Arboriculture & Urban Forestry 45(4): July 2019 the stress analysis made by Shahbazi et al. (2015) the difference between the maximum stress of elliptical and circular cross-section was not proved. The maximum stress can be usually found near to the branch base but the results shows that significance of elliptical shape to deflection is increasing in the middle part of branches (Figures 7 and 8). There was a high negative correlation within the tapering and the branch top response (R = -0.67). Kane and Farrell (2008) observed the taper to be insignificant to the breaking stress calculation with the comparison of aspect ratio significance, which could correspond to our results for the anchorage rotation. The results show a higher influence of the anchorage rotation at the branch base (R = 0.75) and a higher influence of tapering at the branch top (R = -0.67). The significance of material properties (E) is lower than that of geo- metrical parameters (Rmax = -0.29). The E at the branch base is more significant for the deflection than the other segments. The results showed that the deflection of points is more influenced by a change of E in the previous sections. CONCLUSION The shape of the deflection curve could be predicted by the numerical computations when precise geome- try is known. The significant deviation of the measured deflection curve at a certain point could be conse- quently considered as the indicator of defect, which can be used in branch stability assessment. Sensitivity analysis showed that the parameter’s diameter, ellip- tical shape, and tapering have a high impact on a branch deflection; simultaneously, the curvature and angle of attachment can be neglected within the analysis. If the precise branch geometry is known, the deflection curve may reflect the changes of material properties along the branch length. The branch mechanical response is very sensitive to the branch anchorage properties, which requires high accuracy of its detection during the measurement. The anchorage of a branch which is not full-fixed should be considered in future examina- tions. The results showed that the branch anchorage properties influenced the overall branch deflection, which requires more attention in the case of the branch stability assessment, and this corresponds with the conclusion of Kane (2008). The use of more sophis- ticated tools for the assessment of branch anchorage should be considered where optical techniques seem to be a promising new tool. LITERATURE CITED American National Standards Institute (ANSI). 2011. American National Standard for Tree Care Operations. Tree Risk Assess- ment a. Tree Structure Assessment. (A300, Part 9) Londonderry: Tree Care Industry Association. Brudi, E., and P. Van Wassenaer. 2001. Trees and Statics: Non- Destructive Failure Analysis. 1–17. Buza, A.K., and F. Divos. 2016. Root Stability Evaluation with Non-Destructive Techniques. ActaSilv Lign Hung 12(2):125–134. Cannell, M.G.R., and J. Morgan. 1987. Young’s modulus of sec- tions of living branches and tree trunks. Tree Physiology 3(4):355–364. Coutand, C., J. Mathias, and G. Jeronimidis. 2011. TWIG: A model to simulate the gravitropic response of a tree axis in the frame of elasticity and viscoelasticity, at intra-annual time scale. Journal of Theoretical Biology 273:115–129. Dahle, G.A., and J.C. Grabosky. 2010. Variation in modulus of elasticity (E) along Acer platanoides L. (Aceraceae) branches. Urban Forestry & Urban Greening 9(3):227–233. Detter, A. 2012. Handout for presentation at ISA Tree Biomechanics Research Symposium Chicago 2012. Accessed 05/20/2017. Dupuy, L.X., T. Fourcaud, P. Lac, and A. Stokes. 2007. A Generic 3D Finite Element Model of Tree Anchorage Integrating Soil Mechanics and Real Root System Architecture. American Journal of Botany 94(9):1506–1514. Ellison, M. 2005. Quantified Tress Risk Assessment Used in the Management of Amenity Trees. Journal of Arboriculture 31(2):57–65. Ennos, A.R., and A. Van Casteren. 2010. Transverse stresses and modes of failure in tree branches and other beams. Proc. R. Soc. B.. 277(1685):1253–1258. Evans, L.S., Z. Kahn-Jetter, J. Torres, M. Martinez, and P. Tarsia. 2008. Mechanical stresses of primary branches: a survey of 40 woody tree and shrub species. Trees 22(3):283–289. Fourcaud, T., F. Blaise, P. Lac, P. Castéra, and P. De Reffye. 2003. Numerical modelling of shape regulation and growth stresses in trees: II. Implementation in the AMAPpara software and simulation of tree growth. Trees - Structure and Function 17(1):31–39. Gilman, E.F. 2003. Branch-to-stem diameter ratio affects strength of attachment. Journal of Arboriculture 29(5):291–293. Gilman, E.F. 2015. Pruning Severity and Crown Position Influ- ence Aspect Ratio Change. Arboriculture & Urban Forestry 41(2):69–74. Gilman, E.F., J.W. Miesbauer, and F.J. Masters. 2015. Structural pruning effects on stem and trunk strain in wind. Arboricul- ture & Urban Forestry 41(1):3–10. Guillon, T., Y. Dumont, and T. Fourcaud. 2012. Conference paper: Simulation of tree branch motion. In: 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualiza- tion and Applications. Accessed 10/30/2015. Jungnikl, K., J. Goebbels, I. Burgert, and P. Fratzl. 2009. The role of material properties for the mechanical adaptation at branch junctions. Trees 23(3):605–610. ©2019 International Society of Arboriculture 129
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