Table of Contents
What Is Stress Concentration?
Stress concentration occurs when the geometry of a structural member causes local stress to increase well beyond the average (nominal) stress. Features such as holes, notches, grooves, fillets, and changes in cross-section create regions of elevated stress. The stress concentration factor, Kt, is the ratio of the maximum stress at the discontinuity to the nominal stress in the member.
Understanding Kt is critical in mechanical design because fatigue failures almost always initiate at stress concentrators. By quantifying the stress amplification, engineers can decide whether to add material, change the radius of a fillet, or select a more fatigue-resistant material. The factor depends solely on geometry, not on material properties.
Formulas & Equations
For a plate with a central circular hole of diameter d in a plate of width W under uniaxial tension:
For a stepped shaft with shoulder fillet (Peterson's approximation):
For a U-notch in a flat bar:
Kt Values for Common Geometries
| Geometry | r/W or r/d | Typical Kt |
|---|---|---|
| Infinite plate, circular hole | 0 (small hole) | 3.00 |
| Plate with hole, d/W = 0.2 | 0.1 | 2.51 |
| Shoulder fillet, r/d = 0.1 | 0.1 | 1.95 |
| Shoulder fillet, r/d = 0.25 | 0.25 | 1.45 |
| U-notch, r/d = 0.05 | 0.05 | 4.47 |
Engineering Applications
- Aerospace: Rivet holes in fuselage panels are a primary fatigue concern. Kt values determine inspection intervals.
- Automotive: Crankshaft fillets, bolt holes, and keyways all require careful Kt evaluation.
- Pressure vessels: Nozzle openings in cylindrical shells create stress concentrations that govern wall thickness.
- Civil engineering: Bridge girders with bolt holes and weld toes require fatigue assessment using Kt.
Frequently Asked Questions
What is the difference between Kt and Kf?
Kt is the theoretical stress concentration factor based on geometry alone. Kf is the fatigue notch factor, which accounts for material sensitivity to notches. Kf is always less than or equal to Kt because not all materials are fully sensitive to geometric stress raisers. The relationship is: Kf = 1 + q(Kt - 1), where q is the notch sensitivity factor (0 to 1).
Can Kt be less than 1?
No. By definition, Kt is always greater than or equal to 1. A value of 1 means no stress concentration (uniform cross-section). Any geometric discontinuity raises the local stress above the nominal value.
How do I reduce stress concentration?
Increase fillet radii, use gradual transitions in cross-section, add relief holes near sharp corners, smooth surface finishes at critical locations, and avoid abrupt geometric changes. Even small radius increases can significantly reduce Kt.