I have built several full size electric guitars using a 1/4 inch steel rod running the length of the fingerboard, all I had to do was to rout the channel for the rod, then I use silicone or a latex type caulk and pipe it down the channel and push the rod into place, make sure the silicone or caulk covers the top of the rod and smooth it down with your scraper or your fingers. Let that cure overnight. Also, make sure that the caulk or silicone is not raised up so the when you put the fingerboard on, it lays flush and has no bumps. This method works great, especially if you have used really good hardwood such as mahogany or maple, but good hard oak or walnut works great too! I guarantee that it will not warp, unless you put really thick gauge strings which will then be too much and you can then not correct the bow in the neck anymore. There is no need for any glue in this situation, the silicone or caulk will dampen any vibrations you might encounter, especially if you use glue or epoxy. I have attached a few pics of the rigs I made using the "Martin method" early years truss rods. I hope all of this helps you and your daughter make an awesome guitar out of that gas can!!!
You are so very welcome, Have a fantastic time building with your daughter, I wish I had someone to build with, but I am alone on my journey, Many blessings and happy playing to you both!! :)
A solid bar reinforcement is simply that, it's not a truss rod, and works in a completely different way. A truss rod allows you to adjust the curvature of the neck by exerting force on the neck, whereas installing a bar reinforcement is creating a composite structure with the intent to create a stiffer and bend-resistant neck. As such, the steel needs to be part for the neck by being a good tight fit and being glued in. Any gaps, especially if its got something soft like caulk or silicone in it will just allow the wood and steel to flex independently, rather than act together. I like solid steel reinforcement (apart from the fact that it can make an instrument neck heavy), but to be fully effective it does need to be glued in with epoxy. Having said that, the shape of the reinforcement and its position in the neck do have an effect on how much strength the steel adds - a narrow deep section will be more effective in resisting bending than a square section, but a square bar will be more resistant to twist.. With a banjo the tension on the strings is much less than a guitar, so it's a moot point as to whether you actually need an additional strength (especially with a good piece of wood such as hard maple, and laminating the neck will really help), but I on long skinny necks I prefer either a fully glued-in steel reinforcement or a 2-way adjustable truss rod.
There is no gap if you rout the channel correctly, I have not had any problems whatsoever with the guitars I have built, and no bending either, even with 11-49 gauge strings, you just have to know what you are doing and to make sure there is no gaps in the routed channel where the rod or square bar is going to go, just like he said, if you glue it in, there is no room for repair in the future.