Moment of inertia (MOI) - Area moment of inertia 1

[MCA1983]

Hello all,

Could you please let me know the significance of area moment of inertia while doing aircraft structural analysis ( eg beam analysis) And also practical importance of MOI..


Thanks

Regards
Manjunathca

 

[3DDave]

https://mathworld.wolfram.com/AreaMomentofInertia.html

says it well enough.

 

[MCA1983]

Hello, I'm not looking for textbook equations or answers.. practical thoughts on MOI.. what happens if it's less or if it's more what will be it's implications..

 

[rb1957]

you're asking about the impact of MoI on beam calcs ? (as opposed to the impact of an airplane's MoI on it's loads)

the equations tell you ... but they are misleading.
MoI is a denominator in the equations, right? so bigger MoI means smaller stress. so far so good
but compact sections (with a smaller "y", in the numerator) have a lower stress (but there is usually a trade-off between y and MoI ... a small "y" from a compact section will probably have a small MoI too).

So the parameter we often use is section modulus, Z = MoI/y.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[3DDave]

The first sentence of the first paragraph told you what it is for. No equation.

The larger the value the stiffer the beam when subject to bending. Observation should have told that much.

 

[sdm919]

The area of a cross-section is a measure of the axial stiffness and strength of the member, that is, how much does it stretch under a given axial load and at what load will it break. The moment of inertia of the cross-section is a measure of the bending stiffness and strength of the member, that is, how much does it bend under a given moment and what moment can it carry before breaking.

If you imagine the cross-section broken up into many small segments, the total area is the sum (integral) of all the segment areas, while the moment of inertia is the sum (integral) of the products of those areas times the square of their distance "y" from a reference axis. Usually the reference axis is chosen as the centroid of the section.

From this definition, you see that HOW THE AREA IS DISTRIBUTED will have a large effect on the moment of inertia (y^2), but no effect on the total area. Put the segments far from the centroid to get a higher moment of inertia. That is the principle behind the shape of an I-section, with material concentrated in the flanges, far from the centroid.

Two sections with the same area can have very different moments of inertia depending on how the material is distributed. Conversely, two sections can have very different areas (and weights) for the same moment of inertia. So we can improve the weight/cost efficiency of our structures by careful consideration of these factors.