Mechanical stress concentration factors describe how holes, notches, grooves, shoulders, and fillets raise local stress above the average stress predicted by simple formulas. Engineers need this cheat sheet because small geometry changes can control yielding, cracking, and fatigue failure. It provides a quick reference for using Kt, Kts, Kf, and notch sensitivity in machine design and structural analysis.
The core idea is that peak local stress equals a concentration factor times the nominal stress. Static analysis commonly uses theoretical stress concentration factors such as Kt for normal stress and Kts for shear stress. Fatigue analysis reduces the theoretical effect using notch sensitivity, so Kf = 1 + q(Kt - 1) and Kfs = 1 + qs(Kts - 1).
Key Facts
- The normal stress concentration factor is Kt = sigma_max / sigma_nom, where sigma_max is peak local normal stress and sigma_nom is nominal normal stress.
- The shear stress concentration factor is Kts = tau_max / tau_nom, where tau_max is peak local shear stress and tau_nom is nominal shear stress.
- Peak local normal stress is estimated by sigma_max = Kt sigma_nom for linear elastic static loading.
- Peak local shear stress is estimated by tau_max = Kts tau_nom for linear elastic static loading.
- For an axially loaded flat plate, nominal stress is sigma_nom = P / A_net or P / A_gross depending on the chart convention used.
- For bending, nominal stress is often sigma_nom = Mc / I at the critical section before applying Kt.
- Fatigue stress concentration is Kf = 1 + q(Kt - 1), where q is notch sensitivity from 0 to 1.
- A larger fillet radius usually lowers Kt, while a sharper notch, smaller hole spacing, or abrupt shoulder usually raises Kt.
Vocabulary
- Stress concentration factor
- A multiplier that relates peak local stress near a geometric discontinuity to the nominal stress in the part.
- Nominal stress
- The average or simplified stress calculated from basic mechanics formulas before local stress concentration is applied.
- Peak stress
- The highest local stress that occurs near a notch, hole, groove, shoulder, or other stress riser.
- Stress riser
- A geometric feature that causes stress lines to crowd together and increases local stress.
- Notch sensitivity
- A material and radius-dependent measure q of how strongly a theoretical stress concentration affects fatigue strength.
- Fatigue stress concentration factor
- The effective concentration factor Kf used for cyclic loading, usually lower than Kt because materials are not perfectly notch sensitive.
Common Mistakes to Avoid
- Using Kt directly for fatigue design, which is wrong because fatigue usually requires Kf = 1 + q(Kt - 1) instead of the full theoretical value.
- Mixing gross area and net area nominal stress, which is wrong because stress concentration charts are based on a specific nominal stress convention.
- Applying a chart outside its geometry range, which is wrong because Kt depends strongly on ratios such as r/d, D/d, hole diameter, and plate width.
- Ignoring the fillet radius in a shoulder or groove, which is wrong because a small increase in radius can significantly reduce peak stress.
- Assuming stress concentration always causes immediate yielding, which is wrong because local yielding may redistribute stress under ductile static loading but can still be critical in fatigue.
Practice Questions
- 1 A flat steel bar has sigma_nom = 80 MPa near a central hole, and the chart gives Kt = 2.4. Find sigma_max.
- 2 A stepped shaft in bending has sigma_nom = 120 MPa at the shoulder and Kt = 1.8. Estimate the peak local bending stress.
- 3 For a notched part, Kt = 2.6 and q = 0.75. Calculate the fatigue stress concentration factor Kf.
- 4 Explain why increasing a fillet radius at a shaft shoulder usually improves fatigue life even if the nominal stress stays the same.