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.
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Notes
Note that a circular cross-section was assumed. In reality, the cross-sections are elliptical in nature due to the reaction wood. However, this error is quite small. The mean ratio of long radius to short radius (accounting for the reaction wood) was determined to be 1.107 with a standard deviation of 0.175. The error using a circular cross-section compared to using the second moment of area with respect to the major axis was 12.9% with a standard deviation of 26.0%. The error associated with respect to the second moment of area about the minor axis was 7.3% with a standard deviation of 7.78%. Furthermore, these errors are exaggerated because the maximum stresses would actually fall on axes between the major and minor axes, thereby reducing the errors even further.
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Acknowledgments
The authors gratefully acknowledge the Catherine and Robert Fenton Endowed Chair to L.S. E. for financial contributions to the project. The names of the plant species were verified with the help of personnel at the New York Botanical Garden, New York. The authors gratefully acknowledge the excellent manuscript reviews by (alphabetically) Ralph Amateis, Thomas Dean, and Daniel Gilmore. These reviewers made important contributions to the final manuscript.
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Communicated by Robert Guy.
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Evans, L.S., Kahn-Jetter, Z., Torres, J. et al. Mechanical stresses of primary branches: a survey of 40 woody tree and shrub species. Trees 22, 283–289 (2008). https://doi.org/10.1007/s00468-007-0182-7
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DOI: https://doi.org/10.1007/s00468-007-0182-7