IntermediateTopic 67 of 106Engineering Mechanics

Stress concentration

Holes and notches raise local stress by a factor Kt.

In depth

Holes, notches, fillets and keyways raise local stress to σ_max=Kt·σ_nom. A circular hole in a wide plate has Kt=3. Reducing it: larger fillet radii, smooth transitions and stress-relief grooves. Critical for fatigue.

Key points

  • Kt depends on geometry only
  • Fatigue notch factor Kf
  • Ductile materials redistribute at yield
Example

A shaft shoulder with a sharp corner may have Kt≈2.5; a generous radius cuts it to 1.5.

Why it matters

Holes, notches and fillets raise the local stress far above the nominal value, and this often starts cracks in real parts.

Where this is used

  • Designing a fillet radius on a shaft shoulder to reduce fatigue risk.
  • Checking the stress around a bolt hole in a plate.
  • Choosing the shape of a keyway to avoid high stress in a gear shaft.

Frequently asked questions

What is Stress concentration?

Holes and notches raise local stress by a factor Kt.

Why is it important to understand stress concentration?

Holes, notches and fillets raise the local stress far above the nominal value, and this often starts cracks in real parts.

What is the stress concentration factor Kt?

It is the ratio of peak local stress to nominal stress. Its value depends on the geometry, such as the ratio of hole diameter to plate width.

How do I reduce stress concentration?

Use larger fillet radii, smooth transitions, and avoid sharp corners, which lowers the peak stress without adding much material.

How is Stress concentration used in practice?

Typical applications include designing a fillet radius on a shaft shoulder to reduce fatigue risk, checking the stress around a bolt hole in a plate and choosing the shape of a keyway to avoid high stress in a gear shaft.

What should I learn before Stress concentration?

Study "Strain energy" first (topic 66 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.

What are the key points of Stress concentration?

Kt depends on geometry only. Fatigue notch factor Kf. Ductile materials redistribute at yield.

Can you give an example of Stress concentration?

A shaft shoulder with a sharp corner may have Kt≈2.5; a generous radius cuts it to 1.5.

What comes after Stress concentration?

The next topic is "Fatigue", which builds directly on this one.

How difficult is Stress concentration?

It is classed as Intermediate in Engineering Mechanics (topic 67 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.

Learning path

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