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Stress concentration

At holes, notches and sharp transitions the stress becomes locally much higher than the uniformly distributed nominal stress. The factor $K_t$ describes how much higher. This matters especially for fatigue, where local peak stresses start cracks.

\sigma_{max} = K_t\,\sigma_{nom}

local maximum stress

Symbols

$K_t$	stress concentration factor
$\sigma_{nom}$	nominal (uniform) stress	Pa
$\sigma_{max}$	local maximum stress	Pa

Example

A small circular hole in a large plate, $K_t \approx 3$ , $\sigma_{nom} = 50$ MPa:

$\sigma_{max} \approx 150$ MPa.

Smooth transitions with a large radius give a lower

K_t

than sharp corners.

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Part of Strength of Materials: Stress and strain.