Keep in mind what structural loads would be altered if the fuselage width were changed. Primarily it would be the column strength of the cross tubes where the wings attach and the tensile strength of the cross tube where the wing struts attach. All others are just basically fillers with respect to changing the fuselage width.
What alloys are used in the original 2+2 or PA-14 fuselage? 1025? Just changing to 4130 would answer your questions. Otherwise just increase the wall thickness of the pertinent tubes.
As I mentioned in an earlier post, most builders I've seen (for pa-style aircraft) tend to put an extra cross-brace up there anyway. I did it in the mid-90s, when I built the first fuselage. It was 1" x 0.049" back then as I recall, which is the same size as the other tubes up there. I would need to confirm that though--I don't have the plans right in front of me.
As to strengthening the structure up there, it would be easy enough to do...yes. And Solidworks would allow you to simulate the deflection(s) for a given load(s), and with a couple of mouse clicks you can simply change the weldment profile to be a different diameter and/or wall thickness...and then just re-run the simulation to check on the stresses and deflections. So it's a true apples-to-apples type of comparison. I'm working on reacquainting myself with Solidworks Simulation now, as I haven't used the simulation aspect in a couple of years. And then of course I'll need to create an accurate model--but that's only a few hours worth of work. So it's definitely something that would not be terribly difficult to do.
EDIT: Forgot to address your materials question. To my knowledge (as the pa-14 aircraft were built 1947-1949), they were built with 1025 mild steel tubing. This is the same as the pa-18 were built, per the original drawings (and now the Northland drawings). So going to 4130 would offer a significant increase in yield and ultimate tensile strength, without even changing a single diameter or wall thickness. For instance some quick math shows me that the yield strength of 4130 is nearly 25% greater than 1025 steel; and the ultimate tensile strength differential is even a bit higher yet.
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