July 2015

198 The result is maximum bending stress (σfmax = Cos a ext) + b − c + −1 ( + 2 2 2(a ext b ) 2 f max = 32Mmax 2 B 1 B 2 (Equation 3) (Equation 2)Slater and Ennos: Included Bark Affects the Strength of Bifurcations in Hazel ) for each bifurcation and was calculated using the equation: [3] branch at its base, taken respectively in line with, and perpendicular to, the plane of the bifurcation (Gere and where B1 and B2 Aſter the rupture testing, a three-point bending 𝜎𝜎硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈 = 8 𝑃𝑃硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈 𝐿𝐿硯鬈𝑠𝑠硯鬈𝑠𝑠硯鬈𝑚𝑚硯鬈𝑠𝑠硯鬈 𝜋𝜋硯鬈 𝐷𝐷硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈2 𝑊𝑊硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈 test was carried out on the smaller of the branches arising from the bifurcation to determine the bend- ing stress it could withstand before yielding. All branches were carefully checked to verify they had not been damaged during the rupture testing prior to this three-point bending. This ensured reliable results during testing. This second test was done to allow for comparison between branch strength and bifurcation strength based on estimations of yield stresses at the base of the smaller branches during the rupture tests (Equation 3) and at the middle of the smaller branches during the three-point bending tests (Equation 4). Limitations of the load cell avail- able meant that branches above the diameter of 23 mm could not be bent to their yield point, limiting the sample size for this second test to 83 branches. In this three-point bending test, the smaller M m =ax branch was placed upon steel supports set 295 mm apart, and a semicircular plastic probe of 30 mm diameter, attached to a 1 kN load cell in the crosshead of the testing machine, was lowered until it was in contact with the middle of the sup- ported branch. The span length available for these tests was necessarily limited to 295 mm because of the location of two side columns on the UTM. The testing machine’s crosshead was then driven downward at a rate of 35 mm min-1 F peak b Sin (Equation 1) = Cos a ext) + b − c + −1 ( + 2 2 2(a ext b ) 2 (Equation 2) , bending the branch until it failed, while an interfacing com- puter recorded a graph of force versus displace- ment. This loading rate has been successfully used in previous experiments of this nature (van Cast- eren and Ennos 2010; Slater and Ennos 2013). This test was used to calculate the maxi- ) acting upon the f max = 32Mmax 2 B 1 B 2 mum bending stress (σbmax (Equation 3) branch before it yielded using the equation: [4] 𝜎𝜎硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈𝑏𝑏硯鬈 = 8 𝑃𝑃硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈 𝐿𝐿硯鬈𝑠𝑠硯鬈𝑠𝑠硯鬈𝑚𝑚硯鬈𝑠𝑠硯鬈 𝜋𝜋硯鬈 𝐷𝐷硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈2 𝑊𝑊硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈𝑚𝑚硯鬈 (Equation 4) Timoshenko 1996). (Equation 4) are two diameters of the smaller where Pmax the diameters of the branch in line with, and per- pendicular to, the load, respectively, and measured where the plastic probe was in contact with the branch during the test (Gere and Timoshenko 1996). The completion of the rupture tests and three- distance between the supports, Dmid and Wmid point bending tests allowed for comparison between the maximum bending stresses of the bifurcations tested with the maximum bending stresses of the smaller branches that arose from these bifurcations. MORPHOLOGICAL MEASUREMENTS Measurements of Included Bark For all the bifurcations where bark inclusions were exposed during the rupture testing (n = 104), the fracture surfaces were then excised and digitally scanned using an HP Scanjet 2400® (Hewlett Packard, Palo Alto, California, U.S.). These samples were then categorized as either embedded bark inclusions (n = 17), cup unions (n = 57), or wide-mouthed bark-included bifurcations (n = 30) (Figure 2). The image analysis soſtware ImageJ® (Abramoff et al. 2004) was then used to measure the area of bark relative to that of the fracture surface (Figure 4a). The same technique was used to measure the ratio between the width of the bark inclusion at the apex of the bifurcation and the width of the parent stem at the base of the branch bark ridge, where the pith of the parent stem bifurcates (Figure 4b). This second measure was chosen as researchers suspected that as the highest tensile stresses act at the bifurcation apex when the two branches are pulled apart, so the failure would occur more easily when a higher propor- tion of included bark was present in this location. The bifurcations with included bark that was exposed at the apex (n = 87) were also categorized as to whether they had formed a cup-like bifurca- tion (where two areas of xylem were found at the apex of the bifurcation, formed on either side and above the bark inclusion), or whether there was included bark situated at the apex of the bifurca- tion (Figure 5). Again, this comparison was chosen to try to assess if there was a difference in the strength of these two types of bark-included bifurcation because of the difference as to which material (wood or bark) was situated at the apex. was the maximum load and Lspan was the were ©2015 International Society of Arboriculture α π σ α σ π α

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