Paraphrased rom the Machinery's Handbook Edition 24:
Formulas for Stress Areas and Length of Engagement of Screw Threads.
The critical areas of stress of mating screw threads are: (1) The effective cross sectional area, or tensile stress area, of the external thread; (2) the shear area of the external thread, which depends principally on the minor diameter of the tapped hole; and (3) the shear area of the internal thread, which depends principally on the major diameter of the external thread. The relation of these three stress areas to each other is an important factor in determining how a threaded connection will fail, whether by breakage in the threaded section of the screw (or bolt) or by stripping of either the external or internal thread.
If failure of a threaded assembly should occur, it is preferable for the screw to break rather than have either the external or internal thread strip. In other words, the length of engagement of mating threads should be sufficient to carry the full load necessary to break the screw without the threads stripping.
If mating internal and external threads are manufactured of materials having equal tensile strengths, then to prevent stripping of the the external thread, the length of engagement should be not less than that given by Formula 1:
L
e = 2 X A
t / 3.1416 K
nmax {1/2 + 0.5773
n (E
3min - K
nmax)}
In the formula, the factor of 2 means that it is assumed that the area in shear of the screw must be twice the tensile stress area to develop the full strength of the screw (this value is slightly larger than required and thus provides a small factor of safety against stripping); L
e = length of engagement, in inches;
n = number of threads per inch; K
nmax = maximum minor diameter of internal thread; E
3min = minimum pitch diameter of external thread for the class of thread specified; and A
t = tensile stress area of screw thread given by formula (2a) or (2b) or the thread tables on pages 1530 to 1539 for Unified threads which are based on Formula (2a):
A
t = 0.7854 (D - 0.9743 /
n)
squared
Where D = basic major diameter of threads.
Have fun with the math 'yall.
