Arboriculture & Urban Forestry 34(5): September 2008 309 Figure 1. V-shaped (left) and u-shaped branch attachments; the branch bark ridge is clearly present in the u-shaped at- tachment. Attachments were attached by chains and slip hooks to a uni- versal testing machine (MTS, Eden Prairie, MN) (133 kN [30,000 lbf] capacity) and loaded at a rate of 5.1 cm (2 in) per minute. The rate of loading was chosen primarily out of conve- nience to conduct the tests in a reasonable amount of time; it was faster than the rate at which ice or snow would accrete on branches but slower than the rate at which a wind load acts. Attachments were always placed so that the larger branch (or trunk) was closer to the bed of the machine during testing (Fig- ure 2). Bending stress () (MPa) was calculated in the branch cross-section as follows: = 32PLsind3 1 where P is the maximum load (kN), L is the distance (m) be- tween the point of application of the load and the attachment (measured parallel to the longitudinal axis of the branch), is the angle between the branch and the chain that secured it, and d is the inside-bark branch diameter (m). Figure 2 presents a free body diagram of the testing setup that illustrates the variables in Equation 1. The inside-bark branch diameter was measured im- mediately distal to the branch collar, both parallel and normal to the applied load. If the branch collar was not obvious, diameters were measured immediately distal to the branch bark ridge. Di- ameters did not vary by more than 10% for almost all branches and trunks, so they were averaged and that value was used as the diameter in Equation 1. Because the load was applied close to the attachment (within 5.1 cm [2 in]), shear stress was also calcu- lated for each attachment. The results for shear stress did not differ from the results for bending stress, so shear stress values have not been reported below. After breaking, a 2.5 cm (1 in) thick disk was taken from each branch to determine moisture content and specific gravity as described by Simpson and Ten- Wolde (1999). Before breaking, several morphologic characteristics and ra- tios that described the attachment were measured. Morphologic measures that described the branch attachment were grouped into the following three categories: angles between the branch and trunk, ratios of branch to trunk size, and dimensions of the attachment itself. All morphologic measurements are listed in Table 1, some are illustrated in Figure 3. The angle between intersecting lines parallel to the branch and the trunk was the branch angle. In some cases, however, the branch changed di- rection distal to the attachment, so attachment angle was also measured. This was the angle between intersecting lines parallel to the trunk and the branch at the point of attachment. For branches that did not change direction beyond the point of at- tachment, branch angle and attachment angle were equal. Diam- eter ratio was calculated as inside-bark branch diameter divided by the average of trunk diameters measured above and below the attachment. The length of the attachment was the distance from the intersection of the lines that determined attachment angle to the point on the trunk where it met the adaxial branch surface. Width of the attachment was measured as the straight-line dis- tance below the attachment between the terminations of the branch bark ridge. Length of the branch bark ridge was measured as the straight-line distance from one end of the branch bark ridge to the center of the adaxial surface of the branch where it met the trunk. Angle of the branch bark ridge was measured at the intersection between lines parallel to the trunk and the branch bark ridge. Failures were categorized as follows (see Figure 4): “flat sur- Figure 2. Image showing an attachment being pulled apart in the testing machine (left) and a free body diagram of the setup, where P is the applied load; RP is the reaction force; L is the distance from the point of applied load to the attach- ment, measured parallel to the longitudinal axis of the branch; and is the angle between the longitudinal axis of the branch and the applied load. face” failures occurred when the trunk split longitudinally in half where the branch was attached; “embedded branch” failures ap- peared superficially similar to flat surface failures, except that wood associated with the branch separated from the trunk, leav- ing an obvious groove in the trunk; “ball and socket” failures (after Shigo 1985) occurred when the branch simply pulled out from the trunk, leaving the trunk mostly undamaged below the branch attachment and a hollow where the branch had been attached. After failure, the surface area of both the attachment (i.e., the exposed area after failure) and the area of included bark (if present) were measured by applying a dot grid overlaid on a tracing of the areas. The percentage of attachment area covered by included bark was the ratio of the respective areas. A one-way analysis of variance (ANOVA) was used to deter- mine whether breaking stress and diameter ratio varied by the type and form of the attachment, the presence of included bark, and failure mode within each species. Because sample size was unequal in some comparisons, Levene’s test was used to test for homogeneity of variance within each comparison. For compari- ©2008 International Society of Arboriculture
September 2008
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