Bolting

There may be lots of technical jargon and mathematical formulas that some people will offer but I think there is a very easy answer to this question.

The recommended minimum depth is equal to the thickness (height) of a nut for "that" size bolt (which is often the same as the diameter of the bolt itself).

As PP said it is complicated and depends upon the material of the nut (ie the tapped hole) , the recommended torque (or to be precise pre-load - which is again decided by the bolt grade)

However in our company, as a thumb rule, we go for 1.25 to 1.5d (where d is the size of bolt, we are metric) for normal carbos steels and 8.8 grade. ie for M24 we go for 36 deep full tapped hole (= engagement) preferably , minimum being 30mm.

For grade 12.9 it is 2d and above.

To be approximate you can take the tensile strength of them and the ratio will give you the engagement. Not precise (a lot of other modulus and strength are involved, but quick for a safe thumb rule - avoids the thread stripping with sufficient factor of safety)

PP's/Guest's answers look OK to me.

Always heard that 3 threads was enough. Don't have any books here to reference.

That is correct the fact is first 3 threads take about 75% of the load.

Thread#1 - typically 33%

Thread #2 - 23%

Thread #3 - Typically 16%

Thread #4 - 11%

etc

One of the links is here.

But in case of overload, before stripping, they yield, and that changes the loading pattern and makes it more uniform.

Also, the above is just a thumb rule we apply. The actual calculations differ and is much more complicated, however as I mentioned, this thumb rule ensures that the failure is by tensile mode and not thread strip.

There is no "rule of thumb".

The answer to your question depends on the dynamics of the joint and how much clamp load must be generated and retained. You can't take a shortcut: You need to do a proper and full joint analysis.