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How can i derive an equation to prove that a bolt wont fail due to shear stress if the length of thread engagement of the bolt with nut is equal to the diameter of the bolt.

I got a formula, but i dont know whether it is useful in this case.

A_s,e = pi*n*L_e*K_nmax*[1/2n + 1/sqrt3*(E_s,min-K_nmax)]

where

n=threads/inch

L_e=Length of engagement

K_nmax=maximum inner diameter of nut

E_s,min=minimum pitch diameter of bolt

thanks

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# Shear failure in threaded fasteners

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