Mechanical Properties of Primary Branches of 29 Desert Species

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Mechanical Properties of Primary Branches of 29
Desert Species

• Christina Pereira

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Trees and shrubs show a variety of morphologies

• Some are tall and slender with main stem and
  short primary branches

• Some are short and wide with less dominant stem
  and very long branches

Cercidium floridum
Pinus ponderosa
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Many other tress show other forms and shapes
Cedrus atlantica
Fraxinus cuspitada
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To date, there has been very little research into
a unifying principle of tree and shrub
morphologies
Prunus ilicifolia
Fraxinus velutina
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Main Stem
Olive Primary Branch
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Main Stem
Olive Primary Branch
Green Secondary Branch
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Main Stem
Olive Primary Branch
Green Secondary Branch
Orange Tertiary Branch
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Main Stem
Olive Primary Branch
Green Secondary Branch
Orange Tertiary Branch
Blue Quaternary Branch
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Hypotheses

• Mechanical stress is constant from the base to
  the tip of the branch.
• 2. Branches of Desert species will have less
  mechanical stress than species from New York
• 3. The addition of secondary branches is a
  reiterative process in the mechanical structure
  of tree branches.
• 4. Mechanical stresses of primary branches are
  constant among tree species

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Mechanical Properties Bending Moment (M)
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Bending Moment (M) low
Bending Moment (M) intermediate
Bending Moment (M) high
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Mechanical Properties Section Modulus (S)
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Materials Methods Measurements

• Diameter of segment
• Length of segment
• Weight of segment
• Weight of Side branches

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Mechanical Properties Stress
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1. Mechanical stress is constant from the base to
the tip of the branch Desert
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1. Mechanical stress is constant from the base to
the tip of the branch New York
Example 2 Pinus thunbergii
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Table 1 Properties of tree branches
Species Location Bending Stress
Species Location MPa r2
Arctostaphylos manzanita San Bernandino, CA 1.23 0.973
Bursera microphylla Tucson, AZ 2.33 0.901
Cedrus atlantica Prescott, AZ 1.98 0.959
Cercidium floridum Tucson, AZ 6.11 0.873
Cercidium microphyllum Tucson, AZ 4.01 0.912
Condalia globosa Prescott, AZ 1.05 0.974
Larrea tridentata Tucson, AZ 2.47 0.913
Fraxinus cuspidata Prescott, AZ 4.23 0.915
Fraxinus dipetals San Bernandino, CA 1.97 0.93
Fraxinus velutina San Bernandino, CA 2.27 0.931
Gladitisia triacaithus Prescott, AZ 4.16 0.914
Juniperus deppeane Prescott, AZ 2.59 0.953
Juniperus osteosperma Blanding, UT 4.27 0.961
Liquidamber styraciflura San Bernandino, CA 5.38 0.912
Arbutus arizonica Prescott, AZ 2.73 0.928
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Species Location Bending Stress
Species Location MPa r2
Pinus cembroides Prescott, AZ 1.9 0.945
Pinus ponderosa San Bernandino, CA 2.16 0.977
Platanus racemosa San Bernandino, CA 4.57 0.96
Populus trichocanpu Blanding, UT 2.41 0.96
Populus tremuloides Blanding, UT 6.13 0.989
Prosopis pubescens Tucson, AZ 4.83 0.992
Prosopis velutina Tucson, AZ 3.19 0.926
Prunus ilicifolia San Bernandino, CA 1.78 0.813
Quercus turbinella Prescott, AZ 1.95 0.861
Artemia tridentata Blanding, UT 0.415 0.818
Salix exigua Blanding, UT 3.57 0.955
Sambucus cerulea Prescott, AZ 3.48 0.963
Tamarix chinensis San Bernandino, CA 3.32 0.987
Ulmus americana Prescott, AZ 3.59 0.924
MEAN 3.11 0.931
STDEV 1.45
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New York
Combine the two histograms, ny and desert
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1st hypothesis Bending Stresses of desert
species are lower than New York species
SIDE BRANCHES INCLUDED Desert New York
Mean 4.8 7.2
Standard Deviation 1.45 1.89
T-Test Probability 0.026 0.026
Conclusion STRESS VALUES ARE DIFFERENT STRESS VALUES ARE DIFFERENT
SIDE BRANCHES INCLUDED Desert New York
Mean 4.8 7.2
Standard Deviation 1.45 1.89
T-Test Probability 0.026 0.026
Conclusion STRESS VALUES ARE DIFFERENT STRESS VALUES ARE DIFFERENT
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Desert Proportional Weight vs. Proportional
Length and Radius
Alex is correcting the graph
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New York Proportional weight vs. proportional
length and radius
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Second hypothesis

• Small table of means of desert vs new york slopes
• Desert 0.048 slope
• New york 0.072 slope
• T test probability 0.0072
• Conclusion they are different
• Thus the main reason why have lower stress values
  have less weight near the tips

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Desert Volume/Length vs. Proportional Radius
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New York Volume/Length vs. Proportional Radius
Need to ask Alex to make graph
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• Graph of new york cum v/l
• Are they different? If so make table
• Is this enough?
• If not then we do terminals vs main for desert
  only

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3. The addition of secondary branches is a
reiterative process in the mechanical structure
of tree branches.