I would avoid loading the fastener in bending if at all possible, my experience has been that it will be dificult to get the fastener to pass analysis without resorting to detail FEA and testing.
As for bearing (tensile?) stress and shear stress you could look in ASME B1.1, it has a section on design.
You want to think about the effects of combined loading, both bending, shear and normal stress at the weakest part of the bolt. On another note, below the hook lifting devices are covered under ASME B30 and there is another ASME document called ASME BTH-1-2005 which is titled "Design of Below the Hook Lifting Devices". Make sure you read through ASME B30 to see where your device falls under the standard. Some parts of the standard are more stringent with design requirements than others.
Based on the pdf that you uploaded, it looks like:
1) The analysis was not of "bearing, bending and shear" of the bolt, rather it is bearing, bending and shear of the threads.
2) I don't know where the 23/24 factor comes from. Your attached calculations look like it is the loaded height of material at the root of the thread. That would probably be within the realm of reason for a vee-thread, which is what a 2-12UN is, though the drawing throws you since it appears to represent an acme/trapezoidal thread. Assuming that it is a vee-thread, I still don't know where the 23/24 comes from, though it seems like it probably isn't completely unreasonable.
Regardless of all that, my experience has been that all of my fastener failures were broken bolts (either at the nut or the transition from threaded to unthreaded shank), not sheared/stripped threads except for the cases when I have fine threads (which you have in a 2-12UN fastener) along with repeated assembly/disassembly. Though it never hurts to be thorough and do the calcs anyway. (And I suggest that you do.)
Engineering is not the science behind building. It is the science behind not building.
Dang -- I really flubbed my response above. You asked about threads and I somehow read that you were asking about the bolt. You can probably disregard a fair amount of what I wrote.
Engineering is not the science behind building. It is the science behind not building.
looking on the diagram you uploaded the (23/24)*P is shown on the sketch where the bending stress is and it looks to me as it represents the thickness of a single thread at the base and its being treated like a cantilever beam.
Just looking through some old books now but thats what I believe it to be.
Just to confirm the 23/24 * 0.25 pitch is to give the thickness of the single thread at the root and then to use this in the formula that I have from "Schaums Outline Series
theory and problems of Machine Design" to calculate the bending stress at thread root:-
stress (bend) = 3*W*h/(2*pi*n*Rm*b^2)
where W=load
h= thread depth
Rm= mean thread radius
n = number of thread turns taking the load
b = width of thread section at the root
in your example you posted b= ((23/24 )*P)^2
I calculated the root width of your thread and it agrees
to within 8% of ((23/24 )*P)^2
A great reference for bolted joints is "An Introduction to the Design and Behavior of Bolted Joints" by John Bickford.
Generally, if you have sufficient engagement, the threads will not be the long pole in the tent. As a matter of fact, best practice is to have enough engagement to ensure that they are not. A mechanic is less likely to notice a failed thread than, for example, a broken screw or bolt.
Bickford gives a simple formula for determining the static shear strength of threads: F = Su*Ats
Su = Ultimate Shear Strength of the Nut or Bolt Materials
Ats = Cross-sectional Area Through Which Shear Occurs
He then gives several formulas for calculating Ats based on the strengths of the respective nut and bolt materials. His chapter on the strength of threads can be found at this link.
