eli5: Can any engineers explain second moment of area intuitively?
In: 5
Think about a 2 by 4 being used as a bridge over a little ditch. If you lay it flat with the 4” side facing up, when you walk across it it’s gonna bend a bit once you get to the middle.
Now imagine the same beam but you twist it 90 degrees so the 2” side is facing up. It’s gonna be harder to walk across with the smaller face but once you get to the middle intuition says it’s going to bend way less ( think also of bending a ruler with the flat but facing up is easy but it can’t be bent with the sharp edge facing up)
But why?
The simple explanation is that the mass of the beam is further away from the bending axis. Both beams will bend halfway between the top and the bottom but flipping the beam 90 degrees means the top gets further away from the bending axis (i.e it’s 1” away in the first example and 2” in the second)
This is second moment of area. It’s a measure of how concentrated the mass is around the bending axis. Less concentrated means the beam is more resistant to bending (this is why I beams are shaped like that to move all the mass away from the bending axis in the middle.) Take note that as in the first example the same beam can have many different second moment of areas as it depends where the force on the beam is being applied.
I’m not going to explain exactly how to find it but there’s general solutions to find the second moment of area for common shapes (squares, triangles etc) and a complicated method for any shape. Feel free to ask questions if you don’t understand and I’ll try get back to you.
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