Article Figures & Data
Figures
- Figure 1.
V-shaped (left) and u-shaped branch attachments; the branch bark ridge is clearly present in the u-shaped attachment.
- Figure 2.
Image showing an attachment being pulled apart in the testing machine (left) and a free body diagram of the setup, where P is the applied load; RP is the reaction force; L is the distance from the point of applied load to the attachment, measured parallel to the longitudinal axis of the branch; and θ is the angle between the longitudinal axis of the branch and the applied load.
- Figure 3.
Diagram of various morphologic measurements that described the attachment. AL is the length of the attachment; BBRL is the length of the branch bark ridge; AW is the width of the attachment; and α and λ are, respectively, the angles of the attachment and branch bark ridge.
- Figure 4.
Examples of the three failure modes clockwise from top left: embedded branch failure on a white oak (not part of this study), flat surface failure on a sawtooth oak with included bark, ball in socket failure on a callery pear.
- Figure 5.
Scatterplots for the prediction of stress (σ) from the ratio of inside-bark diameter and attachment width (ratio). Equations for best-fit lines were σ = 227 – 316 * ratio, σ = 175 – 200 * ratio, σ = 118 – 145 * ratio for sawtooth oak (solid line, ▲), callery pear (dotted line, ●), and red maple (dashed line, ■), respectively. Slopes and intercepts were significant (P < 0.01); the axes do not intersect at 0.
- Figure 6.
Scatterplots for the prediction of stress (σ) from the ratio of branch diameter to trunk diameter (ratio). Equations for best-fit lines were σ = 181 – 152 * ratio, σ = 139 – 114 * ratio, σ = 94.8 – 76.3 * ratio for sawtooth oak, (solid line, ▲), callery pear (dotted line, ●), and red maple (dashed line, ■), respectively. Slopes and intercepts were significant (P < 0.01); the axes do not intersect at 0.
- Figure 7.
Scatterplots for the prediction of stress (σ) from the percent of attachment area covered by included bark (area). Equations for best-fit lines were σ = −126 * area + 93.4 and σ = −71.1 * area + 50.3 for sawtooth oak (solid line, ▲) and red maple (dashed line, ■). Intercepts were greater than 0 (P < 0.01), but slopes were not (P > 0.05).
- Figure 8.
Frequency table of failure modes (ball and socket (BS), embedded bark (EB), and flat surface (FS)) for all species by diameter ratio.
Tables
- Table 1.
Coefficients of determination for the relationship between breaking stress and each prediction measure within each species.
Measure Red maple Callery pear Sawtooth oak Mean R2 n R2 n R2 n R2 Diameter ratio 89 0.56 106 0.59 87 0.56 0.57 Branch diameterz/attachment width 73 0.51 105 0.65 87 0.56 0.57 Trunk diametery/attachment width 73 0.36 105 0.53 87 0.49 0.46 Rough branch diameter/attachment width 73 0.37 105 0.40 87 0.38 0.38 Branch angle 89 0.17 106 0.35 87 0.47 0.33 Branch bark ridge angle 87 0.15 106 0.31 87 0.36 0.27 Trunk diameterx/attachment width 71 0.24 102 0.02 87 0.34 0.20 Attachment length 86 0.11 106 0.41 87 0.15 0.22 Attachment angle 89 0.06 106 0.31 87 0.27 0.21 Branch bark ridge length 87 0.11 106 0.38 87 0.13 0.21 Specific gravity 88 0.01 106 0.01 87 0.18 0.06 Percent area of included bark 88 0.07 106 N/Aw 87 0.08 N/Aw Mean 0.22 0.29 0.29 - Table 2.
Means (SEs in parentheses) for breaking stress and diameter ratio by type and form of attachment, failure mode, and the presence of included bark (IB)z.
Type N Stress (MPa) Diameter ratioy Formx N Stress (MPa) Diameter ratio IB N Stress (MPa) Diameter ratio Modew N Stress (MPa) Diameter ratio Red maple Trunk–branch 58 60.6 (2.10) a 0.47 (0.016) a U 71 52.5 (2.43) a 0.58 (0.025) a No 68 53.2 (2.47) a 0.58 (0.116) a BS 51 62.2 (2.26) a 0.45 (0.016) au Branch–branch 8 38.5 (4.30) b 0.84 (0.030) b V 18 33.6 (5.24) b 0.68 (0.050) a Yes 21 34.1 (5.32) b 0.68 (0.106) a EB 16 40.8 (3.65) b 0.72 (0.033) bu Codominants 23 22.4 (2.23) c 0.86 (0.019) b FS 22 23.3 (2.17) c 0.88(0.016) cu Callery pear Trunk–branch 71 71.3 (2.43) au 0.61 (0.015) a U 105 N/Av N/A No 105 N/A N/A BS 54 75.3 (2.87) a 0.57 (0.014) a Branch–branch 6 45.9 (6.30) bu 0.90 (0.034) b V 1 N/A N/A Yes 1 N/A N/A EB 36 47.2 (2.65) b 0.82 (0.016) b Codominants 29 32.1 (2.12) bu 0.89 (0.016) b FS 16 31.2 (3.36) c 0.91 (0.017) c Sawtooth oak Trunk–branch 59 104 (4.26) a 0.53 (0.018) au U 56 100 (4.96) a 0.57 (0.022) a No 39 104 (5.15) a 0.56 (0.086) a BS 51 105 (4.56) a 0.57 (0.019) a Branch–branch 10 55.0 (7.03) b 0.85 (0.045) bu V 31 56.1 (5.38) b 0.76 (0.036) b Yes 48 68.49 (6.57) b 0.71 (0.098) b EB 14 56.8 (5.63) bt 0.79 (0.038) bt Codominants 18 36.7 (2.82) b 0.87 (0.015) buv FS 15 34.0 (3.45) bt 0.89 (0.014) bt ↵zWithin each species, read down the column; means followed by the same letter are not significantly different (P > 0.05) by Tukey’s honestly significant difference test.
↵yInside-bark branch diameter/trunk diameter at the attachment.
↵xForm refers to the presence (u-shaped) or absence (v-shaped) of a branch bark ridge.
↵wBall and socket (BS), embedded bark (EB), and flat surface (FS).
↵vTest was not conducted as a result of insufficient v-shaped attachments and attachments with included bark.
↵uWelch’s analysis of variance was used because variance was nonhomogeneous among categories.
↵tFor these comparisons, P < 0.10.
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