Arboriculture & Urban Forestry 38(4): July 2012 Arboriculture & Urban Forestry 2012. 38(4): 141–145 141 Determining if Lateral Imbalance Exists in First-order Branches Leading to a Potential Development of Torsional Stress Gregory A. Dahle and Jason C. Grabosky Abstract. The management of urban trees requires an ability to appraise the stability of trees to select where and when a maintenance task is required to increase the functionally useful period of the tree. Torsion is often ignored during static bending trials and the goal of this study was to determine if first- order branches on open grown trees are laterally balanced. It is not known if lateral branch development leads to a parent branch that is evenly balanced. Second-order branch mass and center of gravity were measured and used to estimate the load acting on first-order branches. It appears that development can lead to imbalance in branches, because more than 60% of the first-order branches were imbalanced. Furthermore, 80% of the first-order branches in this specific study had more loading to the left side of the branch. Researchers should consider whether it is appropriate to ignore torsion when predicting how branches will behave during loading exercises. Additionally, the data suggests that it is possible to develop a strong predictive equation between branch length and the center of gravity (r2 = 95%) which, tied with predicted branch mass, could be useful when modeling self-loading and later balance in branches. Key Words. Biomechanics; Branches; Center of Gravity; Mass; Stress, Tilia cordata; Torsion. πr4 The management of urban and landscape trees requires an ability to appraise the stability of whole trees and tree parts for risks and value, and also to select where and when a maintenance task is required to increase the functionally useful service period of the tree or tree part. The normal stress formula (Formula 1) includes three load components: axial, bending, and shear stresses (Hib- beler 2005). This formula is utilized by engineers to determine the amount of stress at a given point on a structure whether under ev- eryday loading or to estimate the failure load for the structure. Por- tions of this formula, axial (Px /πr2 and Sydnor 1995; Dahle et al. 2006; Kane and Clouston 2008), yet the researchers did not include a shear stress (Tr/1.57r4 ) have been applied to branch and tree pulling exercises (Lilly ) com- ) and bending stress (Py ponent. Many of the biomechanical models and studies in the ar- boricultural arena utilize static loading of trunks and branches. These studies have applied a bending load which often includes an axial load by default (Lilly and Sydnor 1995; Clair et al. 2003; Dahle et al. 2006; Kane 2007; Kane et al. 2008a; Kane and Clous- ton 2008; Smiley 2008). The researchers often stated that tor- sion was not applied since they were pulling downward and not twisting the branch, therefore shear stress was likely negligible. While failures can occur during static external loadings, such as with the accumulation of snow or ice, many failures occur during a combination of static and dynamic events that add wind gusts, hurricanes, or tornados (James et al. 2006). During such events, not only do branches sway and bend but they twist as the lateral branches intercept the wind (James 2003; James et al. 2006). The shear stress component may be of interest to help fully understand how branches behave and fail during dynamic loading events. The normal stress equation for compression failures of a circular branch that is solid in cross section is as follows: LY/0.25 [1] Px r 2 P L( ) y 0.25 r 3 T 1.57r 3 r = radius at failure, σ = normal stress, and T = torque applied. Whether or not shear stress is induced during a failure testing where L = failure moment arm, Px = axial force, Py exercise of first-order branches (i.e., those arising from the central trunk), is a somewhat open question since they may develop in such a manner that they are relatively balanced in terms of torsion as a consequence of phyllotaxy (Harlow et al. 1991). As first-order branches grow over time, second-order (lateral) branches are pro- duced, and many of the lateral branches grow for a period of time and then die while others continue to grow. This natural pattern of growth and death might lead to a branch that has a relatively even distribution of torsion applied from lateral branches growing on either side (left or right) of a vertical plane along the branch’s lon- gitudinal axis. Yet it is not known if lateral branch development (and subsequent death) leads to a parent branch that is evenly bal- anced, or if it becomes unbalanced in torsion due to a torque cre- ated by self-loading. Understanding whether a preload exists may be important to the arboricultural community. The removal of lat- eral branches during pruning could change the existing balance or unbalance, leading to a substantial shift in the self-loading of a branch, which therefore could increase the likelihood of branch failure during either external static or dynamic loading events. The primary goal for this study was to determine if first- order branches on open grown trees are laterally balanced. As shear strain, stress, and modulus of rigidity were not measured in this study, the torsional rigidity or overall sta- bility of the branches cannot be addressed. This paper at- tempts to determine if more in-depth research is warrant- ed on the torsional development and stability of branches. ©2012 International Society of Arboriculture = bending force,
July 2012
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