Second Moment of Inertia - Area Moment of Inertia

[jazzymechanisms]

The concept of the second moment of inertia is boggling to me, it seem so impossible to grasp the concept to be able to appreciate the problems put upon me.

I have got some information on the second moment of inertia yet i still cannot seem to understand it.

I do not understand why there is an extra y in the expression of I.
i.e. I = integral (y^2) dA

I have consulted my friend about it as well, the only thing he said was that the second moment of inertia is the centroidal area of the whole entity.

It is easy to understand that the if you were to have both the same cross-sectional area, yet you act loads at different directions, i.e. acting perpendicular to the centroidal axis, you will get different results, that is one will be harder and the other will be easier.

I appreciate all of your efforts in explaining the concept to me and I hope someone out there can make it as comprehensive as possible. Coming across a post in this forum, a person said 75% of university work is complex in descriptions, but simple in nature, that i agree. I hope this explanation will be concise and simple.

 

[radou]

You should not loose your head thinking about this - while solving applied mechanics problems, specially regarding strength of materials, you should be able to understand why the second moment of inertia is defined in that particular way it is defined.