What is the second moment of area?

[mzha109]

Hi I'm a second year uni student and we're learning the engineering beam theory, and part of the engineering beam theory requires us to know what the second moment of area is. I've scrawled wiki and the internet but I haven't found anything very helpful.

So my question is, what exactly is the second moment of area?

 

[Rajini]

Hi,
Is this link not useful? particularly for beams:
http://en.wikipedia.org/wiki/Second_moment_of_area
If you want some information about quantum details (not beam):
see Lipkin's sum rules for 1st 2nd and 3rd moment of density of dos.

 

[mzha109]

We wish to describe the effects on beam stiffness due to the cross-sectional shape of the beam as a single number (or, in the case that we want to consider more than one loading direction, as a symmetric tensor, which we can represent as a 2×2 matrix); this will be the second moment of area

That's not particularly descriptive.

And also, the definition of the second moment of area is I_{yy}=\int_A z^2 \, dA

But why is the lower limit of intergration A, and there is no upper limit?

 

[Rajini]

A is not the limit! In that case the integral symbol represents the area of the region A.
It is some part of the cross-section of the beam.

 

[mzha109]

*face palm*

Thanks, I might have some more questions in the near future but I'm done for now.

 

[mzha109]

Hey one more question about the second moment of area. How do you find it for any shape and about any axis? I'm still rather confused about the integral thing and it'd be helpful if someone went through the process of getting the second moment of area step by step.

Thanks.