Arboriculture & Urban Forestry 34(2): March 2008 105 Table 4. Predictions of stress at the point of failure from tree morphometric data and wood strength (MOR) for all trees, stem failures, and codominant failures. Variablez MOR (kPa) Tree height (m) dbh (m) Slenderness Crown height (m) Crown width (m) Stem volume (m3) (dbh)3 (m3) n Estimate (SE) All trees P −0.052 (0.250) 0.8369 RMSE/R2 n Estimate (SE) Stem failures P 0.71 (0.61) 0.2803 Codominant failures RMSE/R2 n Estimate (SE) P −0.04 (0.21) 0.8517 132 (975) 0.8954 RMSE/R2 By 21 42,214 (17,428) 0.0256 21,270/0.00 10 5,444 (38,969) 0.8923 20,780/0.14 10 31,337 (15,404) 0.0724 15,536/0.00 y B 24 42,050 (16,419) 0.0182 23,034/0.00 11 77,714 (21,133) 0.0051 19,827/0.16 12 22,006 (16,723) 0.2176 16,695/0.00 −288 (913) 0.7553 −52,155 (24,778) 0.0469 324 (454) 0.4828 −1,473 (1126) 0.2232 B 24 70,256 (16,289) 0.0003 20,581/0.17 11 86,741 (22,942) 0.0043 19,084/0.22 13 31,329 (19,047) 0.1282 16,347/0.01 −62,068 (38,776) 0.1439 −48.8 (890) 0.9575 −408 (2477) 0.8737 −8,879 (26,930) 0.7478 B 23 27,513 (14,226) 0.0667 22,813/0.02 11 52,749 (29,128) 0.1036 21,627/0.00 12 21,420 (11,718) 0.0975 16,655/0.01 100 (391) 0.8024 B 16 75,623 (34,499) 0.0458 22,849/0.08 9 55,667 (37,272) 0.1789 20,957/0.00 7 94,889 (68,880) 0.2268 19,376/0.18 −2,435 (2229) 0.2932 −2,435 (2229) 0.2932 −2,967 (1432) 0.0931 −4,385 (4,243) 0.3487 B 16 75,623 (34,499) 0.0458 22,849/0.08 7 90,734 (23,481) 0.0118 13,441/0.46 7 45,985 (29,390) 0.1927 21,372/0.11 −1,504 (2159) 0.5245 B 23 49,156 (9,816) 0.0001 22,092/0.08 11 64,497 (10,547) 0.0002 19,314/0.20 12 29,673 (13,276) 0.0494 16,547/0.02 −1,716 (1233) 0.1786 −37,601 (18,834) 0.0584 −1,927 (1274) 0.1646 zdbh diameter at breast height; slenderness tree height/dbh; stem volume tree height*(dbh)2 −58,430 (35,380) 0.1330 . −770 (1733) 0.6661 B 24 48,830 (7,232) 0.0001 20,799/0.15 11 64,419 (9,838) 0.0001 18,949/0.23 13 27,241 (8,411) 0.0079 16,368/0.01 −5,229 (18,409) 0.7817 yB, intercept and slope, respectively, of best fit line for the plot of stress at the point of failure and the variable listed in the first column. SE standard error; RMSE root mean square error. when roots were not decayed or restricted by soil conditions (Fraser 1962; Somerville 1979; Moore 2000; Peltola et al. 2000). Codominant stems were clearly a significant structural defect for large maples, which agreed with prior observations of fail- ures of multitrunk trees and branches (Gibbs and Greig 1990). More than half of the maples considered hazardous in Helsinki, Finland, were deemed hazardous by virtue of poor branch at- tachments, including codominant stems (Terho and Hallaksela 2005). A frequency analysis of the International Tree Failure Database (ITFD; data downloaded in March 2007 from http:// ftcweb.fs.fed.us/natfdb/) shows that 36% of 1627 trunk failures occurred when codominant stems were involved. Although it was not part of this investigation to determine the cause of weakness of codominant stems, two explanations offer some insight. One codominant failure was observed not to have bark occluded among the stems, unlike every other codominant failure. The failure stress for this tree was 74% greater than the next largest value for a codominant failure. Although our study supports the idea that the presence of occluded bark reduces tree strength, the influence of bark occlusions with respect to failure stress is not entirely clear in the literature. Smiley (2003) found that bark occlusions reduced the strength of the attachment among codominant branches of small red maples, but others suggested that the most reliable predictor of branch attachment Table 5. Predictions of bending moment at the point of failure from tree morphometric data and wood strength (MOR) for all trees, stem failures, and codominant failures. Variablez MOR (kPa) Tree height (m) dbh (m) Crown height (m) Crown width (m) Slenderness Stem volume (m3) dbh3 (m3) n Estimate (SE) By 21 y B 23 B24 B16 B 13 B 23 B 23 B 24 All failures P −0.0004 (0.0011) 0.7013 75.6 (70.2) 0.2936 97.2/0.02 11 2.65 (3.91) 0.5056 −53.2 (66.6) 0.4334 84.2/0.26 11 280 (101) 0.0113 −22.6 (141) 0.8751 90.5/0.06 9 8.82 (9.07) 0.3468 42.0 (90.8) 0.6527 87.8/0.09 7 6.27 (5.99) 0.3176 172 (60.1) 0.0092 96.4/0.04 11 −1.74 (1.92) 0.3753 26.5 (36.9) 0.4794 83.0/0.29 11 13.5 (4.63) 0.0085 56.9 (28.9) 0.0617 83.1/0.28 11 217 (75.1) 0.0084 169 (77.8) 0.0430 95.0/0.01 10 RMSE/R2 n Estimate (SE) 162 (207) Stem failures P −0.0007 (0.0033) 0.8386 14.5 (111) 5.29 (5.93) 0.3954 −156 (93.7) 0.1309 78.0/0.49 13 464 (158) 0.0169 −26.2 (204) 9.69 (13.5) 0.4973 −79.4 (190) 13.9 (11.6) 0.2831 263 (137) −4.81 (4.18) 0.2804 16.6 (46.4) 0.7288 84.9/0.39 12 13.5 (5.60) 0.0392 3.42 (36.1) 0.9266 69.5/0.59 13 470 (130) zdbh diameter at breast height; slenderness tree height/dbh; stem volume tree height*(dbh)2 0.0056 . 0.6934 109/0.22 6 0.087 102/0.13 12 0.4567 110/0.01 11 RMSE/R2 n Estimate (SE) 210 (83.5) 0.8989 104/0.08 12 Codominant failures P −0.0007 (0.0011) 0.5300 121 (96.7) 0.2404 96.5/0.00 0.6607 (5.64) 0.9091 21.9 (104) 168 (148) 0.8373 89.5/0.11 0.2789 0.9012 115/0.07 7 −73.83 (230) 0.7616 64.8/0.11 11.3 (14.2) 0.4634 134 (85.4) 0.1926 62.1/0.01 −0.8982 (6.27) 0.8931 146 (67.8) −0.5386 (2.26) 0.8165 38.3 (70.8) 0.6004 88.2/0.17 13.0 (9.24) 0.1881 86.0 (45.0) 0.0827 87.6/0.14 134 (98.6) 0.2026 yB, intercept and slope, respectively, of best fit line for the plot of bending moment at the point of failure and the variable listed in the first column. SE standard error; RMSE root mean square error. ©2008 International Society of Arboriculture 0.0563 96.3/0.01 RMSE/R2 0.0328 84.2/0.05
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