}_{\text{i}}\) is the width of the effective cross-section, h\({}_{\text{i}}\) is the height of the individual layer, \(A_{i}\) is the area of the effective cross-section, and \(z_{i}\) is the distance of the neutral axis of the individual layer from the neutral axis of the panel,  
\[GA_{eff}=\frac{a^{2}}{\left[\left(\frac{h_{i}}{2\times G_{i}\times \mathrm{g}}\right)+\left(\sum_{i=2}^{n-1}\frac{h_{i}}{G_{i}\times k_{i}} \right)+\left(\frac{h_{i}}{2\times G_{n}\times b}\right)\right]} \tag{4}\]  
where, \(GA_{eff}\) is the effective shear stiffness in the span direction, a is the distance between the neutral axis of the outer layers, \(b_{i}\) is the width of the effective cross-section, \(h_{i}\) is the height of the individual layer, and \(G_{i}\) is the shear modulus of the individual layer that can be \(G_{0}\) for outer layers and \(G_{\alpha}\) for inner layers,  
\[EI_{app}=\frac{EI_{eff}}{1+\frac{K_{e}EI_{eff}}{GA_{eff}\times(l)^{2}}} \tag{5}\]  
where, \(EI_{app}\) is the apparent bending stiffness in the span direction including both bending and shear deformation, \(EI_{eff}\) is the effective bending stiffness in the span direction using the shear analogy method, \(GA_{eff}\) is the effective shear stiffness in the span direction using the shear analogy method, \(K_{s}\) is a factor based on the ratio of deflection due to bending to deflection due to shear (12.96 for four-point loading [13]), and \(1\) is the length of the span.  
Initially, lay-up alternatives for the hardwood and softwood species selection were assumed. Due to the higher rate of shrinkage/swelling of the hardwood species, black locust, the optimal lay-up was assumed to be a hybrid of both hardwood and softwood to increase the dimensional stability of the panels while still providing higher bending stiffness values. As Figure 3 shows, the stiffest hybrid lay-up was found to be the panel with hardwood in the outer layers and softwood in the inner layers.