Stress Concentration Factor Estimator
A geometric discontinuity — a hole, fillet, groove, keyway or shoulder — forces stress to flow around it, raising the local stress well above the average (nominal) stress on the section.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the nominal stress σ_nom — the average stress on the section, as you would calculate it from F/A or M/Z ignoring the notch. Use a ± sign for compression.
- Either type a stress concentration factor Kt from a Peterson/Roark chart, handbook or FEA, OR leave Kt blank and enter the hole diameter d and plate width W to estimate Kt for a holed plate in tension.
- Read off the peak local stress σ_peak = Kt × σ_nom and compare it to the material yield/ultimate strength with an adequate factor of safety.
How it works
A geometric discontinuity — a hole, fillet, groove, keyway or shoulder — forces stress to flow around it, raising the local stress well above the average (nominal) stress on the section. The stress concentration factor Kt captures this: σ_peak = Kt × σ_nom, where σ_nom is the nominal stress you compute ignoring the discontinuity and σ_peak is the theoretical maximum elastic stress right at the feature. Kt is purely geometric (it does not depend on the material) and is always ≥ 1.
When you don't supply Kt, this tool estimates it for the common case of a transverse circular hole in a finite-width plate loaded in tension, using the Heywood/Peterson approximation Kt = 3 − 3.14(d/W) + 3.667(d/W)² − 1.527(d/W)³ referenced to the gross-section stress. As the hole shrinks (d/W → 0) Kt approaches 3, the classic value for a small hole in a wide plate. For other geometries (fillets, grooves, stepped shafts) read Kt from the appropriate Peterson/Roark chart or an FEA and enter it directly.
Worked example
Bar with a central hole in tension. A steel plate 50 mm wide carries a nominal (gross-section) tensile stress of 80 MPa and has a 10 mm transverse hole. With d/W = 0.20 the estimator gives Kt ≈ 2.435, so the peak local stress at the edge of the hole is σ_peak = 2.435 × 80 = 194.79 MPa — nearly 2.4× the nominal stress and the location where a fatigue crack would start.
Common mistakes
- Mixing up nominal-stress conventions. Some charts define Kt relative to the NET-section stress (through the reduced area at the hole) and others to the GROSS-section stress. This tool's built-in estimate is gross-section; make sure your σ_nom and Kt use the same reference or the peak stress will be wrong.
- Treating Kt as a fatigue factor. Kt is the theoretical ELASTIC peak. For fatigue you normally use a fatigue notch factor Kf, which is smaller than Kt (Kf = 1 + q(Kt − 1) with notch sensitivity q ≤ 1). Using Kt directly for fatigue is over-conservative for many materials and under-conservative near yield.
- Assuming the peak stress is real once the metal yields. In ductile metals local yielding at the notch redistributes stress, so the true peak is lower than Kt × σ_nom under static load — but the elastic Kt still governs fatigue and brittle fracture.
Frequently asked questions
What is the difference between Kt and Kf?
Kt is the theoretical (geometric) stress concentration factor — the peak elastic stress divided by the nominal stress, depending only on shape. Kf is the fatigue notch factor, the ratio of the fatigue strength of a smooth specimen to that of the notched part. Kf is generally smaller than Kt because real materials have a notch sensitivity q (0 ≤ q ≤ 1): Kf = 1 + q(Kt − 1). Use Kt for peak-stress checks and Kf when assessing fatigue life.
Why does Kt approach 3 for a small hole?
For an infinitely wide plate with a small circular hole in uniaxial tension, elasticity theory gives an exact peak stress of three times the far-field stress at the hole edge, so Kt = 3. As the hole grows relative to the plate width, the finite-width correction changes Kt — the Heywood/Peterson formula used here captures that trend.
Can I use this for a stepped shaft or a fillet?
Not with the built-in geometry estimate, which is specific to a holed plate in tension. For shoulder fillets, grooves, keyways or stepped shafts, look up Kt for your specific r/d and D/d ratios in a Peterson or Roark chart (or run an FEA) and enter that Kt directly — the tool will still compute σ_peak = Kt × σ_nom.
Is this suitable for final design?
No. This is a guidance/estimate tool. Stress concentration factors, notch sensitivity and fatigue assessment must be verified against the relevant standard (AS, Eurocode, AISC, etc.) and signed off by a competent structural or mechanical engineer.
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