Unformatted text preview: ss? (ii) maximum tensile stress? (iii) maximum shear stress? Describe a theory that explains how these stress locations may influence the cracking and delamination
damage mechanisms in the plastic component of a total knee prosthesis. B. [15 points] Starting with an equilibrium analysis of an element of the beam of length dx, derive the
following equations for bending of a beam on an elastic foundation. State clearly all the
assumptions.
∂V
i)
= –p + kJ
∂x
∂M
ii)
= –V
∂x
∂
∂2 J
EI
+ kJ = p
∂x2
∂x2
where x is the distance along the length of the beam, V is the shear force acting on the beam, M is
the bending moment acting on the beam, p is a uniformly distributed force/length acting on the
beam, k is the foundation modulus, EI is the flexural stiffness of the beam with respect to its neutral
axis, and J = J(x) is the displacement of the neutral axis of the beam.
iii) Hint: For bending of a beam with “small” deformations of the neutral axis J, the following holds:
d 2J
M = EI 2
dx Page 2 of 10 ME/BioE C176 Final Exam, Spring 2001 Page 3 of 10 Name:__________________________________ ME/BioE C176 Final Exam, Spring 2001 Name:__________________________________ C. [4 points] What is the difference between “stiff” vs. “rigid” behaviors in the context of beam on
elastic foundation theory? D. [4 points] Indicate if the maximum contact stress in the artificial knee joint (Figure) should
increase or decrease if:
a) Rf is decreased (all else constant)
b) Rt is increased (all else constant)
c) t is increased (all else constant)
d) the modulus of the plastic is decreased (all else constant) Figure: Frontal vie...
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 Fall '10
 Lee
 Shear Stress, rf, Erector Spinae, C176 Final Exam, Design of Knee Prostheses, ME/BioE C176 Final

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