Stress Concentration — Kt, Kf & Fatigue Design Implications

Stress concentration factors (Kt) for holes, fillets, notches, and welds in structural steel. Fatigue notch sensitivity (Kf), Peterson chart values, and AISC fatigue category mapping.

What is stress concentration?

Stress concentration is the localized increase in stress that occurs at geometric discontinuities — holes, notches, sharp corners, cross-section changes, and weld toes. The theoretical stress concentration factor Kt is the ratio of peak local stress to nominal (average) stress in the net section:

Kt = sigma_peak / sigma_nominal

For static loading of ductile steel, stress concentrations have limited effect because local yielding redistributes stress. However, for fatigue loading and brittle fracture assessment, stress concentrations dominate the design. A bolt hole with Kt = 3.0 means the local stress at the hole edge is three times the average stress — this is where fatigue cracks initiate.

Common Kt values for structural steel details

Static vs fatigue — why it matters

Under static (monotonic) loading, structural steel grades (A36, A992, Grade 300) are ductile enough that local yielding at stress concentrations simply redistributes load to adjacent material. The member reaches its full plastic capacity regardless of the hole or notch. This is why AISC 360 and AS 4100 allow net section tension rupture checks based on uniform stress across the net area, without applying Kt.

Under cyclic (fatigue) loading, the story is different. Fatigue cracks initiate at the point of highest stress range, which is always the stress concentration. Even if the nominal stress range is well below yield, the local stress range at Kt = 3 exceeds yield, and repeated plastic cycling drives crack growth. This is why fatigue design is governed by detail category, not member strength.

Fatigue notch factor Kf

Not all of the theoretical Kt is effective for fatigue because the stress gradient at a sharp notch is steep — the high stress only exists in a tiny volume that may not contain a critical flaw. The fatigue notch factor Kf is:

Kf = 1 + q x (Kt - 1)

where q is the notch sensitivity factor (0 to 1). For structural steel:

• Mild steel (Fy = 250 MPa): q is approximately 0.75-0.85 for r >= 3 mm, dropping to 0.5-0.6 for r = 1 mm.
• High-strength steel (Fy = 690 MPa): q approaches 0.95 for r >= 3 mm. High-strength steels are more notch-sensitive.

For a 20 mm diameter bolt hole (r = 10 mm) in Grade 350 steel: Kt = 2.5, q = 0.88, Kf = 1 + 0.88 x (2.5 - 1) = 2.32.

Worked example — fatigue life at a cope

A W16x40 beam with a bottom flange cope (radius r = 25 mm) at the connection. The cope creates Kt = 2.5. The beam supports a crane trolley inducing a nominal stress range at the cope of delta_sigma_nom = 50 MPa.

Local stress range = Kt x delta_sigma_nom = 2.5 x 50 = 125 MPa.

Per AISC 360 Appendix 3, Table A-3.1, a coped beam is Fatigue Category E (if the cope is flame-cut and not ground smooth). The allowable stress range for Category E at 500,000 cycles is 44.8 MPa (nominal). Since 50 MPa > 44.8 MPa, the detail fails the fatigue check at 500,000 cycles.

Solution options: (1) grind the cope radius smooth to upgrade to Category D (allowable 55.2 MPa at 500,000 cycles — marginal), (2) increase the cope radius to r = 50 mm to reduce Kt, or (3) reinforce the cope with a reinforcement plate.

Code comparison — fatigue provisions

AS 4100 and EN 1993-1-9 use the same detail category numbering system (the number represents the characteristic stress range at 2 million cycles in MPa). This makes cross-referencing between Australian and European practice straightforward.

Common pitfalls

• Ignoring stress concentrations at fatigue-loaded details. Static design does not require Kt, but fatigue design is entirely governed by detail category, which is a proxy for Kt. Treating a fatigue check like a static check leads to grossly unconservative designs.
• Assuming grinding removes stress concentration entirely. Grinding a weld toe reduces Kt from perhaps 3.5 to 1.5-2.0 and upgrades the fatigue category by one or two steps. It does not eliminate the stress concentration.
• Using theoretical Kt for fatigue instead of the detail category approach. AISC Appendix 3 and EN 1993-1-9 already incorporate the stress concentration effect into the detail category S-N curves. Applying Kt on top of the detail category double-counts the effect.
• Specifying tight cope radii without considering fatigue. A 12 mm cope radius at the bottom flange of a crane beam creates Kt approximately 4.0 and drops the fatigue category to E or E'. Specify minimum 25-50 mm radii and drill the end of the cope.

Run this calculation

• Section Properties Database
• Beam Calculator

Related references

• Steel Fatigue Design
• Fracture Toughness
• Weld Joint Types
• Residual Stress
• How to Verify Calculations
• steel beam capacity calculator
• column capacity calculator

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.