Homework_6_Solutions

Homework_6_Solutions - 14:125:208 Introduction to...

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Unformatted text preview: 14:125:208: Introduction to Biomechanics Spring 2007 Homework Assignment #6 Due 3/27/07 Problem 2: Two cylinders are subjected to an equally distributed load F = 6 kN in two different configurations. The aluminum (gray) rod (E = 69 GPa) has a diameter of 25 cm; the steel (purple) rod (E = 200 GPa) has a diameter of 10 cm. For both the parallel and series configurations, calculate the (a) strain in the aluminum rod (b) strain in the steel rod (c) the total deformation (d) the force carried in each rod, and (e) the stress in each rod. (f) If the parallel model was a composite material, what would the effective modulus be (in other words what is the relationship between total stress and total strain)? (g) Why is it difficult to generalize a modulus for the series model? ( ) ( ) 2 2 2 2 2 2 9 9 0491 . 125 . 14 . 3 00785 . 05 . 14 . 3 10 69 10 200 m r A m r A Pa E Pa E Al Steel Al Steel = ⋅ = = = ⋅ = = × = × = π π For the element in series N P P Al Steel 6000 = = (a) 6 10 3 10 77 . 1 10 9 . 6 10 3 . 122 3 . 122 0491 . 6000 − × = × × = = ⇒ = = Al Al Al Al E kPa σ ε σ (b) 6 11 3 10 82 . 3 10 2 10 3 . 764 3 . 764 00785 . 6000 − × = × × = = ⇒ = = Steel Steel Steel Steel E kPa σ ε σ 14:125:208: Introduction to Biomechanics Spring 2007 Homework Assignment #6 Due 3/27/07 (c) The total strain and deformation ( Δ L total ) are oSteel Steel oAl Al total Steel Al total L L L ε ε ε ε ε + = Δ × = × + × = + = − − − 6 6 6 10 59 . 5 10 82 . 3 10 77 . 1 (d) The force carried in each rod is 6000 N (e) The stress in each rod was calculated above to be 122.3 kPa in the Al rod and 764.3 kPa in the Steel rod. For the element in parallel (a,b) 6 11 6 10 11 10 10 21 . 1 10 2 00785 . 1899 10 21 . 1 10 9 . 6 0491 . 4101 4101 1899 16 . 3 16 . 2 6000 16 . 2 10 2 00785 . 10 9 . 6 0491 . 6000 − − × = × ⋅ = = × = × ⋅ = = = ⇒ = ⇒ = + = = × ⋅ × ⋅ = = = ∴ = = + = = = Steel Steel Steel Steel Al Al Al Al Al Steel Steel Steel Steel Steel Steel Steel Steel Al Al Steel Al Steel Steel Steel Al Al Al Steel Steel Steel Steel Al Al Al Al Steel Al Steel Al E A P Check E A P N P N P P P P P P E A E A P P E A P E A P E A P E A P P P N P ε ε ε ε ε ε (c) The total deformation is ε *L o (d) The force in each rod was found to be 1899 N in the Steel Rod and 4101 N in the Al rod (e) The Stress in each rod is kPa kPa Steel Al 242 00785 ....
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This note was uploaded on 01/31/2012 for the course BIOMEDICAL 208 taught by Professor Zhann during the Spring '11 term at Rutgers.

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Homework_6_Solutions - 14:125:208 Introduction to...

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