312 able predictor of breaking stress for red maple (Table 1). Branch diameter was a reliable predictor of breaking stress (average coefficient of determination for all species0.50), but this was an artifact of Equation 1 and thus not included in Table 1. The percentage of attachment area covered by included bark did not influence breaking stress for red maple and sawtooth oak, the two species for which there were sufficient attachments to test the effect of included bark (Figure 7). This finding contradicted the finding that red maple and sawtooth oak had significantly stronger attachments when included bark was not present (Table 2). It is important to point out the differences among species with respect to other predictors, aside from the two best. For example, length of the branch attachment and length of the branch bark ridge were somewhat reliable predictors of breaking stress for callery pear, but not for red maple or sawtooth oak (Table 2). Conversely, branch angle and branch bark ridge angle were somewhat reliable predictors of breaking stress for callery pear and sawtooth oak, but not for red maple. Attachment Type For all species, trunk–branch attachments were the most com- mon and the strongest (Table 2). Branch–branch attachments were the least common for all species; for red maple, they were stronger than codominants, but this was not true of callery pear and sawtooth oak (Table 2). For all species, diameter ratio was significantly smaller (i.e., the branch was comparatively smaller than the trunk) for trunk–branch attachments than for branch– branch and codominant attachments (Table 2). Attachment Form and Included Bark For red maple and sawtooth oak, u-shaped attachments were stronger than v-shaped attachments (Table 2). Diameter ratio was greater for v-shaped attachments of sawtooth oak, but this was not true of red maple (Table 2). Included bark was present in all of the v-shaped attachments on sawtooth oak and 17 of 18 Kane et al.: Strength of Branch Attachments v-shaped attachments on red maple. The presence of included bark was closely associated with form of the attachment in red maple (Table 2). This was not true of sawtooth oak; many u- shaped attachments also had included bark. Attachments with included bark were not as strong as those without included bark (Table 2). For sawtooth oak, diameter ratio was greater for at- tachments with included bark, but this was not true of red maple (Table 2). Failure Mode and Included Bark For all species, ball and socket failures required the greatest breaking stress, whereas flat surface failures required the least (Table 2). Breaking stress of embedded branch failures was about midway between that of the other modes of failure, but the comparisons were not as robust for callery pear and sawtooth oak (Table 2). Branch diameter averaged 45% of trunk diameter for ball and socket failures of red maple and 57% of trunk diameter for callery pear and sawtooth oak. These diameter ra- tios were smaller than for flat surface failures, the branch diam- eter of which was approximately 90% of trunk diameter for all species (Table 2). Diameter ratio of embedded branch failures was closer to that of flat surface failures, but still significantly different from the other modes of failure for all species (Table 2). When data from all species were pooled together, the mode of failure was clearly related to diameter ratio; an apparent thresh- old diameter ratio occurred at 0.70. At smaller diameter ratios, failures were almost exclusively ball and socket failures; when diameter ratio met or exceeded 0.70, however, failures were almost exclusively flat surface and embedded branch (Figure 8). DISCUSSION The results largely agree with previous studies that diameter ratio was negatively correlated to and a better predictor of break- ing stress than branch angle. Branch angle was also correlated with diameter ratio (R2 0.23, P < 0.01), which agrees with Miller’s (1959) explanation as to why MacDaniels (1923) had Figure 7. Scatterplots for the prediction of stress () from the percent of attachment area covered by included bark (area). Equations for best-fit lines were = −126 * area + 93.4 and = –71.1 * area + 50.3 for sawtooth oak (solid line, ) and red maple (dashed line, ). Intercepts were greater than 0 (P < 0.01), but slopes were not (P > 0.05). ©2008 International Society of Arboriculture
September 2008
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