# Effect of Dimensional Variables on the Behavior of Trees for Biomechanical Studies
## 3 Results and Discussion
### Deflection
#### 3.1.2 Behavior of Trunk Deflection with Tree Height  
The deflection calculated by the model (Tables 4-6) is complex because it involves root-plate and trunk deflection under the interactions of self-load, horizontal load (simulating wind), and moments (simulating the branches' effect). The trunk self-load only causes compression stress if the trunk is in a vertical position, but with the deflection of the trunk, this self-load will also have a horizontal component that will add bending. Moments representing branches also increase bending above the first bifurcation, and part of these moments are acting above the horizontal load position. Horizontal load causes bending of the trunk below this point, which is proposed as the center of gravity of the canopy. In a simplified way, until the break an increasing linear deflection with the height from the base to the top of the trunk is expected, but as the deflection is due to all load components in addition to the variation in dendrometric characteristics (conical trunk), this was not the behavior obtained for all scenarios. In scenario 1, only the smaller tree (\(H\) = 5 m) showed increasing deflection with the tree's height to the top (from 0%\(H\) to 100%\(H\)) (Figure 3). Independent of the load level, deflection values in scenario 1 for trees with a height of 10 m to 25 m show deflections at the top (\(dM\)) very similar (\(\geq\)95%) or even equal to those at the point of horizontal-load application (\(dL\)), maintaining the line practically constant for the section above the point of application of the horizontal load (Figure 3). For the smaller tree (\(H\) = 5 m), the differences between the deflection at the top and at the horizontal-load point increase as the load level increases (horizontal-load position 76.9% of the top position for 5 kN horizontal load, 72.7% for 10 kN horizontal load, and 67.7% for 15 kN horizontal load) (Tables 4-6). This behavior is probably related to the association of the magnitude of the top diameter and the concentration of moments arising from the branch effect. In taller trees, the diameters are greater than about 0.2 m (Table 1), and as the position of the first bifurcation is fixed at 2 m, the height of the canopy increases with increasing tree height, and thus increasing the distance from the points of the trees where moments are applied, reducing its concentration in the canopy. In scenario 2, the differences between the deflection in the horizontal-load position and the top position increase with increasing slender, and are influenced by the load level (Figure 4). For the first load level (5 kN), the only tree with 1 = 40 has the deflection growing from the base to the top. As the load level increased to 10 kN and 15 kN, this behavior started to be observed in the tree with 1 = 32 and 1 = 24, respectively (Figure 4). The slender is related to the height of the tree and the diameter at breast height, which is associated with the diameter of the top (conical trunk). In this scenario, the tree's height is fixed (7.5 m), so the distance of the moments from branches is also fixed. The most significant differences of deflection at the top and the horizontal load point came from top diameters less than 0.127 m (above slender = 24, Table 1). In scenario 3, as in scenario 2, the height of the tree is fixed (7.5 m); all conditions have the same moment concentrations, but the top diameter decreases as the taper increases, and as in the other two scenarios, more significant differences are obtained for the smaller top diameter. Up to 10 kN load level, the behavior is the same for all taper levels, keeping the deflection line practically straight for the section above the horizontal-load-application point (Figure 5). The behavior in scenario 3 started to change to load = 15 kN. Figure 4: Behavior variation of the slender versus tree height (m) for the scenario 2 (tree height 7.5 m; taper 0.030) and for the simulated horizontal forces (5 kN, 10 kN and 15 kN).