Arboriculture & Urban Forestry 33(4): July 2007 289 (1959) noted was the underlying cause of reduced branch strength when the angle of attachment was small. The absence of an effect of taper on failure type is unex- pected because taper can influence the location of maximum bending stress (Leiser and Kemper 1973). The lack of influ- ence, however, may be the result of the small range of mea- sured branch tapers (−0.25 taper −0.02) or the super- seding effect of aspect ratio. Strong taper, i.e., a large length to diameter ratio, is generally considered to increase tree stability (Petty and Swain 1985; Mattheck et al. 2002). That suggestion might not apply to branches because strong taper in a branch may increase aspect ratio and thus reduce branch attachment strength. The unexpected lack of influence of GS, MOR, or MOE on BE(IB) and BC is probably the result of the greater likeli- hood of juvenile and/or tension wood present in wood samples taken from each branch. Both juvenile and tension wood have highly variable strength properties compared with normal trunk wood (Haygreen and Bowyer 1996). Wood samples were not explicitly tested for tension wood, but 14 of the 16 images of branch cross-sections revealed an eccentric pith. Although it is not the best way to confirm the presence of tension wood (Koch et al. 1968), tension wood is often as- sociated with an eccentric pith (Haygreen and Bowyer 1996). The likelihood of reaction wood (tension wood in angio- sperms, compression wood in gymnosperms) or juvenile wood in branches will vary by species and branch size. Using average values for MOR from a source such as the Wood Handbook (USDA 1999) may be misleading because those values are based on trunk wood samples. The ability to ex- trapolate wood properties’ values from trunks to branches varies among species (Rozens 1969; Ueda and Tanaka 1997; Kothiyal et al. 1999) and even height within the tree (Rozens 1969). The results also illuminate some fundamental consider- ations in biomechanics research. First, estimating branch or trunk cross-sections as circular is inappropriate without con- firming that the cross-section closely resembles a circle. Mea- suring the cross-section of a branch or trunk as an ellipse would confirm (or reject) that the cross-section is essentially circular. Resistance to bending stress is determined by the moment of inertia, which, for a circle, increases as the fourth power of diameter (Kane et al. 2001). As a branch or trunk cross-section becomes more elliptical, the small dimensional disparities also increase in proportion to the fourth power. Such disparities are responsible for the dramatic differences between BE(OB) and BC as well as between SRE and SRC despite relatively small differences in x and y measurements of each branch cross-section. Visual inspection of cross- sections is probably not sufficient to determine whether the x and y measurements differ enough to cause differences in moment of inertia calculations, because the x and y measure- ments in this study did not differ widely. Because of the constant unidirectional load from gravity, branches have a tendency to form elliptical cross-sections (Fegel 1955), so future examinations of branch failure should consider using equation 1 to calculate stress. It is interesting to speculate on the adaptive growth of elliptical branch cross-sections. Such cross-sections strengthen branches in the direction of static gravitational loads while facilitating lateral bending and swaying during wind loads. It may be unwise to assume that branch strength will be less than MOR determined from wood samples. Previous studies have found this to be untrue of Japanese cedar (Cryp- tomeria japonica) and Hinoki cypress (Chamaecyparis ob- tusa) (Onwona-Agyeman et al. 1994). Although shear stress did not contribute to Bradford pear failures, accounting for only 1% of bending stress, future studies should consider the effect of shear stress when the distance from the applied load to the point of failure is short. For a circular beam, the ratio of shear stress to bending stress is d/(6l), where d and l are the diameter and length of the beam, respectively. Thus, on long, slender beams, shear stress becomes less important relative to bending stress. Impor- tantly, however, the shear strength of wood is on average only 12% of MOR (USDA 1999). If the distance from the applied load to the point of failure causes the ratio of shear to bending stress to exceed 12% (e.g., Farrell 2003; Gilman 2003), the effect of shear stress should be investigated. Acknowledgments. The author thanks the following individuals for their valu- able assistance collecting data: Caitie Hutter, Dwayne Jones, Joe Murray, Rob- ert Hopper, and Chris Tooley; and ma- chining test samples: David Jones, Dan Pepin, and Andrew Putnam. The author also thanks two anonymous reviewers for suggesting revisions to the manuscript. This study was funded in part by a Duling grant from the TREE Fund and a San- tamour grant from ISA’s Mid-Atlantic Chapter. LITERATURE CITED Albers, J., and E. Hayes. 1993. How to Detect, Assess and Correct Hazard Trees in Recreational Areas. MN Dept. of Natural Resources. ASTM. 2000. D-143-94(2000)e1 Standard Test Methods for Small Clear Specimens of Timber. American Society for Testing and Materials, West Conshohocken, PA. Dahle, G.A., H.H. Holt, W.R. Chaney, T.M. Whalen, D.L. Cassens, R. Gazo, and R.L. McKenzie. 2006. Branch strength loss implications for silver maple (Acer saccha- rinum) converted from round-over to V-trim. Arboricul- ture & Urban Forestry 32:148–154. Dirr, M.A. 1990. Manual of Woody Landscape Plants. 4th ed. Stipes Publishing Co., Champaign, IL. Eisner, N.J., G.F. Gilman, and J.C. Grabosky. 2002. Branch morphology impacts compartmentalization of pruning wounds. Journal of Arboriculture 28:99–105. ©2007 International Society of Arboriculture
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