## 1 Introduction
Over time, researchers have proposed modifications to the base formula [7]; however, recent studies have confirmed the validity of fit to the experimental data for the original formula. For instance, [PERSON] et al. [8] studied [PERSON]'s formula to determine its effectiveness in predicting shear moduli and strength based on grain orientation. The shear stiffness and strength results from the short-span bending tests on three-ply CLT and DCLT panels appeared to fit the data fairly well. Another study regarding the impact of grain orientation on the mechanical properties of DCLT was conducted by [PERSON] et al. [9]. They developed a 3D FEM DCLT model with four configurations having the same total thickness but different spans and the mid-layers of the panels orienting from 0\({}^{\circ}\) to 90\({}^{\circ}\) with an increment of 10\({}^{\circ}\). Their findings confirmed that the failure load and the deflection are functions of grain orientation. Their resultsstate that the effect on bending stiffness of rotating the grain orientation becomes more significant for DCLT panels with shorter span-to-depth ratios. This study continues the investigation on the effectiveness of orienting the inner layer of CLT products at another angle rather than the conventional 90\({}^{\circ}\) on the overall panel stiffness. This work focuses on the apparent bending stiffness of DCLT panels with various grain orientations in two asymmetric inner layers featuring a feasible lay-up for the future manufacturing of DCLT. In this study, three approaches were used: a theoretical approach, experimental testing, and FEM modeling. For this work, twelve four-ply DCLT \(\pm\alpha\) panels and one four-ply CLT panel were fabricated from a local hardwood species, black locust (_Robinia pseudoacacia_), for the parallel (0\({}^{\circ}\)) top and bottom layers, and a local softwood species, eastern white pine (_Pinus strobus_), was used for the two diagonal (\(\pm\alpha^{\circ}\)) inner layers. Before the experiment, an analytical model was developed using [PERSON]'s criterion with the shear analogy approach to predict the bending performance of each set of DCLT panels. The shear analogy method proposed by [PERSON] [10], and used in the US CLT Handbook [11], gives the composite bending and shear stiffness (E\({}_{\text{left}}\), GA\({}_{\text{eff}}\), and EI\({}_{\text{app}}\)) of the CLT panels using the values of the elastic and shear moduli parallel and perpendicular to the grain (E\({}_{0}\), E\({}_{90}\), G\({}_{90}\)) of the species in each layer [12]. The bending stiffness properties of the DCLT and CLT panels from this theory were then compared to the experimental results from the four-point bending test. The finite element analysis also simulated the four-point bending test, and the results were compared with the results of the shear analogy method and experimental tests. This study provides methods of predicting the bending stiffness of DCLT and CLT panels with the available or measured elastic modulus parallel to the grain of the species used in the panel fabrication. These methods of prediction could help utilize and introduce non-standard species for the fabrication of these products.