American Journal of Mechanical Engineering
ISSN (Print): 2328-4102 ISSN (Online): 2328-4110 Website: http://www.sciepub.com/journal/ajme Editor-in-chief: Kambiz Ebrahimi, Dr. SRINIVASA VENKATESHAPPA CHIKKOL
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American Journal of Mechanical Engineering. 2015, 3(2), 32-40
DOI: 10.12691/ajme-3-2-1
Open AccessArticle

Mechanical Stress Analysis of Tree Branches

Zahra Shahbazi1, , Allison Kaminski1 and Lance Evans2

1Manhattan College, Mechanical engineering department, Riverdale, NY, United States

2Manhattan College, Biology department, Riverdale, NY, United States

Pub. Date: March 24, 2015

Cite this paper:
Zahra Shahbazi, Allison Kaminski and Lance Evans. Mechanical Stress Analysis of Tree Branches. American Journal of Mechanical Engineering. 2015; 3(2):32-40. doi: 10.12691/ajme-3-2-1

Abstract

Various models have been developed to calculate stresses due to weight along tree branches. Most studies have assumed a uniform modulus of elasticity and others have assumed that branches are tapered cantilever beams orientated horizontally or at an angle. Astress model was evaluated in which branches are curved and that the modulus of elasticity may vary along the branch. For this model, the cross-sectional areasof branches were divided into concentric rings in which the modulus of elasticity may vary. Next, areas of rings were transformed according to their modulus of elasticity. Branches with curved shapes were also considered and best fit lines for branch diameters were developed. A generated diameter equation was used in the stress calculations to provide realistic results. From these equations, a Graphical User Interface (GUI) in Matlab, was developed to calculate stress within tree branches. Moreover, a Finite Element Model (FEM) was created in Abaqus to compare with the models.

Keywords:
stress analysis tree branches Finite Element

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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References:

[1]  Evans, L., Kahn-Jetter, Z., Torres, J., Martinez, M., and Tarsia, P., “Mechanical stresses of primary branches: a survey of 40 woody tree and shrub species,” Trees, Vol. 22, No. 3, 2008, pp. 283-289.
 
[2]  Sone, K., Noguchi, K., and Terashima, I., “Mechanical and ecophysiological significance of the form of a young acer rufinerve tree: vertical gradient in branch mechanical properties,” Tree Physiology, Vol. 26, No. 12, 2006, pp. 1549-1558.
 
[3]  Mencuccini, M., Grace, J., and Fioravanti, M.,“Biomechanical and hydraulic determinants of tree structures in Scots pine: anatomical characteristics,” Tree Physiol, Vol. 17, No. 2, 1997, pp. 105-113.
 
[4]  Beer, F. P., Johnston, R. E. Jr., DeWolf, J. T., and Mazurek, D. F., Mechanics of Materials, 6th ed., McGraw Hill, New York, 2012, Chaps. 2, 4, 5.
 
[5]  Almeras, T., Thibaut, A., andGril, J., “Effect of circumferential heterogeneity of wood maturation strain, modulus of elasticity and radial growth on the regulation of stem orientation in trees,” Vol. 19, No. 4, 2005, pp. 457-467.
 
[6]  Kaminski, A., Mysliwiec, S., Shahbazi, Z., and Evans, L., “Stress Analysis Along Tree Branches”, ASME 2014 International Mechanical Engineering Congress and exposition, 2014, Montreal, Canada.