When a bolt is torqued into a tapped hole, two failures compete: the bolt can break in tension, or the internal threads can strip out. Good design makes the threads stronger than the bolt, so this calculator finds the minimum engagement length that achieves that for the material you are actually tapping into.
How it works
First the bolt’s tensile stress area At is found from its thread geometry, then
multiplied by the bolt strength to get its tensile capacity. The engagement
length must provide at least that much thread-shear strength in the weaker parent
material:
At (metric) = 0.7854 × (D − 0.9382 × pitch)²
bolt capacity = At × bolt strength
parent shear strength = 0.58 × parent tensile strength
L = bolt capacity / (pi × D × parent shear × 0.5)
The factor 0.58 is the von Mises shear-to-tensile ratio, and the 0.5 reflects
that only about half of the engaged cylindrical area is load-bearing thread
flank. Because the parent shear strength is in the denominator, a soft material
forces L to grow.
Example and notes
An M10 x 1.5 class 8.8 bolt (830 MPa) into 6061-T6 aluminium (310 MPa tensile) needs roughly 1.9 times the diameter of engagement, near the familiar 2D rule for aluminium, whereas the same bolt into steel of similar strength needs about one diameter. Always round up to a practical drilling and tapping depth, leave a few extra threads for incomplete first turns, and switch to a threaded insert if the result climbs past about 2.5 diameters.