Mechanical Stress Analysis of Tree Branches

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.

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