= Stress concentration factor
{title2=$K_t=\sigma_{\max}/\sigma_{\mathrm{ref}}$}
A \b[stress concentration factor] compares a specified local peak <stress> with a defined nominal reference:
$$
K_t=\frac{\sigma_{\max}}{\sigma_{\mathrm{ref}}}.
$$
It is dimensionless. Both the stress component and the reference geometry belong in its definition; a number quoted without them can be ambiguous. In the infinite circular-hole <Kirsch equations>, the maximum tangential tension is three times the remote uniaxial stress, so that particular reference gives $K_t=3$.<Isotropic Linear Elastic Stress Concentration by MIT Mechanical Engineering>[§4.1, circular-hole result and reference stress]{ref}
For an original finite-plate normalization example, let width $W=50\,\mathrm{mm}$, thickness $t=2\,\mathrm{mm}$, central-hole diameter $d=10\,\mathrm{mm}$ and tensile force $P=1000\,\mathrm N$. The gross and minimum-net reference stresses are
$$
\sigma_g=\frac P{tW}=10\,\mathrm{MPa},\qquad
\sigma_n=\frac P{t(W-d)}=12.5\,\mathrm{MPa}.
$$
If the local peak is stipulated as $28\,\mathrm{MPa}$, the same specimen has $K_{tg}=2.8$ and $K_{tn}=2.24$. In general $K_{tn}=K_{tg}(1-d/W)$ for these reference definitions. This conversion does not solve the finite plate's stress field or predict its peak.
The reference can also be a nominal <bending stress> or another stress appropriate to the applied loading. A factor obtained for axial tension cannot automatically be reused for a bending problem with different boundary conditions.
An elastic concentration factor is distinct from the crack-tip <stress intensity factor>, which has units of stress times square root of length. Nor does $K_t$ by itself supply fatigue life or a failure load: yielding, defects, residual stress and the loading history require additional analysis. The factor describes amplification within its stated elastic model.
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