Calculating the Moment of Inertia of an Irregular Rod Shape

[mercuri2]

To give you a better idea, I have it drawn out here: http://tinypic.com/r/eq6ln5/6

I am calling the thickness of a rod t and the thickness of the shaft t2. I am using the basic equation Ixx = (integrate over area)(y^2)dA on different sections and then adding them all together, following the guidelines of this website:

http://www.brighthubengineering.com...-inertia-of-irregular-sections-in-five-steps/

I split the shaft into sections, as follows: http://tinypic.com/r/2j5mc8l/6
I calculated the moment of inertia of each section and added them together.

Referring to half of one rod (aka half of the inner diameter) as L, I have come up with this equation:

=2*L^3*(SQRT(2)/2)^3 (three rods)
+2*(t*L*(1-(SQRT(2)/2))) (top of center rod)
+L*t^3/12 (middle horizontal rod)
+(PI()/4)*((L+t2)^4-(L)^4) (hollow cylinder)

Am I going about this the correct way? Any suggestions would be appreciated.

Thank you!

 

[Uncivil]

Calculate the Ixx of the ring
then calculate the Ixx of an entire length of internal bar (spanning the diameter) and multiply by 4

If you want I could show you the process of manually calculating the second moment of inertia of the structure.