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Engineering Geometric Properties of Bones: Part 1 and Part 2

Explore bone properties like compression, flexibility, and articulation, understanding forces, stresses, and strains for different materials. Learn about the relationship between Young's modulus and shear modulus in engineering units. Discover how bones fail in tension and compression.

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Engineering Geometric Properties of Bones: Part 1 and Part 2

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  1. BE 105, Lecture 10 Geometric Properties II Part 1: Bone, continued

  2. post cranial, axial cranial flexible rod that resists compression network of flexible linkages

  3. inactive muscle laterally flexible, but resists compression active muscle How to make a fish ‘back bone’ head fin muscle

  4. tunicatelarva

  5. Garstang Hypothesis

  6. early tetrapods

  7. How do bones articulate? joint types

  8. Four bar system

  9. Four bar system e.g. 4 bar system

  10. 4 bar system

  11. F Force shear stress, t = force/area shear strain, g = angular deflection Area g DL A L s = force / cross sectional area e = change in length / total length E = s/e G = t/g E = Young’s modulus, s = stress, e = strain G = Shear modulus, t = shear stress, e = shear strain Part 2: Torsion and Shear For a given material, what is relationship between E and G?

  12. Engineering units Force force Area stress (s) = F / A 0 strain (e) = D L / L 0 DL L length But…what if strain is large? Area will decrease and we will underestimate stress. True units: stress (s) = F / A (e) strain (e) = ln ( L / L 0) 1 L dL = ln ( L / L 0) strain (e) = ‘Engineering’ vs. ‘True’ stress and strain

  13. for an isovolumetric material (e.g. water) where n is Poisson’s ratio E G = 2(1+n) Poisson’s ratio also tells us relationship between shear modulus, G, And Young’s modulus, E: y x z • The ratio of ‘primary’ to ‘secondary’ strains is known as: • Poisson’s ratio, n: • n = e2/e1 • n measures how much a material thins when pulled. Simon Denis Poisson (1781-1840)

  14. DT E DL G = 2(1+n) L T Material n Incompressible materials (e.g. water) 0.5 Most metals 0.3 Cork 0 Natural rubber 0.5 Bone c. 0.4 Bias-cut cloth 1.0

  15. Mlle Vionnet ‘bias-cut’ dress gravity

  16. fiber windings

  17. compression apply torsion tension shear r dA where J = polar second moment of area J = ò r2 dA = ½ pr4 (solid cylinder) R 0 q L How to measure J? q = ML/(GJ) x F M = Fx cantilever beam tension compression GJ = Torsional stiffness EI = Flexural stiffness

  18. Bone fractures

  19. compression apply torsion tension Bones fail easily in tension: G (compression) = 18,000 MPa G (Tension) = 200 MPa Bone is a a great brick, but a lousy cable!

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