Tubular Column Moment of Inertia

[SALMAN22]

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.

 

[hutchphd]

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.

 

[SALMAN22]

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?

 

[256bits]

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.

 

[256bits]

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