I'm at uni starting off engineering, and I'm looking for a walk through in this algebra involved in the second moment of area. While I know it's probably pretty basic I'm undertaking a bridging course to try and keep up with my maths.
Here's a picture of the most relevant lecture slide discussing the problem.
I'll type out the steps they undertook to get the final formula for the second moment of area for a rectangle.
On the next page we take the integral of this, which I can do fine.
1. with limits +h/2 and -h/2
Taking it further we end up with
and finally we take it to the step
Ok, I can understand a bit about this but here are my questions.
- Why are the limits h/2 and -h/2, isn't this simply the middle of the rectangle?
- Why is , where does the come from?
- I understand that the is , but where / why does the b jump in with step 1? why are we multiplying it by b?
Any help is greatly appreciated.