Tubular Column Moment of Inertia

In summary, the conversation discusses the moment of inertia for a tubular column in a textbook and the discrepancy in the formula (I=MR^2) due to assuming uniform mass density. The conversation also mentions deriving the formula for polar area moment of inertia and the correct approximation for Ix and Iy. The formula for a thin ring is also discussed and corrected.
  • #1
SALMAN22
12
2
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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  • #2
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.
 
  • #3
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?
 
  • #4
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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  • #5
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
 
Last edited:
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1. What is the definition of Tubular Column Moment of Inertia?

The Tubular Column Moment of Inertia is a measure of an object's resistance to changes in rotation. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

2. How is the Tubular Column Moment of Inertia different from the Moment of Inertia of a solid cylinder?

The Tubular Column Moment of Inertia takes into account the hollow space inside the column, while the Moment of Inertia of a solid cylinder only considers the mass and shape of the outer surface. This makes the Tubular Column Moment of Inertia a more accurate representation of the object's resistance to rotation.

3. Why is the Tubular Column Moment of Inertia important in structural engineering?

The Tubular Column Moment of Inertia is an important factor in determining the stability and strength of a structure. It helps engineers design structures that can withstand external forces and maintain their shape and stability.

4. How is the Tubular Column Moment of Inertia calculated?

The Tubular Column Moment of Inertia can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation. This formula can be applied to different cross-sectional shapes, such as circles, rectangles, and triangles, to determine the moment of inertia.

5. Can the Tubular Column Moment of Inertia be changed?

Yes, the Tubular Column Moment of Inertia can be changed by altering the mass or shape of the object. For example, increasing the thickness of the tube or adding internal supports can increase the moment of inertia, making the object more resistant to rotation. However, changing the moment of inertia may also affect the overall stability and strength of the structure.

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