self larnin' goin' on--narrowing rear axle

So today I dragged home a Ferd 9" out of a 78 Mark. Worthless gears, but factory rear disc!! brakes. So I'm gonna try my hand at larning to narrow the housing.

Now I have a lathe and can do basic stuff, so I intend to build a jig. I'm confident I can build the bushings to fit the bearing journals, and two more for the bearing recesses.

My QUESTION concerns the "big bar" through the middle. Why in heck can't I use a big chunk 'o heavy wall tube? Seems to me that would be plenty strong enough to line things up, and..-----if so, what technical term do I want to use to ASK for appropriate tube? That is, STRAIGHT?