Mechanical Properties of Primary Mechanical Properties of Primary Branches of 29 Desert SpeciesBranches of 29 Desert Species

Christina Pereira

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

Many other tress show other Many other tress show other forms and shapesforms and shapes

Cedrus atlantica

Fraxinus cuspitada

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

Main Stem

Olive = Primary Branch

Main Stem

Olive = Primary Branch

Green = Secondary Branch

Main Stem

Olive = Primary Branch

Green = Secondary Branch

Orange = Tertiary Branch

Main Stem

Olive = Primary Branch

Green = Secondary Branch

Orange = Tertiary Branch

Blue = Quaternary Branch

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

Mechanical Properties: Mechanical Properties: Bending Moment (M)Bending Moment (M)

Bending Moment (M) [low]

Bending Moment (M) [intermediate]

Bending Moment (M) [high]

Mechanical Properties: Mechanical Properties: Section Modulus (S)Section Modulus (S)

Materials & Methods: Materials & Methods: MeasurementsMeasurements

Diameter of segmentLength of segmentWeight of segmentWeight of Side branches

Mechanical Properties: StressMechanical Properties: Stress

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

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

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

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

-1

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7

0 20 40 60 80 100 120 140

section modulus, m3 x 10-8

Ben

din

g m

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wit

h s

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bra

nce

s (N

-m)

-20

-10

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0 500 1000 1500 2000 2500 3000

Section modulus, m3x 10-8

be

nd

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nc

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s,

N-m

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Stress Value (10^6 Pa)

Freq

uenc

y

New York

Combine the two histograms, ny and desert

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

Desert: Proportional Weight vs. Desert: Proportional Weight vs. Proportional Length and RadiusProportional Length and Radius

Alex is correcting the graph

New York: Proportional weight vs. New York: Proportional weight vs. proportional length and radiusproportional length and radius

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

Desert: Desert: Volume/Length vs. Proportional Volume/Length vs. Proportional

RadiusRadius

New York: New York: Volume/Length vs. Proportional Volume/Length vs. Proportional

RadiusRadius

Need to ask Alex to make graph

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

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.