Stress Concentration Factor Calculator Fillet

Stress Concentration Factor Formula:

\[ k_t = 1 + 2 \times \sqrt{\frac{a}{\rho}} \]

Stress Concentration Factor (k_t):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Stress Concentration Factor?

The stress concentration factor (k_t) is a dimensionless factor that quantifies how much a geometric discontinuity (like a fillet or notch) increases the local stress in a material compared to the nominal stress.

2. How Does the Calculator Work?

The calculator uses the stress concentration factor formula:

\[ k_t = 1 + 2 \times \sqrt{\frac{a}{\rho}} \]

Where:

\( a \) — Notch depth (m)
\( \rho \) — Notch radius (m)
\( k_t \) — Stress concentration factor (dimensionless)

Explanation: The equation shows that stress concentration increases with deeper notches and sharper radii.

3. Importance of Stress Concentration Factor

Details: Understanding stress concentration is crucial for designing mechanical components to prevent failure at stress raisers like fillets, holes, or notches.

4. Using the Calculator

Tips: Enter notch depth and radius in meters. Both values must be positive numbers. The calculator will compute the theoretical stress concentration factor.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for k_t?
A: For fillets, k_t typically ranges from 1.1 to 3, but can be higher for very sharp notches.

Q2: How accurate is this formula?
A: This is a theoretical formula that works well for simple geometries. For complex shapes, finite element analysis may be needed.

Q3: What materials is this applicable to?
A: The formula is material-independent, but the effects of stress concentration vary with material ductility.

Q4: How can I reduce stress concentration?
A: Increase the fillet radius, use gradual transitions, or add relief features to distribute stress.

Q5: Does this account for fatigue?
A: No, this is the static stress concentration factor. Fatigue considerations require additional factors.