Homework: Machine Design
1.
Will the mast described in Homework No. 1 buckle during a magnitude 8 earthquake?
a. Recall the earthquake produced a transverse uniform load of w  ngA resulting from the
inertia of the mast.
b. For the mast assume that half of the mass (i.e., AL / 2 ) is concentrated at the center.
c. The buckling load, Pcr , for a simply supported beam is given by
Pcr 
 2 EI
L2
where I 
 b 4  a 4 
4
.
2. Estimate the critical speed of a toy motor in RPM. You can use the data I found: The mass of the
shaft and armature is 6.9 g, the distance between supports is 24.98 mm, the diameter of the
shaft is 2.01 mm and the shaft is made of steel.
a. Use the internet to find the Young’s modulus and density of steel.
b. The natural frequency (radians per unit time) for a uniform simply supported beam is given
by

2
2
L
EI
.
A
3. Use the internet to find S-N data for an aluminum alloy of your choice. What is the number of
cycles your mast survive is likely to survive in a magnitude 8 earthquake?