Thread Engagement Length

If mating internal and external threads are manufactured of materials having equal tensile strengths,
then to prevent stripping of the external thread, the length of engagement should be not less than that given by

L_e: length of engagement (inch)
A_t: tensile stress area (inch²)
E_smin: minimum pitch diameter of external thread for the class of thread specified (inch)
K_nmax: maximum minor diameter of internal thread (inch)
n: number of threads per inch

Stripping of Internal Thread

When the internal thread is made of material of lower strength than the external thread

Q: length of engagement (inch)
A_s: shear stress area of external thread (inch²)
A_n: shear stress area of internal thread (inch²)
D_smin: minimum major diameter of external thread (inch)
E_nmax: maximum pitch diameter of internal thread(inch)
TS_e: tensile strength of external thread material (pound/inch²)
TS_i: tensile strength of internal thread material (pound/inch²)

Machinery Handbook, 28th Edition