# Effect of Dimensional Variables on the Behavior of Trees for Biomechanical Studies
## 4 Conclusions  
* The deflections' behavior showed that the linearity with height is valid up to the point of application of the horizontal load, but from that point onwards, it depends on the diameter and, in some cases, also on the loading level. * Since the model considers the geometric variations of the section (deflections and diameter variations), the stresses show smooth variations along the trunk. However, the maximum values positive and negative, in module, are not equal and can undergo sudden variations in position along the trunk when local maximum stresses become global maximums. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**C**} & \multicolumn{6}{c}{**Force of 5 kN**} & \multicolumn{6}{c}{**Force of 10 kN**} & \multicolumn{6}{c}{**Force of 15 kN**} \\ \cline{3-14}  & & \(\sigma_{-}\) & \(\sigma_{+}\) & \(\tau_{-}\) & \(\tau_{+}\) & \(\sigma^{-}\) & \(\sigma_{+}\) & \(\tau_{-}\) & \(\tau_{+}\) & \(\sigma^{-}\) & \(\sigma_{+}\) & \(\tau_{-}\) & \(\tau_{+}\) \\ \hline \multirow{4}{*}{1} & 1 & 7.8 & 7.7 & 3.9 & 3.8 & 2.6 & 2.5 & 3.7 & 4.3 & 1.9 & 2.2 & 1.2 & 1.4 \\  & 2 & 24.8 & 29.9 & 13.3 & 13.7 & 9.1 & 8.9 & 4.0 & 6.1 & 4.0 & 6.1 & 4.0 & 4.6 \\  & 3 & 12.5 & 28.2 & 12.4 & 28.2 & 10.3 & 27.1 & 2.6 & 2.0 & 2.6 & 2.0 & 2.6 & 2.0 \\  & 4 & 8.4 & 10.5 & 8.4 & 10.5 & 7.9 & 10.5 & 1.0 & 1.3 & 1.0 & 1.3 & 1.0 & 1.3 \\  & 5 & 6.1 & 8.4 & 6.1 & 8.4 & 5.9 & 8.4 & **0.9** & **0.9** & **0.9** & **0.9** & **0.9** \\ \hline \multirow{4}{*}{2} & 1 & 28.4 & 120 & 23.6 & 104 & 18.2 & 66.9 & 7.0 & 7.5 & 7.0 & 7.5 & 7.0 & 7.0 \\  & 2 & 31.8 & 56.6 & 16.1 & 26.2 & 10.8 & 17.1 & 7.0 & 7.5 & 7.0 & 7.5 & 4.9 & 6.7 \\  & 3 & 9.5 & 11.8 & 4.7 & 6.0 & 3.1 & 4.0 & 3.6 & 3.4 & 1.9 & 1.8 & 1.3 & 1.2 \\  & 4 & 4.8 & 4.5 & 2.4 & 2.2 & 1.6 & 1.5 & 2.0 & 2.3 & 1.0 & 1.1 & 0.7 & 0.8 \\  & 5 & 2.3 & 2.0 & 1.1 & 1.0 & **0.7** & **0.7** & **0.8** & **0.7** & **0.4** & **0.3** & **0.3** & **0.2** \\ \hline \multirow{4}{*}{3} & 1 & 21.5 & 35.3 & 11.6 & 15.3 & 7.8 & 9.8 & 6.3 & 6.6 & 4.6 & 4.2 & 3.0 & 2.8 \\  & 2 & 20.4 & 16.1 & 10.4 & 8.3 & 6.9 & 5.6 & 7.0 & 8.0 & 4.0 & 3.9 & 2.6 & 2.6 \\ \cline{1-1}  & 3 & 18.6 & 18.8 & 9.4 & 9.1 & 6.3 & 6.0 & 5.2 & 6.2 & 3.0 & 1.7 & 2.0 \\ \cline{1-1}  & 4 & 14.0 & 9.7 & 6.9 & 4.9 & 4.6 & 3.2 & 4.0 & 4.1 & 1.9 & 2.1 & 1.3 & 1.4 \\ \hline \hline \end{tabular} Scenario 1: slenderness 22; taper 0.030; and height conditions: 5 m, 10 m, 15 m, 20 m, and 25 m. Scenario 2: tree height 7.5 m; taper 0.030; and slenderness conditions: 8, 16, 24, 32, and 40. Scenario 3: tree height 7.5 m; slenderness 22; and taper conditions: 0.010, 0.020, 0.030, and 0.050.  
\end{table} 
Table 9: Safety factors (relationship between load capacity and acting load) of normal and shear stresses for three horizontal load levels, three scenarios, and conditions (C) in each scenario. **Author Contributions:** Conceptualization, R.G. and M.R. ; software, M.R. and W.V. ; formal analysis, R.G., M.R. and W.V. ; investigation, M.R. ; writing--original draft preparation, M.R. and R.G. ; writing--review and editing, R.G., M.R. and W.V. ; funding acquisition, R.G. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by National Council for Scientific and Technological Development (CNPq) grant number (426130/2018-9) and by Coordination of Improvement of Higher Level Personnel (CAPES) grant number (001) and the APC was funded by University of Campinas and by University of Santiago de Compostela (IOAP). **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data Repository, University of Campinas, [[https://doi.org/10.25824/redu/78](https://doi.org/10.25824/redu/78) XHCT]([https://doi.org/10.25824/redu/78](https://doi.org/10.25824/redu/78) XHCT), accessed on 20 February 2022.