## 2 Materials and Methodology
### Finite Element Method  
In order to further understand the bending performance of DCLT panels and the experimental results of the four-point test on the specimens, a numerical finite element (FE) model was developed using the research version of ANSYS Workbench 2022 [19] finite element software. The panels were modeled using two different linear elastic orthotropic element types, one for black locust in the top and bottom layers, and one for eastern white pine in the cross layers. Nine independent elastic constants are required to define the mechanical response of an orthotropic material in the simulation. These constants are three elastic moduli (E), three Poisson's ratios (\(\
u\)), and three shear moduli (G). For the material property values input in the simulations, the longitudinal elastic moduli values (\(\mathrm{E_{L}}\)) for black locust and eastern white pine were obtained from the USDA Wood Handbook [20]. There are no available published values for the ratio of \(\mathrm{E_{T}}/\mathrm{E_{L}}\), \(\mathrm{E_{R}}/\mathrm{E_{L}}\), \(\mathrm{G_{TR}}/\mathrm{E_{L}}\), \(\mathrm{G_{LR}}/\mathrm{E_{L}}\), \(\mathrm{G_{TR}}/\mathrm{E_{L}}\) or the Poisson's ratios for the species used in this study. The USDA Wood Handbook [20] provides elastic ratios with respect to the longitudinal elastic modulus for some softwood and hardwood species. However, there are no available published values or elastic ratios for the constants of \(\mathrm{E_{R}}\), \(\mathrm{G_{TL}}\), and \(\mathrm{E_{T}}\) or the three required Poisson's ratios for eastern white pine. To predict these elastic constants using the available longitudinal (parallel to the grain) modulus of elasticity value, linear regressions (confidence level of 95%) were performed on each constant of the species in the USDA Wood Handbook [20] with available elastic ratios, regarding the longitudinal MoE as the predictor using Microsoft Excel [21]. The regressions showed R-squares ranging from 80% to 99% and a \(p\)-value less than the significance level (0.05) indicating a validation for prediction with a statistically significant correlation between the MoE and the response elastic constant [22]. Figure 7: Actual testing arrangement for DCLT bending specimens. The found ratios were repeated for another set of modeling considering the measured longitudinal MoE (from a simply supported bending test prior to panel fabrication) of black locust and eastern white pine boards as the longitudinal modulus of elasticity values. The final elastic constants for materials in FEM simulations are reported in Table 1.  
FEM ANSYS Workbench [19] simulations were performed under the \"Static Structural\" analysis system on one model of each DCLT \(\pm\) 10\({}^{\circ}\), DCLT \(\pm\) 20\({}^{\circ}\), DCLT \(\pm\) 40\({}^{\circ}\), DCLT \(\pm\) 70\({}^{\circ}\), and CLT specimens. The panels were modeled with the specifications for material, loading, and boundary conditions as shown in Figure 8 identical to the experimental four-point bending test to assure the accuracy of the comparison and validation. Mesh refinement as shown in Figure 9 was also performed under mechanical physics preference (program-controlled element order) by subdividing the mesh size to the rectangular elements with the size of 7 mm for each solid geometry. The mesh elements used for the sample specimens were higher order elements: SOLID186 element: 3D 20 nodes, TARGE170 3D target surface for the associated contact element of CONTA174: 3D 8 nodes surface-to-surface, and SURF154: 3D structural surface effect. Table 2 shows the details of the mesh sizing and the refinement quality of the model. For each set of simulations, three coordinate systems were defined regarding the parallel (0\({}^{\circ}\), global coordinate system) and two diagonal layers with \(\pm\alpha^{\circ}\) rotation of the main axis direction (x-y). The simulation's details and the details of different coordinate systems designed in the modeling are shown in Figure 10. After each simulation, load