106 strength was the ratio of branch diameter to trunk diameter at the point of attachment, regardless of whether bark occlusions were present (Miller 1959; Gilman 2003). Bark occlusions were pres- ent for 21% of 1627 trunk failures recorded in the ITFD (data downloaded in March 2007 from http://ftcweb.fs.fed.us/natfdb/). A second explanation considered the orientation of wood fi- bers and the corresponding initial mode of failure of codominant stems. Video footage revealed that failure initiated in a complex combined stress state at the attachment: through combined shear and tension. Both shear and tension perpendicular to the grain are significantly weaker failure modes of wood than tension parallel to the grain (Green et al. 1999) and therefore more likely the governing factors. A crack was then observed to have formed pulling the fibers apart parallel to the long axis of the trunk and effectively splitting it in two. Supporting this speculation, the mean stress at the point of failure of codominant failures was approximately one-half of stress for stem failures—the value expected if the cross-section that resisted bending were one-half of the measured cross-section. In some cases, there was obvious splintering of fibers (typical of tensile parallel-to-grain failure) in the side of the trunk expected to be under compressive stress if the entire trunk were stressed, i.e., proximal to the applied load. Furthermore, for six of the nine codominant failures that oc- curred within 2.5 m (8.3 ft) of the ground, no trunk strains were recorded, indicating that that side of the trunk was separate and did not contribute to tree strength. The effect of shear and tension perpendicular to the grain should be considered more carefully in future investigations of codominant stems and branch attach- ments. Bending moment was found to be statistically similar for stem and codominant failures, but distance to failure was significantly larger for codominant trees. This implies that failure load was lower, but that was not the case, presumably as a result of large variability among trees within each failure type. Such variability can be attributed to size differences among trees. It is also spec- ulated that the difference in calculated stress at the point of failure between stem and codominant failures was partially the result of differences in cross-sectional dimension at the point of failure and the weaker failure mode of codominants. Differences in diameter at failure were the result of the greater height of failure of stem failures. The apparently contradictory findings that bending moments were similar between failure types whereas stem failures re- quired twice the stress of codominant failures can be explained by the weaker failure mode of the codominants. Furthermore, greater diameter at the point of failure for codominant failures resulted in lower stresses. Because stress is inversely propor- tional to the cube of diameter, a small increase in diameter can cause a large decrease in stress. Variations in stem shape help explain why the correlation coefficients for predictions of bending moment were greater than for stress for both failure types. Stem cross-sections were con- sidered ellipses, but none was a perfect ellipse, which introduced some error into the calculation of stress. For codominant failures, the weak correlation between dbh and bending moment was presumably the result of the influence of tension perpendicular to grain failure. Furthermore, the lack of correlation between dbh and stress was likely the result of orientation of stress (perpen- dicular to grain) and the assumed shape and orthotropy of the stem cross-section at failure. Future studies could focus on re- finement of prediction models for codominant tree failures. ©2008 International Society of Arboriculture Kane and Clouston: Tree Pulling Tests of Large Shade Trees Although codominant stems constituted a significant struc- tural defect, none appeared to be in imminent danger of failing. As a point of comparison, for a wind speed of 11.9 m/s (27 mph), the maximum stress measured on the sycamore maple was 510 kPa. On the sugar maple, the maximum stress was 2190 kPa when the maximum wind speed was 11.4 m/s (25 mph). Both of these values were much less than the average stress at breast height for all stem and codominant failures (Table 2), but the lack of foliage certainly reduced stress on the trees measured in the wind. It is also important to consider that stress determined by a static pull test will overestimate breaking stress endured during dynamic loading that occurs during windstorms (Oliver and Mayhead 1974). Although stem failures occurred at greater stress than codom- inant failures, it was likely that lateral branches still constituted a trunk defect. The orientation of branch and trunk fibers at the point of branch attachment presumably causes the point of weak- ness. Moore (2000) also observed that stem failures often oc- curred at lateral branches. Fredericksen et al. (1993) noted that stem failures of winched loblolly pines (Pinus taeda L.) gener- ally occurred closer to ground than trees damaged during a storm, an artifact of the height of the applied load. This was not the case for maples, presumably because defects (i.e., lateral branches and codominant stems) were incorporated below the height of applied load. The mean height of failure for all maples was 26% of tree height, which is almost identical to the mean of 25% from the ITFD (data downloaded in March 2007 from http://ftcweb.fs.fed.us/natfdb/). The lack of stem failures close to the ground and the substan- tially smaller stress at breast height compared with the point of failure have important implications for practitioners, who often assess tree risk by investigating trunk decay within a few meters of the ground. For stress at breast height to have been equal to stress at the point of failure, maples would have to have been 82% hollow at breast height. This value is larger than the com- mon guideline that a trunk that is 70% hollow constitutes a substantial defect (Kane et al. 2001). Assessing defects higher in the crown may be more useful in predicting failure. Bending Moment and Stress at the Point of Failure Elementary mechanical principles explain why stress and bend- ing moment at the point of failure were greater than and less than, respectively, stress and bending moment at breast height. Bending moment is the product of the applied load and the lever arm. At the point of failure, the lever arm was the distance between the block and the point of failure; at breast height, it was the height of the block less 1.4 m (4.6 ft). For the maximum applied load, the greater lever arm at breast height caused the bending moment to be greater. Because stress was inversely proportional to the cube of diameter, and diameter at breast height was larger than at the point of failure, stress was expected to be less. This was true although the bending moment was greater at breast height because the inverse relationship between stress and diameter is nonlinear. Stress at the point of failure for stem and codominant failures, respectively, was 79% and 45% of the MOR of wood samples. For stem failures, Fons and Pong (1957) reported that failure stress was 70% of published MOR values for ponderosa pine (Pinus ponderosa P&C Lawson), and Peltola et al. (1999) sug- gested that failure stress was 85% of published MOR values for
March 2008
| 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
