2

Given a beam ($\rho, A, l$) rotating with angular velocity $\omega$, find the maximum stress in the beam and its location.

enter image description here

I think the maximum stress occurs at the base, because the resultant force is the entire axial force. The total axial force is:

$$F = \int_0^l\frac{m}{l}\omega^2r\ dr = \frac{m\omega^2l}{2}$$ $$m = \rho Al$$ $$\sigma_{max} = \frac{F}{A} = \frac{\rho\omega^2 l^2}{2}$$

Did I do this right?

The follow-up question is, what happens when the beam is extremely thin: $t << l$

I don't know how to answer the follow-up.

Beamy
  • 21
  • 1
  • 2
    Your picture doesn't make a lot of sense. Is this a column with a torque on it? What are the arrows pointing right? – grfrazee Mar 31 '16 at 15:29
  • I agree with @grfrazee's assessment. There is definitely something missing to be able to answer the question. What kind of load is being applied to the column? Is the loading due to its own mass? (Also please don't use lowercase "L" to represent a radial value, it would be preferred to use capital "R" so as to avoid ambiguity with lengths. And ideally don't use lowercase "L" at all because it can be confused with a number of other symbols when handwritten or in a sans serif font) – do-the-thing-please Mar 31 '16 at 15:46

0 Answers0