Product moment of inertia of an inclined section of a beam

[emRage]

Hi guys,

I would like to derive the Ixy equation from simple integration and I can't seem to get the right answer (third equation down the picture). I seem to be able to derive Ixx and Iyy easily but product moment of area requires first moment of area to be calculated and I just don't know how to do that on an inclined section.

Any help would be apprecited on this issue.

Thank you.

 

[tiny-tim]

Welcome to PF!

Hi emRage! Welcome to PF!

Is the rod in the x-y plane? And what is t?

ok, you need to prove that I_xy = L³t(sin2θ)/24.

Show us the integral you have for this. ​

 

[emRage]

This one I've figured out!

x = cos(theta) . s
y = sin(theta) . s
dA = ds . thickness
limits for s = L/2 and -L/2

Thanks anyway!