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I've wondered about this for a while but never seen an explanation. Why do builders scallop braces rather than simply making them lighter? Obviously, there is a point where the structural strength would be equal. Is there something else associated with scalloping besides changing the stiffness of the brace?

Since the practice of scalloping braces is so well established, I am afraid I'm missing something obvious.

Thanks,
Gerry

scalloping allows you to control the top differently than lighter braces. When you study the top you have different forces being applied.
From the neck block to the bridge we have a compressive load and on top of that there is a rotational force also. The strings are pulling the bridge towards the nut and the neck on to the guitar. Then on top of that , the ball end of the strings are pulling up , this is causing a rotation force.
Below the bridge we have a tensional load.

What this tell us is that the forces are working different areas and by scalloping , we can manipulate the bracing to allow to the top to move in different area. In a light brace scheme you can't influence this as you can when you scallop.

Wood is able to take a tension load more efficiently than under compression.

Just consider that bracing is a way to control the top. How you control it for the support and the tone you want is what you must learn. Martin uses a number of bracing schemes 5/16 scalloped 5/16 X standard 1/4 in standard and scalloped.
Wood can be very strong and resilient and we can influence the support and movement by the shape. For an example a brace that is 1 in square is only 1/8 as strong as a brace that is 1/2 by 2 in, yet it has the same amount of wood. By manipulating the cross sectional shape we can use that as a way to control top movement.

So now you can see , you can manipulate the strength of the braces where you need it , and allow the top to move where you want it. Making braces lighter makes it more static and you loose that ability to add stiffness where you want.

John,
Thank you for the explanation. I do see what you mean that the braces can be used to control how much and where the top moves. This of course leads to another set of questions; exactly how can you shape the sound of the guitar using the braces. I don't know if a detailed discussion of a topic like this is possible in a discussion forum since a complete explanation might require a book rather than a few paragraphs.
I've built two guitars to date. The first from a kit and the second from scratch. They both sound good. They are not great mind you, just good. I got this far by following the directions in your videos and searching the discussions here when I had questions. The amount of information and the wealth of knowledge here is very deep. It really is a treasure for a beginning like myself.
Now that I know how to glue a guitar together it's time to pay attention to how to shape the sound. I realize that there is no substitute for experience but I'm looking for a framework. Are there any agreed upon principles that must be followed. I imagine that there are different schools of thought on the details. Is there any literature available on this?

Regards,
Gerry

Your right that topic can fill a book. It is not only the shaping of the braces but the positioning, the number, the wood type, the radius and on and on that go into that formula and let's not forget the top itself must be considered. I would say it all comes under the heading of "top voicing" of which brace shaping is one factor.

the best advice is to go get a good book on top voicing. I could type for a week and not scratch the surface.
Start with proven plans and then you can modify in small steps to learn the cause / effect relationship. The biggest point that I can make is the enemy is weight and dampening.
Find the balance. What makes this so difficult is that we all hear things differently , and what one person like another may not.

John, is there any specific book that you recommend on the subject? I've seen a couple out there but wondering if there is one that explains things best in your opinion.

the guitarmaking is one that I used to start but to be totally honest , the best is to do it. I found for me that once I started building it took me about 14 guitars till I dialed in the sound I liked. The old martin designs are still valid.

I'm sorry John but I don't know what guitar making book you are referring to.
Two authors of books on voicing that I see mentioned the most often are Somogyi and Siminoff. Are there other names in the field?

the book is called Guitarmaking written by Cupiano
check that out. It was written in the 70's and while technology pass surpasses some thing in the book the theory is still very good.