16.21 ­ Techniques of structural analysis and
design
Spring 2005
Final Exam
Instructors: Raúl Radovitzky
May 17, 2005
Student’s name:
Question Grade
1) 30 points
2) 30 points
3) 30 points
4) 10 points
Total:
1
Student’s name:
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ω
A=A
x
0
[ 1 − x / (2 L) ]
Density:ρ
L
The structure of the figure is made of an elastic material with Young’s Modulus E, and mass
density ρ and rotates at an angular velocity ω. (Questions start on the next page)
16.21, Spring 2005
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Final Exam
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1. (30 points) Compute an approximate value of the radial displacement at x = L. Use an
approximate method of your choice. Discuss the reason of your choice of method and
your additional assumptions, if any.
16.21, Spring 2005
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Final Exam
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16.21, Spring 2005
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2. (30 points) Show how you can use an energy method to compute the exact value of the
radial displacement at x = L. You do not have to (but are welcome to) evaluate the
final expression, if it is too complex to do by hand.
16.21, Spring 2005
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16.21, Spring 2005
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3. (30 points) From the approximate solution compute an approximation of the stress at
the rotating axis (x = 0) and compare with the exact solution. Why can you compute
the exact solution in this case without much effort?
16.21, Spring 2005
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16.21, Spring 2005
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4. (10 points) What is the maximum angular velocity attainable before the material starts
to deform plastically if the structure has a length L = 2m and is made of an Aluminum
with mass density ρ = 2700 Kg
and yield stress σ0 = 200M P a.
m3
16.21, Spring 2005
End of Final Exam
Final Exam