286 Kane: Branch Strength of Bradford Pear larger (based on absolute magnitude) of Ti or Ci by MOR. Thus, three stress ratios were calculated, one based on the elliptical cross-section dimensions measured inside bark [SRE(IB)], one based on the elliptical cross-section dimensions measured outside bark [SRE(OB)], and one based on the cir- cular cross-section calculations (SRC). Branch taper was calculated as described by Leiser and Kemper (1973): Taper =−R − rRL (7) where R is the radius of the branch at the point of failure, r is the radius of the branch at the loading point, and L is the distance between the loading point and the failure point. As- pect ratio was calculated as described by Eisner et al. (2002): aspect ratio = dD (8) where d is the diameter of the branch measured at the point of failure and D is the diameter of the trunk, or, if the branch failed at a lateral branch, the diameter of the lateral branch measured above the point of attachment of the branch to which the load was applied. Linear regression was used to investigate the effect of at- tachment angle, aspect ratio, and taper on BE(IB), BC, SRE(IB), and SRC. Linear regression was also used to inves- tigate the effect of GS, MOE, and MOR on BE(IB) and BC. Analysis of variance (ANOVA) was used to investigate whether BE, BC, SRE(IB), SRC, attachment angle, aspect ratio, taper, GS, MOE, and MOR differed by the type of failure (branch or attachment). ANOVA was also used to investigate the difference between BE(IB), BE(OB), and BC and between SRE(IB), SRE(OB), and SRC. Means were sepa- rated using Tukey’s highly significant difference test. A pre- liminary analysis indicated that there was no effect resulting from individual trees, so tree was not included as an inde- pendent variable. All analyses were conducted using SAS version 9.3 (SAS Institute, Cary, NC). To compare results for Bradford pear, values from previ- ous studies were converted to SI units where necessary. Be- cause MacDaniels (1923) did not calculate stress, his data were used to calculate stress values instead of the normalized force measurements that he presented. RESULTS Of the failures that occurred at an attachment, only one showed any included bark, and it did not constitute a sub- stantial portion (less than 5%) of the exposed surface area of the broken attachment. Its values for SRE(IB) and BE(IB) were slightly higher than, but within one standard deviation of, the mean SRE(IB) and BE(IB) for all attachment failures. Both BE(IB) and SRE(IB) were inversely proportional to aspect ratio, although the relationships were somewhat weak (Figures 2 and 3). Similar and slightly more robust relation- ships emerged for plots of BC and SRC against aspect ratio ©2007 International Society of Arboriculture Figure 3. Scatterplot and best fit line between stress () and aspect ratio (AR). Stress was calculated using inside bark branch depth and width [BE(IB) = 0.19, P = 0.0242). Figure 2. Scatterplot and best fit line between stress ratio (SR) and aspect ratio (AR). Stress ratio was calculated using inside bark branch depth and width [SRE(IB) ()] and outside bark branch diameter [SRC (s)]. Both fits are lin- ear; SRE(IB) = −0.2829 * AR + 0.9298; R2 SRC = −0.4347 * AR + 0.7266; R2 = 0.16, p = 0.04); = 0.20, p = 0.0227). (Figures 2 and 3). Neither the angle of attachment nor branch taper influenced BE(IB), BC, SRE(IB), or SRC (P values all greater than 0.20). None of the measured wood properties (GS, MOR, MOE) influenced BE(IB) or BC (P values all greater than 0.10). Mean values for BE(IB), BC, SRE(IB), SRC, aspect ratio, GS, MOR, MOE, angle of attachment, and taper were not different between branch and attachment failures (Table 2). Reanalyzing MacDaniels’ (1923) data produced a weak but significant positive relationship between breaking stress and angle of attachment (Figure 4). There was no relationship bark branch diameter [BC (s)]. Both relationships are linear; BE(IB) = −17541 * AR + 63,122 (R2 BC = −29430 * AR + 49,927 (R2 ()] and outside = 0.16, P = 0.04);
July 2007
| Title Name |
Pages |
Delete |
Url |
| Empty |
Search Text Block
Page #page_num
#doc_title
Hi $receivername|$receiveremail,
$sendername|$senderemail wrote these comments for you:
$message
$sendername|$senderemail would like for you to view the following digital edition.
Please click on the page below to be directed to the digital edition:
$thumbnail$pagenum
$link$pagenum
Your form submission was a success. You will be contacted by Washington Gas with follow-up information regarding your request.
This process might take longer please wait
