Stress Concentration Factor Calculator (Kt) — Elliptical Hole

Formula

How this is calculated

When a plate containing a hole is loaded in tension, the stress field is disturbed and the maximum stress at the edge of the hole exceeds the nominal applied stress. The ratio of maximum stress to nominal stress is the stress concentration factor Kt. For an ELLIPTICAL hole in a large plate under uniaxial remote tension σ∞, the Inglis (1913) solution gives the exact result Kt = 1 + 2(a/b), where a is the semi-axis perpendicular to the applied load and b is the semi-axis parallel to the load. The maximum stress σ_max = Kt × σ∞ occurs at the ends of the a-axis (the sides of the hole transverse to the load).

For a circular hole (a = b): Kt = 3, recovering the Kirsch (1898) solution — a result independent of hole size. For a/b = 2 (wider than tall hole): Kt = 5. As the hole becomes a crack (b → 0): Kt → ∞. For a/b < 0.5 (taller than wide): Kt < 3. At the top and bottom of the ellipse the hoop stress equals σ∞(1 − 2a/b), which can be compressive (negative) — a detail that matters for fatigue crack initiation.

This solution assumes an infinite plate (the hole is small compared with the plate dimensions), isotropic linear-elastic material, and plane stress or plane strain conditions. For finite-width plates, the Kt exceeds the infinite-plate value when the hole is large relative to the plate width. Plasticity at the hole root also reduces the effective Kt in ductile materials under static loading.