Arboriculture & Urban Forestry 38(6): November 2012 same way, except two post-cut values (putting the cut in ten- sion and in compression) were calculated for each cut depth. To compare the effect of sapwood loss versus heart- wood loss, the concentric area of heartwood that would need to be removed to cause a magnitude of stress equiva- lent to that induced by cutting sapwood was calculated. For concentric loss of heartwood, stress was calculated: [3] s = 32PLsinq/[p(do 3 - di )] + 4Pcosq/[p(do 3 2 - di 2)] quently converted into the area of concentric loss of heartwood. Data were subjected to analysis of covariance using PROC MIXED of the Statistical Analysis Systems (SAS) Software (SAS Institute, Cary, North Carolina, U.S.). Differences among species with respect to 1) the percent change in stress and 2) the percent loss of concentric heartwood were assessed with percent reduction in cross-sectional area as a covariate. Large red maples tested in Ohio were considered a separate spe- cies in the analysis and the effect of site was not considered. Regression analyses using PROC REG of SAS were used to fit the best linear relationships between reductions in cross- sectional area and the dependent variables (percent change in stress and area of concentric loss of heartwood). Second- and third-order polynomials were assessed but did not contribute significantly more understanding of the relationships than did linear models alone. The experimental design confounded the effect of the tree with that of the area of removed wood, so tree-to-tree variation was lumped with random error, a more conservative approach. Mean separation among species was by Tukey’s HSD (P = 0.05). For the subset of small red maples, similar analyses were conducted to assess the dif- ference between pulling under tension or compression and potential interacting effects with percent reduction in cross- sectional area. A paired t-test was used to determine wheth- er pre-cut stress differed between the two directions of pull. diameter of the concentric loss of heartwood; and L and q are described in Equations 1 and 2. Equation 3 was set equal to the pre-cut magnitude of stress and solved for di is trunk diameter; di , which was subse- RESULTS Prior to cutting, the stress required to deflect the trunks one degree was greater for large red maples than for small sweetgums (Table 1). As the percent reduction in cross- sectional area increased, the percent reduction in stress to deflect trunks one degree decreased linearly, regard- less of species (Figure 3). As the percent reduction in cross-sectional area increased, the calculated percent loss in concentric heartwood increased linearly, regardless of species (Figure 4). The mean calculated percent loss in concentric heartwood for all species and cuts was 70%, while the mean loss in area due to cutting was only 39%. The mean pre-cut stress required to deflect the trunks one degree was similar when the subset of small red ma- ples was pulled in tension (17.2 MPa) and in compres- sion (17.2 MPa) (p = 0.7808). After cutting, the mean percent reduction in stress to deflect trunks one degree ©2012 International Society of Arboriculture where the first and second terms in the right-hand side of the equation are bending and axial stress, respectively; P is the post-cut load for each depth of cut; do is 289 was greater when trees were pulled on the side of the tree with the cut (62%) than on the side opposite the cut (54%) (p = 0.0003). As the percent reduction in cross- sectional area increased, the percent reduction in stress to deflect trunks one degree decreased linearly, regardless of the direction in which the trees were pulled (Figure 5). Figure 3. Scatterplot and best-fit line for the relationship between the percent reduction in area (DA, abscissa, x-axis) and the per- cent change in stress due to cutting (Ds, ordinate, y-axis). The latter ratio was calculated assuming an uncut cross section. The scatter plot includes data from small red maple (<), large red ma- ple (=), sweetgum (5), and sawtooth oak (u). The relationship (Ds = 1.10 - 1.08 * DA) was significant (P < 0.001), robust (r2 and similar for all species (p = 0.258). = 0.84) Figure 4. Scatterplot and best-fit line for the relationship between the percent reduction in area (DA, abscissa, x-axis) and the per- cent loss in concentric heartwood to cause an equivalent magni- tude of stress to that induced by cutting (DsC, ordinate, y-axis). The scatter plot includes data from small red maple (<), large red maple (=), sweetgum (5), and sawtooth oak (u). The relationship (DsC = 0.17 + 0.92 * DA) was significant (P < 0.001), robust (r2 0.76), and similar for all species (p = 0.740). =
November 2012
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