ME/BioE C176 Final Exam, Spring 2001
Name:
__________________________________
Page 1 of 10
Thursday, May 17, 12:30–3:30 PM, 2001.
Answer all questions for a maximum of 100 points. Please write all answers in the space provided. If you
need additional space, write on the back sides. Indicate your answer as clearly as possible for each
question. Write your name at the top of each page as indicated.
Read each question very carefully!
____________________________________________________________________________________
1. Biomechanical Analysis of the Skeleton [15 points total]
A popular web site (
http://www.backpain.org/exercise.htm
) recommends a number of exercises to help with
back problems. One exercise goes as follows: “Stretch one arm forward in front, at the same time stretching
the opposite leg out behind.” Using a static free body diagram analysis, determine which of either the
erector spinae or stomach muscles for this exercise is active (assume only one muscle group is active), and
estimate its magnitude in terms of bodyweight and any relevant dimensions. State any other assumptions
made in your analysis.
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View Full DocumentME/BioE C176 Final Exam, Spring 2001
Name:
__________________________________
Page 2 of 10
2. Design of Knee Prostheses [28 points total]
A.
[5 points]
For the classical Hertz contact problem for contact between two convex cylinders, where
are the locations of the:
(i) maximum compressive stress?
(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.
i)
∂V
∂x
=
–p
+
k
J
ii)
∂M
∂x
=
–V
iii)
∂
∂x
2
EI
∂
2
J
∂x
2
+
k
J
=
p
where
x
is the distance along the length of the beam,
V
is the shear force acting on the beam,
M
is
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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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