Stress Concentration Factor Calculator

A stress concentration occurs wherever a structural discontinuity forces stress to flow around an obstacle. Holes, notches, fillets, grooves, and keyways all act as stress raisers. The peak stress at the discontinuity can be several times higher than the average (nominal) stress in the cross-section.

Stress concentration factor Kt:

sigma_max = Kt * sigma_nom

For a circular hole of diameter d in a flat bar of width W under uniaxial tension, the gross-section Kt follows Peterson’s polynomial (Pilkey and Pilkey, 3rd ed.):

Kt = 3 - 3.13(d/W) + 3.66(d/W)^2 - 1.53(d/W)^3

For an infinitely wide plate (d/W approaching 0), Kt approaches the classical Inglis result of 3.0. As d/W increases toward 1, the net section shrinks and the formula breaks down — use this formula for d/W below 0.8.

Net section stress. The nominal stress can be referenced to either the gross section area (W x t) or the net section area ((W - d) x t). The net section stress is always higher than the gross section stress:

sigma_net = sigma_gross * W / (W - d)

Why it matters for fatigue. Under cyclic loading, cracks initiate at stress concentrations. The stress concentration factor enters the fatigue life calculation directly. A Kt of 3 at a hole reduces the fatigue life of the structure far more than three times, because fatigue life scales roughly as sigma^(-3) to sigma^(-4) for metals.

Reducing stress concentrations. Larger fillet radii at notch roots, relief grooves adjacent to sharp features, and compressive residual stresses from shot-peening all reduce effective Kt in practice.