Need for a Rear Hoop?

My cousin and I recently bought a near mint '78 XS400 with 6,000 miles for a good price to customize. After timing and carb cleans, the bike runs like clockwork in all rev ranges.
More to the point of this thread, we are now in the process of building it "Brat-ish" style with a flat seat, but have opted for a shorter one person seat. We have chopped the upper frame back to the suspension mounts on both sides so the rails fit the seat, and would like to leave them straight and hidden under the seat.

My concern is that without the original fender support we chopped off or the traditional frame hoop of Brats and cafe racers, the frame will not be sturdy enough at the shock mounts backwards with the rest of the frame stock. Is this the case?

We would both prefer to not have to weld in a hoop for aesthetics and cost, as paying $100 to have a simple straight brace welded in seems awful, and even more for a hoop would be worse, but for safety we would obviously have to bite the bullet. Any recommendations or advice go on would be appreciated.

The "bridge" between the frame segments (just infront of the shock mounts) is what provides rigidity for the frame at that location. I'm pretty sure the loss of the fender won't compromise the strength of the frame. Coincidentally, I did the same thing (although I removed the shock mounts... ended up having to re-build them) and have a brat seat coming in today or tomorrow. No loop on my bike, but we'll see how that works out.

oh man, I just had this same convo in the garage a few nights ago. I too don't want to waste the $$$ if its just aesthetic. We came to the conclusion its dependent on what seat you run, more as a support for the café hump or up curve a lot of seats seam to have. I'll be following this post.

also completely agree with devastator and the bridge being the main rigidity of the frame.

Exactly my thoughts. Right now with the seat I will be running I think that the bridge will be enough, as it essentially connects the shock mounts directly. I don't plan on going off-roading or jumping any time soon with it, so I don't see why the very back end of the frame with no load on it would be getting twisted even in the most aggressive turns

UPDATE: so we just kind of let it go as is. I have ridden maybe 25-30 miles on it as such, mostly flat streets, no aggressive turns or anything, some minor bumps here and there. The bike seems sturdy, tracks straight, all that good stuff. Plus I think it looks badass. So for the time being, I would say in my unprofessional opinion that a hoop is NOT necessary but would probably be a good idea.