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I know how to calculate the bolt capacity for tension and shear, also how to check bolt bearing against different elelment such as steel or aluminum.

There is a hanging bolt by which a bar is hanging and the bolt subject to pure tension loads.

How can I calculate the force will make the bolt to fail the thread and come out of the nut?

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    $\begingroup$ tensile load is simple stress vs material strength. In practice, bolts usually fail not via their threads. Few bolts experience shear stress, as the shear load is held by friction of the joined surfaces. $\endgroup$
    – Tiger Guy
    Commented Nov 1, 2023 at 13:35
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    $\begingroup$ It doesn't pull out of the nut unless the threads are badly damaged. The bolt will snap off near the nut or just at the nut. Bolts are designed to handle all the tensile strength of the bolt. There are different nuts for different grades of bolt. $\endgroup$
    – Phil Sweet
    Commented Nov 1, 2023 at 18:31
  • $\begingroup$ erm, I meant nuts are designed to handle all the tensile strength of the bolt. $\endgroup$
    – Phil Sweet
    Commented Nov 2, 2023 at 19:43

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Nuts are designed to grip the bolts with greater force than the bolt's tensile strength. So theoretically pull out tensile force T is, $$T_{bolt}=Area_{bolt}*\sigma_{y_{bolt}}$$

Depending on the application there are code factors applied.

Here is an AISC commentary article on bolt codes. source

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Approximately the force in bolt $$ F = A \cdot \sigma, ~A= \pi d^2/4$$ Shear Load $$ F_s = \pi \cdot d \cdot L_{nut}$$ For nut to hold $$ F_s < F.$$

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