# Shear failure in threaded fasteners

by krithika
 P: 9 Hi 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
 Sci Advisor P: 5,095 Are you talking shear stresses in the threads or in the bolt shank? You are listing the shear area for failure of the threads.
 P: 9 The shear stress in thread. Thanks for your response :)
 Sci Advisor P: 5,095 Shear failure in threaded fasteners The equation you state is the calculation of the shear area of an external threaded fastener. It is in a slightly different form than what I am used to, but it is fine the way you have it. The easy thing about your question is that you are putting the constraint that the engagement is equal to 1D. That is the way most shear area tables for fasteners is made. The tables list shear area for threads when Le = 1D. Tables like this are available in texts like Bickford and others on fastener strength.
 P: 9 Thanks for your reply. I think the formula what is stated (FOR Shear area) is of no use. What i'm looking for is a derivation or a formula which can say that the bolt wont fail due to shear stress, if Length of engagement between = the dia of the bolt. But unfortunately i couldn't find it anywhere :(. Thanks for your support
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P: 11,155
 Quote by krithika What i'm looking for is a derivation or a formula which can say that the bolt wont fail due to shear stress, if Length of engagement between = the dia of the bolt. But unfortunately i couldn't find it anywhere :(.