Hi again Ozzie,
Yes, a lot of the frame structure gets it's strength and rigidity from the shapes of the sheet metal, rather than its thickness.
Another thing... as an experienced welder you probably already know this better than most... When doing this type of work it's important to be careful not to warp the frame. That usually results from too much heat on one section or area at a time. So, working on several areas, each a little at a time, is a better technique. A spot or short stitch weld here, then one on the opposite side, gradually filling things in and allowing things to cool between short welds is a wise precaution.
Most ideal would be some sort of jig to keep the frame squared up while working on it, but that's not a luxury most of us have to work with. Some frame repair shops and custom frame builders use large work surfaces and support structures with various adjustable clamps and vises to try to keep everything straight and square. But, even with it all clamped down tight, overheating one area while welding can still warp or twist things as it cools down.
Even the car's body itself can add to rigidity and is worth checking carefully. Most are also spot welded and seam welding is sometimes used to stiffen things up and strengthen the car.
If you are installing a rollbar or roll cage, careful design and construction of that can really help with frame/body strength and rigidity, too. I'm planning a roll cage for my TR4 that will bolt to the frame in 6 places (maybe more) and also tie to the body at several points.
How much is needed on your car is up to you, depends on how you plan to use the car ( street only? vintage racing? maybe some autocross?) and there are still some very different theories about chassis setup. A really stiff, rigid frame/body assembly might make for a rougher and more uncomfortable ride, but may be like "riding on rails" through fast corners. Some cars are instead designed to flex a bit and have their chassis "tuned" with that in mind (Lotus, for example).
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