eli5: Can any engineers explain second moment of area intuitively?
In: 5
Imagine putting a simple beam across a gap and walking out into the middle of it so as it bends. You’ll see that the top surface compresses and the bottom stretches. The middle stays neutral. Now imagine you look at very thin length ways sections of that beam. The section right at the bottom stretches the most and slowly, as you look at each section in turn, they stretch a little less until the middle section which neither stretches nor compresses, from there they compress a bit more all the way to the top which compresses the most.
In other words how much they have to stretch or compress depends on how far they are from the middle section. Now we know that compressing or stretching any substance takes force. And we know that relationship between how much you strech or compress most substances is linear in the elastic range. Finally we know that torque is a product of force and the distance from the rotational centre.
So if you consider each of those sections earlier as a spring with it’s (k) spring constant dependent on the total area, how much it stretches dependent on how far it is from the middle section, you can see that the torque, or moments, it applies to resist bending will be it’s area times the distance from that middle section squared. If you make these sections infinitesimally small and add them all together you get an accurate figure in m^(4) showing how resistant to bending around the middle axis (called the neutral axis) the whole shape is. In other words you integrate the area with respect to the x axis squared
Sometimes the beam won’t be bending around the neutral axis, in this case you can just integrate to the new axis or use a formula that allows conversion.
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