Mechanical Properties of Primary Branches of 29 Desert Species Christina Pereira

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

Many other tress show other forms and shapes Cedrus atlantica Fraxinus cuspitada

To date, there has been very little research into a unifying principle of tree and shrub morphologies Prunus ilicifolia Fraxinus 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

Hypotheses 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: Bending Moment (M)

Bending Moment (M) [low] Bending Moment (M) [intermediate] Bending Moment (M) [high]

Mechanical Properties: Section Modulus (S)

Materials & Methods: Measurements Diameter of segment Length of segment Weight of segment Weight of Side branches

Mechanical Properties: Stress

1. Mechanical stress is constant from the base to the tip of the branch: Desert

1. Mechanical stress is constant from the base to the tip of the branch: New York Example 2: Pinus thunbergii

Table 1: Properties of tree branches SpeciesLocation Bending Stress MPa r2r2 Arctostaphylos manzanita San Bernandino, CA Bursera microphylla Tucson, AZ Cedrus atlantica Prescott, AZ Cercidium floridum Tucson, AZ Cercidium microphyllum Tucson, AZ Condalia globosa Prescott, AZ Larrea tridentata Tucson, AZ Fraxinus cuspidata Prescott, AZ Fraxinus dipetals San Bernandino, CA Fraxinus velutina San Bernandino, CA Gladitisia triacaithus Prescott, AZ Juniperus deppeane Prescott, AZ Juniperus osteosperma Blanding, UT Liquidamber styraciflura San Bernandino, CA Arbutus arizonica Prescott, AZ

SpeciesLocation Bending Stress MPa r2r2 Pinus cembroides Prescott, AZ Pinus ponderosa San Bernandino, CA Platanus racemosa San Bernandino, CA Populus trichocanpu Blanding, UT Populus tremuloides Blanding, UT Prosopis pubescens Tucson, AZ Prosopis velutina Tucson, AZ Prunus ilicifolia San Bernandino, CA Quercus turbinella Prescott, AZ Artemia tridentata Blanding, UT Salix exigua Blanding, UT Sambucus cerulea Prescott, AZ Tamarix chinensis San Bernandino, CA Ulmus americana Prescott, AZ MEAN STDEV1.45

New York Combine the two histograms, ny and desert

1 st hypothesis: Bending Stresses of desert species are lower than New York species SIDE BRANCHES INCLUDEDDesertNew York Mean Standard Deviation T-Test Probability0.026 Conclusion:STRESS VALUES ARE DIFFERENT SIDE BRANCHES INCLUDEDDesertNew York Mean Standard Deviation T-Test Probability0.026 Conclusion: STRESS VALUES ARE DIFFERENT

Desert: Proportional Weight vs. Proportional Length and Radius Alex is correcting the graph

New York: Proportional weight vs. proportional length and radius

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

Desert: Volume/Length vs. Proportional Radius

New York: Volume/Length vs. Proportional Radius Need to ask Alex to make graph

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

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