222 Spatz and Pfisterer: Mechanical Properties of Green Wood and Tree Risk Assessment When bending extends beyond the linear range of elas- tic behavior (i.e., beyond the yield point), plant materials will usually undergo plastic deformations. In green wood it is easy to observe that this deformation is accompanied by buckling of fibers on the compression side (Figure 5). Compression failure by fiber buckling can therefore be identified as the pri- mary failure event (Spatz and Niklas 2013). Although correla- tions are not necessarily causalities, this notion is supported by a close correlation and a ratio near 1:1 between compression strength and yield strength in bending apparent in the data from the Jessome catalog (see Appendix). This and other relations between strength properties as listed can be summarized: Maximal compression stress ≈ yield stress ≈ ½ maximal bend- ing stress. This critical bending moment calculated on the basis of Equa- tion 4 is compared to the bending moment imposed on the tree at maximal wind loads expected at the particular site and under the particular environmental conditions (Gardiner 1995; Wood 1995; Peltola 2006). Not taking into account the actual wind profile (Spatz and Bruechert 2000), the lever arm is taken as the height of the mid- point of the crown. For steady wind the drag force is calculated as: [5] FDrag = 0.5 r AU2 CD cient. The practical problem to determining the drag coefficient of a tree is formidable (Vogel 1994). For low wind speeds, the drag coefficient is approximately 0.5 for a fully leaved tree (Mayhead 1973). At high wind speeds, the branches bend to the leeward side to an extent depending on their flexibility. This “streamlining” reduces the sailing area as well as the drag coefficient substan- tially (Mayhead 1973; Rudnicki et al. 2004; Telewski 2012). This is why for any estimate of the actual wind load on a tree arborists need to know the mechanical properties of the tree investigated. Under natural conditions, the situation is considerably more where r is the density of air, A is the “sailing area” (i.e., the pro- jection of the crown facing the wind), U is the wind velocity at the height of the midpoint of the crown, and CD is the drag coeffi- complex because real winds are gusty winds and trees react to wind as dynamic structures (James 2003; Spatz et al. 2007; Rodriguez et al. 2008; Sellier et al. 2008) in such a way that flexible branches do not move in line and in phase with the trunk, but rather somewhat independently. In well branched trees this leads to a considerable damping of potentially dangerous oscillations: mechanical energy is distributed quite effectively within the tree and is not so much focused on the trunk and the roots. The energy is also dissipated more effectively in a tree crown with flexible branches than in a tree with stiff branches (Spatz et al. 2007). At the present time, this phenomenon, known as structural damping (Niklas 1992), was described quantitatively only for model trees (Rodriguez et al. 2008). Thus, it is not clear which correction factors for the critical bending moment should be used in Equation 5 to account for the gusti- ness of wind and the special architecture of the tree crown. It should be noted that these considerations do not invalidate pulling tests, they just point to the limitations in their expressiveness. Due to the number of approximations nec- essary, it seems advisable to allow for safety margins of the order of a factor of two in their interpretation. The diagno- sis, and even more so the prognosis for a living organism can- not yield certainties, but rather probabilities of failure within the limitation of the methods and the accuracy of the data base. ©2013 International Society of Arboriculture LITERATURE CITED Bruechert, F., G. Becker, and T. Speck. 2000. The mechanics of Norway Spruce [Picea abies (L.) Karst]: The mechanical properties of standing trees from different thinning regimes. Forest Ecology and Management 135:45–62. Brudi, E., and P. van Wassenaer. 2001. Trees and Statics: Non Destructive Failure Analysis. In: E. Thomas Smiley and K. Coder (Eds.). 2001. Tree Structure and Mechanics Conference Proceedings: How Trees Stand Up and Fall Down. Savannah, Georgia, U.S. pp. 53–69. Chave, J., H.C. Muller-Landau, T.R. Baker, T.A. Easdale, H. ter Steege, and C.O. Webb. 2006. Regional and phylogenetic variation of wood density across 2456 neotropical tree species. Ecological Applications 16:2356–2367. Eckstein, D., and U. Saß. 1994. Bohrwiderstandsmessungen an Laub- bäumen und ihre holzanatomische Interpretation. Holz als Roh- und Werkstoff 52:279–286. Gardiner, B.A. 1995. The interactions of wind and tree movement in for- est canopies. pp. 41–59. In: M.P. Coutts and J. Grace (Eds.). Wind and Trees. Cambridge University Press, Cambridge. Gilbert, E.A., and E.T. Smiley. 2004. Picus sonic tomography for the quantification of decay in white oak (Quercus alba) and hickory (Carya spp.). Journal of Arboriculture 30:277–281. Gordon, J.E. 1976. The new science of strong materials or why you don’t fall through the floor. 2nd edition. Penguin books, London, UK. James, K. 2003. Dynamic loading of trees. Journal of Arboriculture 29:165–171. Jessome, A.P. 1977. Strength and related properties of woods grown in Canada. Eastern Forest Products Laboratory, Ottawa, Ontario. Forestry Technical Report 21, Ottawa. Kretschmann, D.E. 2010. Mechanical properties of wood. In: Wood Handbook. Wood as an engineering material. Forest Products Labo- ratories, technical report, USDA, Madison, Wisconsin, U.S. 5:1–44. Lavers, G.M. 1983. The strength properties of timber. 3rd, revised ed. London (Department Environment. Build. Res. Establishment). 60 p. Mamdy C., P. Rozenberg, A. Franc, J. Launay, N. Scherman, and J.C. Bastien. 1999. Genetic control of stiffness of standing Douglas fir; from the standing stem to the standardized wood sample, relation- ships between modulus of elasticity and wood density parameters. Part I. Annals of Forest Science 56:133–143. Mattheck, C., and H. Breloer. 1994. The body language of trees, a hand- book for failure analysis. London, England: Her Majesty’s Stationary Office. Mayhead, G.J. 1973. Sway periods of forest trees. Scott. For. 27:19–23. Milne, R. 1991. Dynamics of swaying of Picea sitchensis. Tree Physiol. 9:383–399. Niklas, K. 1992. Plant Biomechanics. Univ. Chicago Press, Chicago, Illinois, U.S. Niklas, K., and H.-Ch. Spatz. 2010. Worldwide correlation of mechani- cal properties and green wood density. American Journal of Botany 97:1587–1594. Niklas, K., and H.-Ch. Spatz. 2012a. Mechanical properties of wood disproportionally increase with increasing density. American Journal Botany 99:169–170. Niklas, K., and H.-Ch. Spatz. 2012b. Plant Physics. Univ. Chicago Press, Chicago, Illinois, U.S. Peltola, H.M. 2006. Mechanical stability of trees under static loads. American Journal of Botany 93:1501–1511.
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