Trees

, Volume 22, Issue 3, pp 283–289 | Cite as

Mechanical stresses of primary branches: a survey of 40 woody tree and shrub species

  • Lance S. Evans
  • Zella Kahn-Jetter
  • Jessica Torres
  • Mabel Martinez
  • Paul Tarsia
Original Paper

Abstract

Land plants have evolved a large number of growth forms and each plant species has a unique morphology. For many tall plants, main stems serve the function of vertical growth while primary and higher order branches are responsible for lateral growth for greater light interception. Herein we search for a mechanical constant for primary branches. Primary branches were sampled from 40 species of trees and shrubs. Among the species sampled, branch lengths ranged from 1.8 to 12.2 m, weights from 0.056 to 16.6 kg, base diameters from 17 to 150 mm, bending moments from 7.1 to 2,200 N-m, and section moduli from 0.039 to 29.0 × 10−3 m3. Primary branches of all 40 tree and shrub species exhibited relatively constant bending stresses along each branch. Moreover stress values among the 40 species were relatively constant at about 11 MPa (mean = 11.1 MPa [range 5.2–18.9]; standard deviation = 3.3 MPa). Furthermore, primary branches without secondary branches attached (1) had similar bending moment distributions as tapered cantilever beams, (2) exhibited relatively constant slope values of stress versus length among all species (stresses increased linearly with length), and (3) exhibited both relatively constant density and relatively constant taper within each species. We conclude that the relatively constant stress of about 11 MPa of primary branches was due solely to the numbers, weights, and distributions of secondary branches and associated higher order branches along primary branches for the 40 plant species. To our knowledge, this is the first publication that shows a unifying mechanical constant for primary branches of plants.

Keywords

Mechanical properties Primary branches Bending stresses 

References

  1. Almeras T, Gril J, Costes E (2002) Bending of apricot-tree branches under the weight of axillary productions: confrontation of a mechanical model to experimental data. Trees 16:5–15CrossRefGoogle Scholar
  2. Almeras T, Thibaut A, Gril J (2005) Effect of circumferential heterogeneity of wood maturation strain, modulus of elasticity and radial growth on the regulation of stem orientation in trees. Trees 19:457–467CrossRefGoogle Scholar
  3. Baldwin VC, Peterson KD, Burkhart HE, Amateis RL, Doughtery PM (1997) Equations for estimating loblolly pine branch and foliage weight and surface area. Can J For Res 27:918–927CrossRefGoogle Scholar
  4. Bertram JE (1989) Size-dependent differential scaling in branches; the mechanical design of trees revisited. Trees 4:241–253Google Scholar
  5. Cannell M, Morgan J, Murray M (1988) Diameters and dry weights of tree shoots: effects of Young’s modulus, taper, deflection and angle. Tree Physiol 4:219–231PubMedGoogle Scholar
  6. Castera P, Mortier V (1991) Growth patterns and bending mechanics of branches. Trees 5:232–238CrossRefGoogle Scholar
  7. Dean T, Roberts S, Gilmore D, Maguire D, Long J, O’Hara K, Seymour R (2002) An evaluation of the uniform stress hypothesis based on stem geometry in select North American conifers. Trees 16:559–568CrossRefGoogle Scholar
  8. Gilmore DW, Seymour RS, Maguire DA (1996) Foliage-sapwood area relationships for Abies balsamea in central Maine. Can J For Res 26:2071–2079CrossRefGoogle Scholar
  9. Keane MG, Weetman GF (1987) Leaf area- sapwood cross-sectional area relationships in repressed stands of lodgepole pine. Can J For Res 17:205–209CrossRefGoogle Scholar
  10. King DA (1986) Tree form, height growth and susceptibility to wind damage in Acer saccharum. Ecology 67:980–990CrossRefGoogle Scholar
  11. Larson PR (1963) Stem form development of forest trees. For. Sci. Monograph #5. Society of American ForestersGoogle Scholar
  12. Mattheck C, Bethge K, Schafer JJ (1993) Safety factors in trees. Theor Biol 165:185–189CrossRefGoogle Scholar
  13. McMahon TA (1973) Size and shape in biology. Science 179:1201–1204PubMedCrossRefGoogle Scholar
  14. Milne R, Blackburn P (1989) The elasticity and vertical distribution of stress within stems of Picea sitchensis. Tree Physiol 5:195–205PubMedGoogle Scholar
  15. Morgan J, Cannell M (1987) Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading. Tree Physiol 3:365–371PubMedGoogle Scholar
  16. Morgan J, Cannell M (1994) Shape of tree stems—a re-examination of the uniform stress hypothesis. Tree Physiol 14:49–55 PubMedGoogle Scholar
  17. Niklas K (1992) Plant biomechanics. University of Chicago Press, ChicagoGoogle Scholar
  18. Niklas KJ, Spatz H-C (2000) Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels. Trees 14:230–237CrossRefGoogle Scholar
  19. Roberts SD, Long JN (1992) Production efficiency of Abies lasiocarpa: influence of vertical distribution of leaf area. Can J For Res 22:1230–1234CrossRefGoogle Scholar
  20. SPSS Institute Inc. (2000) Systat 10 [computer program]. SPSS Institute, Chicago Google Scholar
  21. Wilson B, Archer R (1977) Reaction wood; induction and mechanical action. Ann Rev Plant Physiol 28:23–43CrossRefGoogle Scholar
  22. Wilson B, Archer R (1979) Tree design: some biological solutions to mechanical problems. Bioscience 29:293–298CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Lance S. Evans
    • 1
  • Zella Kahn-Jetter
    • 2
  • Jessica Torres
    • 1
  • Mabel Martinez
    • 2
  • Paul Tarsia
    • 2
  1. 1.Laboratory of Plant Morphogenesis, Biological Sciences Research LaboratoriesManhattan CollegeBronxUSA
  2. 2.Department of Mechanical EngineeringManhattan CollegeBronxUSA

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