ME 176 Final Exam, Fall 1995
Name:
__________________________________________
Page 1 of 10
Saturday, December 16, 12:30–3:30 PM, 1995.
Answer all questions. 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.
(20 points total) Forces and Moments at Joints
A.
[10 points]
Draw a fully labeled freebody diagram of the forearm during a curl exercise (with a
20 kg mass in the hand) that could be used to calculate the
resultant
force and moment acting on
the elbow joint. Include all accelerations in your free body diagram and ignore the mass of the
hand.
B.
[10 points]
Based on your freebody diagram, write out the moment equation of motion (dynamics
equation)
about the elbow joint.
Assume that the elbow joint is fixed in space. Regarding moment
of inertia terms, assume only the value for the forearm about its centroid (
i.e.
this is the only
moment of inertia term that should appear explicitly in your equation).
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View Full DocumentME 176 Final Exam, Fall 1995
Name:
__________________________________________
Page 2 of 10
2.
(25 points total) Bone Mechanics and Beam Theory
A.
[10 points]
When a material such as cortical bone is loaded in pure bending until its collapse, the
neutral axis of bending shifts as the material yields due to the asymmetry of yield strengths of the
bone material. Derive the expression shown here for the distance from the compressive surface of
the beam to the neutral axis,
y
, in terms of the depth of the beam
d
, and the yield strengths in tension
s
t
and compression
c
:
y
=
d
s
t
s
t
+
s
c
Assume elasticperfectlyplastic (Figure 1) behavior of the beam material. The crosssection of the
beam is rectangular, of width
w
and depth
d
, and the beam is loaded in pure bending.
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 Spring '09
 keaveny
 Force, Second moment of area, Tensile strength, Compressive stress

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