Objective In order to assess the wind load safety of trees, the transverse force bending of trees under wind force was studied to determine the effect of factors such as trunk cross-sectional shape, tree ring, and defects on the neutral axis of trunk bending.
Method In this study, the Euler-Bernoulli beam assumption was used to deduce a generalized formula for the slope of neutral axis. Then, trunk models were designed with three types of contours (circle, ellipse, and random), two internal structures (multi-layer concentric structure and circular defects). And different moduli of elasticity were used to simulate variations in material properties. Finally, numerical simulations were performed, the results of numerical simulations were analyzed and predicted using the random forest model, and the relative contribution of each factor was identified.
Result In tree-ring models, the probability that the distance from mass center to form center of the tunk cross-section was less than 4 mm exceeded 97%, and the importance affecting the distance was ratio of the elasticity modulus of the early wood to the late wood > tree-ring number > ratio of the eccentricity distance to the basal circle radius > cross-section roundness. The deflection angles (from the actual neutral axis to the neutral axis of uniform section) were all less than 0.5°, and more than 97% of the total number was less than 0.08°. The importance affecting the slope angle of neutral axis in trunk bending was load azimuth > cross-section roundness > ratio of the eccentricity distance to the basal circle radius > tree-ring number > ratio of the elasticity modulus of the early wood to the late wood. In the circular defect model, there was about 80% of all cases where the distance from mass center to form center was less than 5 mm, about 15% of all cases between 5−15 mm, and about 5% of all cases greater than 15 mm. The importance affecting the distance was the defect radius > ratio of the elasticity modulus of the trunk with defects to the normal trunk > ratio of the eccentricity distance to the basal circle radius > cross-section roundness. More than 90% of all cases had a deflection angle less than 1°, but in some extreme cases, the deflection angle may reach 50°. The importance affecting the slope angle was load azimuth > cross-section roundness > ratio of the eccentricity distance to the basal circle radius > the defect radius > ratio of the elasticity modulus of the trunk with defects to the normal trunk.
Conclusion Tree-ring have a small effect on bending neutral axis of a tree trunk, while defects and cross-section shapes have a large effect on it. In the calculation and detection of trunk stress, the tree-ring can be ignored, but the cross-section shape and defects inside a trunk need to be taken into account.
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