Arch back bracing

Not quite sure what you are asking, but if you are referring to a domed back, you use a radius dish to sand the curve into the braces. The braces are then glued to the back using the same radius dish as a form and a go bar deck. If you are referring to an arch top (carved top) type of instrument, that is a whole different process for fitting the braces to the top, the back does not have any.
Brad
 
I put a compound radius in by arching each brace (so it's flat on the surface facing the sound hole and arched where it glues to the back) to give me the side to side arch, and then get the fore and aft curve by making the braces a different height. But I also sand a fore and aft curve into the sides, so I don't need to make much difference in the arch height for the different braces, except they are obviously higher in the middle of the back than toward the neck and tail blocks. When the back is glued on I clamp it to conform to the arch induced by the bracing. I do this by eye, rather than using a radius dish.

Here is an example:

Curved back.jpg

You could glue up a laminate back over an arched form, and in theory that wouldn't need bracing. But I'd still add a brace or two because the string tension is pulling on the back and thus trying to flatten it out.
 
Just to add that I played a Kala thin line soprano at the weekend and it didn't have back braces, just the arched back. Either the laminate was glued up that way, or it was heat pressed to that shape in a mould.

But the sides are so thin that the string tension on the tail block puts very little longitudinal stress on the back (it's a much shorter lever). On a full depth uke I'd be worried about it flattening the arch quite a bit, though I guess you could experiment to discover how much higher you needed to make the arch to compensate for that flattening.
 
That style of back on a ukulele would most often be laminated and not require braces. That's the way I would do it.

If a larger instrument like a arch top jazz guitar then there are braces and it's quite a process to fit them.
 
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