Second moment of area, storing of energy.

[Pellefant]

I want to point out that this is not a Homework or Coursework question. in wiki we can read the following under the chapter intution:

http://en.wikipedia.org/wiki/Second_moment_of_area

Assuming linear elasticity, the restoring stress that any point in the beam will provide, is proportional to the strain it experiences. This stress-strain relationship can be described by Hooke's law. The energy will be proportional to the square of the strain.

So can anyone explain why the energy is proportional to the square of the strain.

/Thank you

 

[Doc Al]

Try calculating the work required to produce a given strain. See: http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html"

 

[Pellefant]

Thank you!

But why do you integrate hooks law when you do not integrate potential energy; m*g*h?

 

[Doc Al]

But why do you integrate hooks law when you do not integrate potential energy; m*g*h?

The potential energy is found by calculating the work done in both cases.

For spring potential energy you integrate the spring force (kx) over the distance; for gravitational potential energy you integrate the gravitational force (mg) over the distance. That's where m*g*h comes from.