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Stress in bolts

A tightened bolt gets a preload force that clamps the parts together. Stress is calculated on the tensile stress area, which is slightly smaller than the area of the outer diameter because the threads take up room. The bolt must stay below the yield strength.

\sigma = \frac{F}{A_s}

tensile stress in the bolt

F_{max} = \frac{f_y\,A_s}{\gamma_M}

largest allowed force with material factor

Symbols

$\sigma$	stress	MPa
$F$	force in the bolt	N
$A_s$	tensile stress area	mm²
$f_y$	yield strength	MPa
$\gamma_M$	material factor

Example

M12 bolt ( $A_s = 84.3$ mm²) with 20 kN:

$\sigma = 20\,000/84.3 \approx 237$ MPa.

Always use the tensile stress area from a table, not the area of the nominal diameter.

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Part of Machine Design: Bolted and welded joints.