We had one last summer, first time ever, on our 34' TT. We heard a "pop" and I thought "uh-oh," but we were in a construction zone on the interstate and there wasn't a good place to pull over without slowing everyone behind us way down. Within a minute or so, we could see in our mirror shreds of tire flying off, so we knew continuing was not possible. Slow down we did (and luckily the construction zone, which closed off the entire left lane for miles, was not torn up where we were.)
We were lucky - no fire, no damage to the underbelly or the wheel well. The force of the blowout must have gone out the side of the tire & away from the TT. Ditto Terryallen, we didn't feel it in the steering (or braking) either.
End of the story: we waited (quite a while) for someone to come help, called through Good Sam ERS. The guy that came was able to change our tire & put on the spare, but he was missing the part needed to inflate the spare (our fault, we should have done that). He led us to a tire store at the next exit, though, and we were able to get the spare inflated, plus buy a new tire & have it mounted, and be on our way.