Just about all airlines allow 1 carry on and one "personal item", and for lots of folks that don't want to pay for checked baggage, that personal item is just another bag (we can all thank the airlines for adding this extra bit of tension to the boarding process). Your 32" tube would fit in any overhead I've ever seen; the only issue may be when you board the plane - last ones on usually get the dregs when it comes to overhead storage. At least on United, window seats board 1st, aisle seats last.
Regards,
Scott