Tubular Column Moment of Inertia

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Discussion Overview

The discussion revolves around the moment of inertia for a tubular column, specifically addressing discrepancies in the formula presented in a textbook. Participants explore the assumptions regarding mass density and the implications for the calculations involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the moment of inertia formula for a tubular column, suggesting it should follow the form (I = MR^2).
  • Another participant proposes that the textbook may assume uniform mass density, indicating that mass is proportional to area, but suggests there may be an error by a factor of 2.
  • A repeated point emphasizes the potential error by a factor of 2, specifically in the context of polar area moment of inertia.
  • A participant provides a formula for the moment of inertia of a ring and suggests a method for deriving the moment of inertia for a tubular column by substituting values and simplifying the expression.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the moment of inertia formula and the assumptions made in the textbook. There is no consensus on the resolution of these discrepancies.

Contextual Notes

Participants highlight potential limitations in the assumptions regarding mass density and the implications for the calculations, but these remain unresolved.

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.
 

Attachments

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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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