104 Table 2. Means (standard deviation) for tree morphometric data, stress (), bending moment (M), cable tension (P), and modulus of rupture of wood samples (MOR) for stem and codominant failures. Variable dbh (m) n Mean (SD) Stem failures Codominant failures Differencez n Mean (SD) P 11 0.57 (0.16) 13 0.69 (0.17) 0.1072 Tree height (m) 11 18.0 (5.72) 12 16.5 (4.98) 0.5303 Slenderness (height/dbh) 11 31.8 (7.62) 12 27.4 (12.4) 0.3227 Crown height (m) Crown width (m) Block height/tree height Stem volume (m3) P (kN) MFP MBH 9 14.6 (3.00) 7 16.1 (2.03) 0.2698 7 16.2 (3.87) 6 12.9 (4.66) 0.1955 11 0.53 (0.11) 12 0.56 (0.12) 0.5255 11 6.90 (4.79) 12 7.15 (2.88) 0.8843 11 18.0 (11.6) 13 13.9 (7.28) 0.2971 y (kN*m) 11 110 (103) 13 137 (87.1) 0.4989 y (kN*m) 11 278 (209) 13 216 (104) FP (kPa) BH (kPa) MOR (kPa) 11 51,193 (20,521) 13 25,230 (15,442) 0.0029 11 12,117 (5,816) 13 7,138 (3,897) 0.0280 10 62,596 (11,287) 11 71,214 (22,764) 0.3004 Distance to failure (m) 11 3.12 (1.55) 13 5.55 (2.15) 0.0041 Diameter at failure (m) 11 0.30 (0.15) 13 0.45 (0.18) 0.0433 Height of failure (m) 11 6.00 (2.15) 12 3.06 (3.09) 0.0044 Diameter at failure/dbh 11 0.53 (0.20) 13 0.67 (0.27) 0.1406 zP value refers to the probability that the given variable for both failure types is The subscript “FP” indicates that the measurement pertains to the point of failure; the subscript “BH” indicates that the measurement refers to breast height (1.4 m [4.6 ft] aboveground). SD standard deviation; dbh diameter at breast height. the same. y similar in size: there were no significant differences in tree height, slenderness, crown height and width, stem volume, or cable tension. There was weak evidence that dbh of stem failures was less than codominant failures. MOR of samples was similar for both types of failure. There were a few statistical differences between stem and codominant failures, however, and these were important (Table 2). They did not appear to be related to the experimental proce- dure because the ratio of block height to tree height was similar for both types of failure. Although stem and codominant failures experienced similar bending moments at the point of failure, stem failures required more than twice the stress of codominant failures. The distance to failure from the block was 2.4 m (7.9 ft) 0.3847 Kane and Clouston: Tree Pulling Tests of Large Shade Trees longer for codominant failures, which made diameter at the point of failure 0.14 m (0.5 ft) greater for codominant failures. Stem failures occurred twice as high in the crown as codominant fail- ures, and all but one stem failure occurred above the base of the crown. In contrast, two-thirds of codominant failures occurred at the base of the crown. For both failure types, stress at the point of failure was greater than stress at breast height, but the mean difference was more than twice as great for stem failures as codominant failures (Table 3). Stress at the point of failure was less than MOR of wood samples for codominant failures and there was some evi- dence that this was also true of stem failures, but the difference was not nearly as large. Bending moment at the point of failure was consistently less than at breast height regardless of the lo- cation of failure. Only diameter at breast height and diameter at breast height cubed produced statistically significant predictions of stress at the point of failure for all trees, but neither variable explained more than 17% of the variance of stress at the point of failure (Table 4). For stem failures, there was some evidence that stress at the point of failure was inversely proportional to crown width. Although there were no statistically significant predictors of stress at the point of failure when trees were separated by the type of failure, correlation coefficients were generally greater for stem failures than codominant failures (Table 4). When grouping all trees, bending moment at the point of failure was directly and linearly proportional to dbh, dbh cubed, and stem volume (Table 5). These relationships were the same when considering only stem failures, but not for codominant failures, which were independent of stem properties. Correlation coefficients were greater for regressions of bending moment at the point of failure than stress at the point of failure for all trees as well as when trees were separated by type of failure. The single tree that was pulled to ensure root failure required a bending moment at the root flare of 801 kN*m, somewhat greater than the largest bending moment of any other tree, which was 741 kN*m. Both of these trees were sugar maples, approxi- mately 85 cm (33 in) dbh. Stress at breast height was 12,690 kPa for the uprooted tree and 15,400 kPa for the other sugar maple; stress at the point of failure was 24,380 kPa for the other sugar maple. DISCUSSION Failure Type The lack of root failures in the current study does not agree with observations of failed trees after storms (Gibbs and Greig 1990; Duryea et al. 1996; Jim and Liu 1997), but root failures are likely the result of the presence of defects such as decay that compro- mised root systems before wind loading (Gibbs and Greig 1990; Jim and Liu 1997). For forest trees, stem failure was more likely Table 3. Mean difference (standard deviation) and P value between paired comparisons for each failure type. Paired comparison Stem failures n Mean (SD) Stress at failure point – stress at breast height* (kPa) Stress at failure point – MORy (kPa) MOR modulus of rupture. SD standard deviation. y ©2008 International Society of Arboriculture Bending moment at failure point – bending moment at breast height (kN*m) 11 zBreast height is 1.4 m (4.6 ft) aboveground. P 0.0008 13 Codominant failures n Mean (SD) −78.4 (63.7) P 11 39,076 (20,812) 0.0001 13 18,092 (14,125) 0.0006 10 −12,674 (19,862) 0.0744 11 −42,701 (28,839) 0.0006 −169 (119) 0.0008
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