mechanical properties of primary branches of 29 desert species christina pereira
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Mechanical Properties of Primary Mechanical Properties of Primary Branches of 29 Desert SpeciesBranches of 29 Desert Species
Christina Pereira
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Trees and shrubs show a Trees and shrubs show a variety of morphologiesvariety 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 floridumPinus ponderosa
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Many other tress show other Many other tress show other forms and shapesforms and shapes
Cedrus atlantica
Fraxinus cuspitada
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To date, there has been very little To date, there has been very little research into a unifying principle of research into a unifying principle of
tree and shrub morphologiestree and shrub morphologies
Prunus ilicifoliaFraxinus 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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HypothesesHypotheses
1. 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: Mechanical Properties: Bending Moment (M)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: Mechanical Properties: Section Modulus (S)Section Modulus (S)
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Materials & Methods: Materials & Methods: MeasurementsMeasurements
Diameter of segmentLength of segmentWeight of segmentWeight of Side branches
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Mechanical Properties: StressMechanical Properties: Stress
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1. Mechanical stress is constant from 1. Mechanical stress is constant from the base to the tip of the branch: the base to the tip of the branch:
DesertDesert
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1. Mechanical stress is constant 1. Mechanical stress is constant from the base to the tip of the from the base to the tip of the
branch: New Yorkbranch: New YorkExample 2: Pinus thunbergii
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Table 1: Properties of tree branchesTable 1: Properties of tree branches
Species LocationBending
StressMPa r2
Arctostaphylos manzanita San Bernandino, CA 1.23 0.973Bursera microphylla Tucson, AZ 2.33 0.901Cedrus atlantica Prescott, AZ 1.98 0.959Cercidium floridum Tucson, AZ 6.11 0.873Cercidium microphyllum Tucson, AZ 4.01 0.912Condalia globosa Prescott, AZ 1.05 0.974Larrea tridentata Tucson, AZ 2.47 0.913Fraxinus cuspidata Prescott, AZ 4.23 0.915Fraxinus dipetals San Bernandino, CA 1.97 0.93Fraxinus velutina San Bernandino, CA 2.27 0.931Gladitisia triacaithus Prescott, AZ 4.16 0.914Juniperus deppeane Prescott, AZ 2.59 0.953Juniperus osteosperma Blanding, UT 4.27 0.961Liquidamber styraciflura San Bernandino, CA 5.38 0.912Arbutus arizonica Prescott, AZ 2.73 0.928
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Species Location Bending StressMPa r2
Pinus cembroides Prescott, AZ 1.9 0.945Pinus ponderosa San Bernandino, CA 2.16 0.977Platanus racemosa San Bernandino, CA 4.57 0.96Populus trichocanpu Blanding, UT 2.41 0.96Populus tremuloides Blanding, UT 6.13 0.989Prosopis pubescens Tucson, AZ 4.83 0.992Prosopis velutina Tucson, AZ 3.19 0.926Prunus ilicifolia San Bernandino, CA 1.78 0.813Quercus turbinella Prescott, AZ 1.95 0.861Artemia tridentata Blanding, UT 0.415 0.818Salix exigua Blanding, UT 3.57 0.955Sambucus cerulea Prescott, AZ 3.48 0.963Tamarix chinensis San Bernandino, CA 3.32 0.987Ulmus americana Prescott, AZ 3.59 0.924
MEAN 3.11 0.931STDEV 1.45
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-1
0
1
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0 20 40 60 80 100 120 140
section modulus, m3 x 10-8
Ben
din
g m
om
ent
wit
h s
ide
bra
nce
s (N
-m)
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-20
-10
0
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0 500 1000 1500 2000 2500 3000
Section modulus, m3x 10-8
be
nd
ing
mo
me
nt
wit
h s
ide
bra
nc
he
s,
N-m
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0
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1 2 3 4 5 6 7 8 9
Stress Value (10^6 Pa)
Freq
uenc
y
New York
Combine the two histograms, ny and desert
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11stst hypothesis: hypothesis: Bending Stresses of desert Bending Stresses of desert species are lower than New York species are lower than New York speciesspecies
SIDE BRANCHES INCLUDED Desert New YorkMean 4.8 7.2
Standard Deviation 1.45 1.89T-Test Probability 0.026
Conclusion: STRESS VALUES ARE DIFFERENT
SIDE BRANCHES INCLUDED Desert New YorkMean 4.8 7.2
Standard Deviation 1.45 1.89T-Test Probability 0.026
Conclusion:STRESS VALUES ARE
DIFFERENT
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Desert: Proportional Weight vs. Desert: Proportional Weight vs. Proportional Length and RadiusProportional Length and Radius
Alex is correcting the graph
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New York: Proportional weight vs. New York: Proportional weight vs. proportional length and radiusproportional length and radius
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Second hypothesisSecond hypothesis
Small table of means of desert vs new york slopesDesert = 0.048 slope New york = 0.072 slopeT test probability = 0.0072
Conclusion: they are differentThus the main reason why have lower stress values
have less weight near the tips
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Desert: Desert: Volume/Length vs. Proportional Volume/Length vs. Proportional
RadiusRadius
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New York: New York: Volume/Length vs. Proportional Volume/Length vs. Proportional
RadiusRadius
Need to ask Alex to make graph
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Graph of new york cum v/lAre 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 3. The addition of secondary branches is a reiterative process in the is a reiterative process in the mechanical structure of tree branches.mechanical structure of tree branches.