Arboriculture & Urban Forestry 34(5): September 2008 313 considered branch angle a reliable predictor of breaking stress. The more complete list of morphologic variables and ratios con- sidered in the current study lends additional confidence that di- ameter ratio is the most reliable predictor of breaking stress for a range of species. It was also satisfying that this simple ratio was a better predictor of breaking stress than other ratios of branch and trunk size, because diameter ratio is easy to measure and calculate in the field. The ratio of branch diameter to width of the attachment reflects the diameter ratio, so it was not sur- prising that it was a similarly reliable predictor of breaking stress. Both diameter ratio and the ratio of inside-bark branch diam- eter to width of the attachment reliably predicted breaking stress because as the size of the branch increases relative to the size of the trunk, xylem of the branch and trunk do not grow in the overlapping fashion diagrammed by Shigo (1985; Figure 6). Consequently, the branch is only attached to the trunk by the branch fibers directly below the point of attachment parallel to the trunk. Kane and Clouston’s (2008) finding that codominant trunks were roughly one-half as strong as a single trunk supports this idea, as does Pfisterer’s (2003) suggestion that the sum of the cross-sectional area of the trunk and branch above the at- tachment were equal to the cross-sectional area of the trunk below the attachment. Despite its comparatively superior performance, however, di- ameter ratio still only predicted, on average, 57% of the observed variance in breaking stress for all species. This was similar to the coefficient of determination (0.56) reported by Gilman (2003) for the breaking stress of small red maple branches, but substan- tially greater than the value (0.19) reported by Kane (2007) for Bradford pears. Clearly, other variables affect the strength of branch attachments, but it does not appear that obvious external morphologic characteristics are among them. An internal factor that may be expected to predict breaking stress of an attachment is wood strength or modulus of rupture (MOR). Although MOR was not considered in the current study, a useful surrogate, specific gravity, was examined. Previous studies have demonstrated the effect of wood properties on like- lihood of tree failure (Putz et al. 1983; Jim and Liu 1997; Francis 2000), but specific gravity was not a reliable predictor of break- ing stress within a species in the current study. This was likely the result of the limited intraspecies range of specific gravity and the fact that the relationship between specific gravity and MOR has been established on clear, defect-free wood samples (Green et al. 1999), not branches. Specific gravity was, however, a significant and somewhat reliable predictor (R2 0.23, P < 0.01) of breaking stress when species were pooled together. This finding, however, contradicted Lilly and Sydnor (1995), who reported no effect of wood strength with respect to branch fail- ures of Norway (Acer platanoides L.) and silver (Acer saccha- rinum L.) maples, and Hauer et al. (1993) who found no effect of wood properties on the likelihood of tree failure after an ice storm. It was not easy to explain the paradoxic findings that although breaking stress was greater in the absence of included bark, the percent of area of the attachment covered by included bark was not a reliable predictor of breaking stress. Although he did not quantify the amount of included bark, Smiley (2003) reported that the presence of included bark was always revealed in the plane of failure and reduced the breaking force of codominant stems of red maple. Kane and Clouston (2008) also observed that ©2008 International Society of Arboriculture Table 2. Means (SEs in parentheses) for breaking stress and diameter ratio by type and form of attachment, failure mode, and the presence of included bark (IB)z. Type Red maple Trunk–branch 58 60.6 (2.10) a 0.47 (0.016) a U Branch–branch 8 38.5 (4.30) b 0.84 (0.030) b V Codominants 23 22.4 (2.23) c 0.86 (0.019) b Callery pear Trunk–branch 71 71.3 (2.43) au Branch–branch 6 45.9 (6.30) bu Codominants 29 32.1 (2.12) bu N Stress (MPa) Diameter ratioy Formx N Stress (MPa) Diameter ratio IB N Stress (MPa) Diameter ratio Modew N Stress (MPa) Diameter ratio 51 62.2 (2.26) a 0.45 (0.016) au 0.61 (0.015) a U 105 N/Av 0.90 (0.034) b V 0.89 (0.016) b 1 N/A Sawtooth oak Trunk–branch 59 104 (4.26) a 0.53 (0.018) au Branch–branch 10 55.0 (7.03) b 0.85 (0.045) bu Codominants 18 36.7 (2.82) b 0.87 (0.015) buv U V 71 52.5 (2.43) a 0.58 (0.025) a No 68 53.2 (2.47) a 0.58 (0.116) a BS 18 33.6 (5.24) b 0.68 (0.050) a Yes 21 34.1 (5.32) b 0.68 (0.106) a EB FS BS EB FS N/A N/A No 105 N/A Yes 1 N/A N/A N/A 56 100 (4.96) a 0.57 (0.022) a No 39 104 (5.15) a 0.56 (0.086) a BS 31 56.1 (5.38) b 0.76 (0.036) b Yes 48 68.49 (6.57) b 0.71 (0.098) b EB FS zWithin each species, read down the column; means followed by the same letter are not significantly different (P > 0.05) by Tukey’s honestly significant difference test. yInside-bark branch diameter/trunk diameter at the attachment. xForm refers to the presence (u-shaped) or absence (v-shaped) of a branch bark ridge. wBall and socket (BS), embedded bark (EB), and flat surface (FS). vTest was not conducted as a result of insufficient v-shaped attachments and attachments with included bark. uWelch’s analysis of variance was used because variance was nonhomogeneous among categories. tFor these comparisons, P < 0.10. 16 40.8 (3.65) b 0.72 (0.033) bu 22 23.3 (2.17) c 0.88 (0.016) cu 54 75.3 (2.87) a 0.57 (0.014) a 36 47.2 (2.65) b 0.82 (0.016) b 16 31.2 (3.36) c 0.91 (0.017) c 51 105 (4.56) a 0.57 (0.019) a 0.79 (0.038) bt 0.89 (0.014) bt 14 56.8 (5.63) bt 15 34.0 (3.45) bt
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