TS Brace,
Don't know of any direct publications that deal with this other than what you might find through AISC.
One thing to note, though. If you're trying to add to your radius of gyration by adding concrete, you need to remember that the r is based on the square root of I / A. To increase r, you need to add to I in a way that I increase faster than A. To add to I, you can go non-composite with the concrete, but it would only amount to the transformed concrete by itself, not using the total shape of the steel and concrete.
So the new I would be Is plus Ic.
In addition, the Ic by itself may not do you a whole lot of good as a singular piece of concrete within the tube as it will likely crack at a very low flexural stress. Thus, composite action is really required to be effective in adding to your "r".
I didn't notice the I2.4 section...thanks for pointing that out. Is there a way you can use a cap plate (per chandr) to create a bearing reaction at each end?