Young's modulus and shear modulus of solid wood measured by the flexural vibration test of specimens with large height/length ratios

The Young's modulus (modulus of elasticity, MOE) in the longitudinal (L) and radial (R) directions and the shear modulus (SM) in the LR plane of Douglas fir were determined by the flexural vibration (FV) tests under the free-free condition based on Timoshenko's vibration equation. In the tests, the height/length (H/L) ratio was varied from 0.05 to 0.3. In addition, the test data were analyzed numerically and the effectiveness of Timoshenko's equation was examined. The MOE and SM were calculated based on the rigorous and approximated solutions of Timoshenko's equation. The inaccuracy of the approximated solution was enhanced when the H/L ratio of the specimen was too large. In contrast, the rigorous solution enabled the accurate calculation of these moduli in a wider range of length/depth ratios than the approximated solution.