I was looking through NASA's document for "Installation Torque Tables for Noncritical Applications" and noticed their formula for the pullout load of a fastener on a certain material. It goes as follows:
$$P = \frac{\pi\cdot d_m \cdot F_s\cdot L}{3}$$
Where:
- P = pullout load, lbs.
- $d_m$ = pitch diameter of threads, in.
- $F_s$ = material ultimate or yield shear stress, psi
- $L$ = length of thread engagement, in.
Does anyone know what the derivation, or origins for this formula are? It's stated that the /3 is due to a factor of safety. So, the "real" formula would be:
$$P = \pi\cdot d_m \cdot F_s\cdot L$$
I assume the $\pi\cdot d_m$ looks like you get the circumference of a circle with the pitch diameter, then you're multiplying that by the length of the thread engagement, which gives us the area made by a theoretical cylinder made by the pitch diameter and length of thread engagement. Multiply that by the yield strength and we get a maximum force applied over an area which gives us a force. Since stress = force/area, force = stress × area, force = ultimate stress × cylinder. Anyway, that's just my thoughts, was hoping someone who knows more could lend some insight.