Arboriculture & Urban Forestry 45(4): July 2019 stem and root-plate. In the case of branches, there is the assumption of fixed anchorage for mechanical analysis as well (King and Loucks 1978; Shahbazi et al. 2015). Although a significant influence of root- plate inclination to the branch is not expected, the material properties at the branch base shows high flexibility of branch anchorage (Jungnikl et al. 2009). On the contrary, Dahle and Grabosky (2010) found that the modulus of elasticity (MOE) decreases along the branch. They measured modulus of elasticity on the beams which were fully fixed, and the nearest point was 5 cm (1.9 in) from the branch base. The stress distribution along the primary branches seems to be similar to the distribution at the tapered cantilever beam, linearly increasing from the tip. The value of the maximum bending stress within a variety of species is relatively constant (Evans et al. 2008). The detailed branch stress analysis, built on the assumption of the tapered cantilever beam, showed that stress increased with branch length, non-tapered shape, curved shape, and with a higher change in modulus of elasticity in diameter. There was a negli- gible difference between a model with elliptical cross-section and a circular one (Shahbazi et al. 2015). Except the modulus of elasticity change along the diameter, the influence of change along the branch was not investigated (Dahle and Grabosky 2010). Kane (2007) experimentally found that the branch taper, location of failure, and specific gravity, modu- lus of rupture, and modulus of elasticity showed low significance for calculating breaking stress. The importance of aspect ratio (Gilman 2003; Kane 2007) and the effect of tree pruning on the strain distri- bution along branches have been discussed too (Gilman et al. 2015). The right pruning technique helps to keep the aspect ratio between branch and trunk small and reduces the risk caused by branch failure (Gilman 2015). According to Gilman (2003), the strength of branch attachment is correlated to the aspect ratio, while Kane and Farrell (2008) highlighted the fact that there is still a lack of strong correlation coeffi- cients for the prediction of branch failure. To understand the mechanical response of branches to loading, the traditional calculation of stress distri- bution could be supported by the deflection curve (King and Loucks 1978; Morgan and Cannell 1987). The advantage of a deflection curve is that it can be measured directly in contrast to the stress analysis. The branch deflection can be measured directly by the optical technique, which seems to be a prospective tool 121 for the measurement of branch/tree reaction to loading due to the obtaining of full-field data (Lundström et al. 2007; Sebera et al. 2014; Sebera et al. 2016). Addition- ally, the results from the optical technique are well comparable with the results of finite element (FE) analyses too. The FE analyses are widely used nowa- days for the description of branch growth and under- standing the influence of maturation strain (Fourcaud et al. 2003; Coutand et al. 2011; Guillon et al. 2012). The aim of this study is to find the significant param- eters that influence the branch deflection curve within the frame of relationship amongst the load, the material, and the branch geometry. The parameters studied are branch diameter and length, shape of cross-section, curvature, angle of attachment, anchorage rotation, and modulus of elasticity. The emphasis is put on finding a device supported tool for branch stability assessment by a combination of pulling test, optical measurement, and beam deflection theory. Moreover, numerical simulation using FE analyses will be employed to further investigate the mechanical behavior of branches. MATERIALS AND METHODS Trees and Site Four branches from four lime trees (Tilia cordata L.) were measured in April 2016. Trees were chosen from two locations in Brno–Cerna Pole, Czech Republic. Lime no. 1 (GPS: 49°12’28.6”N 16°37’18.2”E) was located in a park with compacted soil condition. Limes no. 2, 3, 4 (GPS: 49°12’36.2”N 16°37’01.5”E) were found in a street line with one site-limited root system. The purpose of the selection was to choose branches with different geometrical parameters to verify FE simulations. The branches differ in diame- ter, shape of cross-section (from circle to elliptical), tapering, and angle of attachment (Figure 1). The diameter of branches was measured in two perpendicular directions at each tracked point. The angle of attachment was measured by hypsometer Nikon Forestry Pro (sensitivity 0.01°), where the hor- izontal level with the ground was considered to be 0°. The branches of limes no. 1 and 4 have more ellipti- cal cross-sections, while branch no. 1 has a base diameter of 36 cm (14 in) and is significantly tapered at the base. Branches no. 2 and 3 are similar regarding the size and more circular cross-section, while branch no. 2 is more curved. Branches no. 3 and 4 are attached to the stem in a high angle to the stem (45°, 33°, respectively) (Table 1). ©2019 International Society of Arboriculture
July 2019
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