I have always wondered why one would build a bolt-on neck, and then glue things. Isn't the idea/usefulness of a bolt-on that the neck can easily be removed? I've had to do it a couple of time to effect repairs, like a parlor guitar that got its top crushed (a week-and-a-half after I sold it, don't ask). Take neck off (easy), put on new top.
But this thread got me to thinking about how much force is really on that bolt. How much force from the string tension does it really need to counteract?
A diagram of the forces is shown below.
We have long beam, the neck, with a shorter beam, the neck heel, at right angles.
N - the length of the long beam
H - the length of the short beam
The long and short beams are attached, and pivot around point P where the top of the neck hits the instrument body.
A force F (the string force) is applied to the outer end of the long beam, offset to the neck at angle A.
This induces in the long beam (neck) a rotational force S.
A corresponding opposite force on the short beam B is such that it balances the rotational force S.
With help from my son at MIT, this is a simple torque problem. The force on the bolt, B is:
B= F*sin(A)*N/H.
Using a total string tension of 39 pounds for a tenor ukulele, with a neck/body join at the 14'th fret. a string height at the 14'th fret of .14" and a bolt location 1.75" below the fingerboard, the force on the bolt necessary to counteract the string tension is about 4 lbs.
Looking up bolt clamping force, a 1/4" bolt (which is what I use) torqued to 4 ft/lbs, which is about hand-tight plus a quarter to half a turn, yields 500 lbs. of clamping force.
So, just hand-tightening the bolt good and snug way over compensates for any string tension. I currently use a threaded brass insert in the neck to receive the bolt and now feel that this is plenty secure. I also insert a cross-dowel in the neck to give the threaded insert cross-grain to grab but even that is probably unnecessary from a string tension standpoint.