Tubular Column Moment of Inertia

AI Thread Summary
The discussion revolves around the moment of inertia for tubular columns, questioning the textbook's formula and its derivation. Participants note that the moment of inertia should follow the I = MR^2 formula, assuming uniform mass density, but identify a discrepancy by a factor of 2. The conversation includes derivations for the polar area moment of inertia and specific calculations for a thin ring. A correction is made to the formula for a ring, emphasizing the relationship between inner and outer radii. The thread highlights the complexities in calculating moments of inertia for tubular structures.
SALMAN22
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Can anyone explain why the moment of inertia for a tubular column in that textbook is like so? (take a look at the attachments). It should be (I = MR^2), as far as I know.
 

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I think they are assuming the material has uniform mass density. So the mass is proportional to the area but then they are off by factor of 2.
 
hutchphd said:
I think they are assuming the material has uniform mass density. So the mass is proportional to the area but then they are off by factor of 2.
Can you derive it?
 
hutchphd said:
but then they are off by factor of 2.
For polar area moment of inertia, yes, but for Ix , or Iy, the approximation should be as given.
 
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SALMAN22 said:
Can you derive it?
For a ring,
Ix = Iy =( π/4 ) ( r24 - r14 )

For a thin ring of small thickness t, r Ξ r2 Ξ r1, but r2 = r1 +t.

Substitute into the formula for the ring, process, and eliminate all elements where t has an exponent.

Edit - corrected the formula for a ring
 
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