Understanding the Area Moment of Inertia

The area moment of inertia (also called the second moment of area) defines the resistance of a cross-section to bending, due to the shape of the cross-section. It is a key parameter for the analysis of beams and columns.
In this video I take a detailed look at the area moment of inertia, how's it calculated, and how it's used. I also cover key related topics, including the polar moment of inertia, the parallel axis theorem and Mohr's circle for moments of inertia.
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The Efficient Engineer is a channel aimed at mechanical and civil engineers. The mission is to simplify engineering concepts, one video at a time!
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[@maliakbulut]

Why square of distance? Why we multiply dA with sqaure of distance? What is the physical meaning of square of distance here ?

[@shashankmohan8422]

If we do not take squared distance, some integrals give out zero. This is practically not possible ie it cannot have zero resistance to bending.

[@maliakbulut]

@@shashankmohan8422 Hmm that makes sense. But then, can we say that any even power of the distance will be ok 2, 4 or 6?

[@jamjamme]

dA's contribution to the bending moment about the neutral axis is the tensile stress on dA times the distance between dA and the neutral axis. The tensile stress equals Young's modulus times the tensile strain. For limited curvature, so when no plastic deformation takes place, the strain at dA is linearly proportional to the distance to the neutral axis. So in the contribution to the bending moment the distance has a squared influence, one time as the "length of the lever" and one time because the local strain in bending is linearly dependent on it.

[@TheEfficientEngineer]

Excellent explanation, thank you Jaap. I should have mentioned this in the video. I will pin this comment to the top.

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Haha, well if you want a clear conscience you can always support the channel on Patreon! www.patreon.com/efficientengineer. Glad you like the videos in any case!

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