1. Mechanical Properties of Primary Branches of 29 Desert Species Christina Pereira

2. 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

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

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

6. Main Stem Olive = Primary Branch

7. Main Stem Olive = Primary Branch Green = Secondary Branch

8. Main Stem Olive = Primary Branch Green = Secondary Branch Orange = Tertiary Branch

9. Main Stem Olive = Primary Branch Green = Secondary Branch Orange = Tertiary Branch Blue = Quaternary Branch

10. 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

11. Mechanical Properties: Bending Moment (M)

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

13. Mechanical Properties: Section Modulus (S)

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

16. Mechanical Properties: Stress

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

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

19. Table 1: Properties of tree branches SpeciesLocation Bending Stress MPa r2r2 Arctostaphylos manzanita San Bernandino, CA 1.230.973 Bursera microphylla Tucson, AZ 2.330.901 Cedrus atlantica Prescott, AZ 1.980.959 Cercidium floridum Tucson, AZ 6.110.873 Cercidium microphyllum Tucson, AZ 4.010.912 Condalia globosa Prescott, AZ 1.050.974 Larrea tridentata Tucson, AZ 2.470.913 Fraxinus cuspidata Prescott, AZ 4.230.915 Fraxinus dipetals San Bernandino, CA 1.970.93 Fraxinus velutina San Bernandino, CA 2.270.931 Gladitisia triacaithus Prescott, AZ 4.160.914 Juniperus deppeane Prescott, AZ 2.590.953 Juniperus osteosperma Blanding, UT 4.270.961 Liquidamber styraciflura San Bernandino, CA 5.380.912 Arbutus arizonica Prescott, AZ 2.730.928

20. SpeciesLocation Bending Stress MPa r2r2 Pinus cembroides Prescott, AZ 1.90.945 Pinus ponderosa San Bernandino, CA 2.160.977 Platanus racemosa San Bernandino, CA 4.570.96 Populus trichocanpu Blanding, UT 2.410.96 Populus tremuloides Blanding, UT 6.130.989 Prosopis pubescens Tucson, AZ 4.830.992 Prosopis velutina Tucson, AZ 3.190.926 Prunus ilicifolia San Bernandino, CA 1.780.813 Quercus turbinella Prescott, AZ 1.950.861 Artemia tridentata Blanding, UT 0.4150.818 Salix exigua Blanding, UT 3.570.955 Sambucus cerulea Prescott, AZ 3.480.963 Tamarix chinensis San Bernandino, CA 3.320.987 Ulmus americana Prescott, AZ 3.590.924 MEAN3.110.931 STDEV1.45

23. New York Combine the two histograms, ny and desert

24. 1 st hypothesis: Bending Stresses of desert species are lower than New York species SIDE BRANCHES INCLUDEDDesertNew York Mean4.87.2 Standard Deviation1.451.89 T-Test Probability0.026 Conclusion:STRESS VALUES ARE DIFFERENT SIDE BRANCHES INCLUDEDDesertNew York Mean4.87.2 Standard Deviation1.451.89 T-Test Probability0.026 Conclusion: STRESS VALUES ARE DIFFERENT

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

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

27. 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

28. Desert: Volume/Length vs. Proportional Radius

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

30. 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

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