liquid steel

Joe Dokes said

I don't know, there are some adhesives by 3M designed for non-structural body panel installation.

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You can find many posts on similar adhesives. Many body shops use them now. They aren't cheap, maybe $40 for a tube and $80 for the special gun. They do always use the caveat "for non-structural repairs", but that could be the lawyers talking rather than a technical analysis.

I hear everybody claim how critical floor pans are to the body structure, but I am a Mechanical Engineer and don't see how one small section of rusted away floor panel compromises the car's integrity. As long as the tranny tunnel is solid and intact and there is sound floor everywhere else to keep the bottom diagonally stiff, and the sills are solid, I doubt it matters. If a 4 door or 2-dr post, it is already much stiffer than a convertible or 2 dr hardtop. If you glue a patch panel down and the glue lines don't break (assuming stiff glue), then it could as well have been a weld line. Either the glue was really strong or (more likely) there was no significant movement that it needed to oppose. Personally, I don't see the glue breaking. Of course Liquid Nails is a different story. That is fairly soft mastic, more like caulk than the referenced products.