lect11 - Zoology 440 Biomechanics 2007 Lecture 11 More on...

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Zoology 440 Biomechanics 2007 Lecture 11. More on shape and stress: architecture in biology and the design of bones •Recap flexural stiffness,I, and biological beam examples. • The stress distribution on a beam. •The design of mammalian long bones. Project proposals due Friday 27 April No homework this week. E I : Flexural stiffness of a structure F x Neutral axis y tension compression M = ! k y 2 dA = ! /y ! y 2 dA M = I ! /y F x = I ! /y ! = F x y/ I ! = E " " = F x y/(E I) M = F x # (x) = F x 2 (3L-x)/6 EI x F L # (x) = f x 2 (x 2 + 6L 2 - 4Lx)/24 EI x f L http://www.aps.anl.gov/asd/me/Calculators/ElasticBeam2.html
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Stress distributions in biological beams: tree branches Moment M = Fx 2 /3L ! = M y/ I x ! = F x 2 y/ 3 L I I = $ R 4 /4 Tree branches support their own weight, plus the weight of leaves, fruit, etc. How does the design of branches affect the distribution of bending stresses? x
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lect11 - Zoology 440 Biomechanics 2007 Lecture 11 More on...

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