Ii maximum tensile stress iii maximum shear stress

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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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