Von Mises Stress Calculator

Von Mises Stress Formula:

\[ \sigma_{vm} = \sqrt{ \frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2} } \]

Von Mises Stress (σ_vm):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Von Mises Stress?

The Von Mises stress is an equivalent stress value used to predict yielding of materials under multiaxial loading conditions. It combines the three principal stresses into a single equivalent stress value that can be compared to material yield strength.

2. How Does the Calculator Work?

The calculator uses the Von Mises stress formula:

\[ \sigma_{vm} = \sqrt{ \frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2} } \]

Where:

\( \sigma_{vm} \) — Von Mises equivalent stress (Pa)
\( \sigma_1 \) — First principal stress (Pa)
\( \sigma_2 \) — Second principal stress (Pa)
\( \sigma_3 \) — Third principal stress (Pa)

Explanation: The equation accounts for the combined effect of all three principal stresses to determine an equivalent stress that would produce the same strain energy as the actual multiaxial stress state.

3. Importance of Von Mises Stress

Details: Von Mises stress is crucial for failure prediction in ductile materials. It's widely used in mechanical and structural engineering to assess whether a material will yield under complex loading conditions.

4. Using the Calculator

Tips: Enter all three principal stress values in Pascals (Pa). The calculator will compute the equivalent Von Mises stress, which can be compared to the material's yield strength to assess safety.

5. Frequently Asked Questions (FAQ)

Q1: When should Von Mises stress be used?
A: It's most appropriate for ductile materials under static loading conditions. For brittle materials, maximum principal stress theory is often more appropriate.

Q2: What if one principal stress is zero?
A: The equation still works. For plane stress conditions (σ₃ = 0), the formula simplifies but the general form can still be used.

Q3: How does Von Mises stress relate to yield strength?
A: If the Von Mises stress exceeds the material's yield strength (with appropriate safety factor), yielding is predicted to occur.

Q4: Can Von Mises stress be negative?
A: No, because it's calculated from squared terms and a square root, it's always positive or zero.

Q5: What are typical units for Von Mises stress?
A: Pascals (Pa) in SI units, but MPa (megapascals) are commonly used in engineering (1 MPa = 10⁶ Pa).