Arboriculture & Urban Forestry 48(4): July 2022 study,” where, after a storm event, standing and failed trees are examined to discern patterns in measurable physical properties or geographic characteristics. Francis and Gillespie (1993) related wind-gust speed to tree damage, where the maximum-damage category was uprooting. They found their uprooting category to be independent of both DBH and gust speed, while stem breakage decreased with increas- ing diameter and was also independent of wind-gust speed (Francis and Gillespie 1993). Additionally, they concluded that large trees are at greater risk than small trees, which supports Reilly (1991). Peterson (2007) observed consistent influence of tree diameter and species on tree failure due to tor- nado blowdowns. He observed that windthrow occur- rence increased with tree diameter, and that uprooting was more common among trees of smaller size classes (Peterson 2007). Kane (2008) examined tree failure after a wind- storm in Brewster, MA. He too found that the likeli- hood of failure increased with trees of greater DBH and height. Yet, the different failure rates were not able to explain variation among species (Kane 2008). Furthermore, Kane (2008) states that the study did not factor in exposure, which is a known predictor of damage (Gardiner et al. 2008). Lastly, explanatory studies are limited in that they typically utilize parametric analyses, such as logistic or linear regression, and/or use R-squared as an indica- tor of predictive accuracy, thus leading to over-fitting (Kabir et al. 2018). Mechanistic Approaches The fundamental premises of tree biomechanics are: trees cannot violate the laws of physics, trees are mechanical objects, and tree size and shape are lim- ited by biomechanical constraints (Niklas 1992; Spatz and Brüchert 2000; de Langre 2008; James et al. 2014; James et al. 2018). Therefore, engineering and physical methods are reasonable methodologies to attempt to understand the structural properties of trees and how they interact with the environment (James et al. 2014). Dependent upon the line of action of a force, trees will experience stress in the forms of ten- sion, compression, and shear when subjected to bend- ing and torsion loading (Dahle et al. 2017). A tree’s material properties are factors which affect its load-bearing capacity (Dahle et al. 2017). The 2 most commonly reported material properties are the elasticity modulus (E) and the modulus of rupture 245 (MOR). These are used to describe a material’s stiff- ness and maximum load-bearing capacity, respec- tively (Burgert 2006; Dahle et al. 2017). Additionally, material properties can influence the mode of failure of a tree (Dahle et al. 2017). There is a large body of literature describing such wood properties (Kollmann and Côté 1968; Kollmann et al. 1975; Panshin and de Zeeuw 1980; Bodig and Jayne 1982; Haygreen and Bowyer 1982; Dahle et al. 2017). Despite this, the application of measured wood properties to living trees may not accurately estimate a given individual tree’s material properties due to the large variability of material properties of wood with age, growing conditions, genetics, moisture content, and location in an individual (Zobel and van Buijtenen 1989; Clair et al. 2003; Dahle and Grabosky 2010; Kretschmann 2010; Dahle et al. 2017). In addition, the values of E and MOR vary longi- tudinally, tangentially, and radially within an individ- ual tree, often decreasing axially with trunk height and/or branch length (Niklas 1992; Lundström et al. 2008; Dahle and Grabosky 2010; Kretschmann 2010; Dahle et al. 2017). Juvenile wood often has lower values of E and MOR than mature wood, and the pro- portion of juvenile wood to mature wood can influ- ence E and MOR (Lundström et al. 2008; Dahle and Grabosky 2010; Dahle et al. 2017). This generally allows for younger, more flexible, distal parts of the tree crown to reconfigure in the wind, and more mature, rigid, proximal tree parts, such as the stem, structural branches, and structural roots, to resist increased loading from self-weight and wind-induced bending and torsional moments (Niklas 2002; Clair et al. 2003; Lundström et al. 2008; Dahle and Grabosky 2010; Dahle et al. 2017). In an attempt to better represent these real-world loading schemes, researchers have utilized dynamic analysis methods. Three different approaches are commonly used to assess the dynamic behavior of trees (Clough and Penzien 1993; James et al. 2014; James et al. 2018). The first is the lumped-mass pro- cedure, where mass is assumed to be concentrated at a discrete point (James et al. 2014). The second uti- lizes generalized displacements for a uniformly dis- tributed mass, with the trunk treated as a beam (James et al. 2014). Lastly, the Finite Element Method (FEM) utilizes complex computer modeling (James et al. 2014). The lumped-mass procedure, which assumes the mass is concentrated at a discrete point as it oscillates ©2022 International Society of Arboriculture
July 2022
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