Arboriculture & Urban Forestry 33(4): July 2007 285 ure (Figure 1). If an attachment failed, it was checked for the presence of included bark. After breaking each branch, a short section immediately adjacent to the point of failure was removed. The cut ends of each section were coated with a wax emulsion sealant (An- chor-seal; U-C coatings Corp., Buffalo, NY) to reduce mois- ture loss, and the sections were stored in plastic bags at 4°C (39.2°F) for several weeks. Sections were machined into two clear, defect-free samples from the top and bottom of the branch, with respect to the direction of the applied load, as close to the outer growth rings as possible. Sample dimen- sions were 2.5 cm × 2.5 cm × 35.6 cm (1 in × 1 in × 14.2 in). Samples were tested in the green condition on a universal testing machine (MTS, Eden Prairie, MN) in a three-point bending test similar to the standard test (ASTM 2000), al- though the dimensions of each sample were smaller than specified by the standard. Modulus of rupture and modulus of elasticity (MOE) were measured during the test. After testing, a small piece was cut from the sample; it was weighed, oven- dried at 104°C (219.2°F) for 4 days, and then its volume was measured to determine its specific gravity (GS) and moisture content. The average value from the two samples was used in data analysis. For one tree, one of the samples failed prema- turely at a defect in the sample; only the remaining sample was used in the analysis of wood properties. Bending stress (), axial stress (A), shear stress (), bending stress in tension (T), bending stress in compression (C), and “stress ratio” (SR) were calculated from the mea- surements. Bending stress was calculated at the point of fail- ure in three ways. First, the branch cross-section was consid- ered as an ellipse of inside bark depth (y) and width (x): BEIB = 32Plcosxy2 (1) where the subscript E indicates ellipse, the subscript (IB) indicates measurements were taken inside bark, P is the ap- plied load, l is the distance from the loading point to the failure point, and is the angle between the cable and the branch. Second, equation 1 was repeated using branch outside bark depth and width measurements (this was only possible for trees from Waynesboro because branch outside bark depth and width were not measured on the branches from trees at Virginia Tech). The subscript (IB) from equation 1 changed to (OB) for this calculation. The third bending stress calcu- lation considered the branch cross-section as a circle of out- side bark diameter (d): BC = 32Plcosd3 (2) where the subscript C indicates circle. Shear stress was cal- culated at the point of failure considering the branch cross- section as an ellipse of inside bark depth (y) and width (x): = 16Pcos3xy (3) Axial stress was calculated in two ways. First, the branch cross-section was considered as an ellipse (indicated by the subscript E) of inside bark depth (y) and width (x): AE = 4Psinxy AC = 4Psind2 (4) Second, the branch cross-section was considered a circle (in- dicated by the subscript C) of outside bark diameter (d): (5) Bending stress is tensile on the top of the branch (side op- posite of the direction of the applied load) and compressive on the bottom of the branch (side in the direction of the applied load). By convention, tensile and compressive stresses are taken to be positive and negative, respectively. To calculate the total tensile (T) and compressive (C) stress in the branch: Ti or Ci = Ai + Bi (6) where the subscript i indicates that the calculations were made considering the branch as both an elliptical and a cir- cular cross-section. If the angle between the winch cable and the branch exceeded 90°, Ai was tensile (and positive). For such branches, the magnitude of tensile stress exceeds that of compressive stress by equation 6. If the angle between the Figure 1. Failures were categorized as either branch (left) in which more than 50% of the failed fibers originated in the branch or attachment (right) in which fewer than 50% of the failed fibers originated in the branch. winch cable and the branch was less than 90°, Ai was com- pressive (and negative). For these branches, the magnitude of compressive stress exceeds that of tensile stress by equation 6. To normalize branch breaking stress by the inherent wood strength, a stress ratio (SRi) was calculated by dividing the ©2007 International Society of Arboriculture
July 2007
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