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Von Mises Equivalent Stress by Components

Calculate von mises equivalent stress by components with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

principal stress 2D = 86.60254. Values use the worked example unit selections.

σvm = √(((σ1−σ2)²+(σ2−σ3)²+(σ3−σ1)²)/2)

Worked example

Enter these known values and leave the other values blank.

Dimensions
2D (plane)
Method
Principal stresses
Maximum principal stress (σ==1==)
100 MPa
Intermediate principal stress (σ==2==)
50 MPa
Von Mises stress (σ==v==)
86.6 MPa

Assumptions and limitations

  • All stress components use the same units and sign convention. Two-dimensional mode assumes plane stress. Equivalent stress is nonnegative; inverse principal/component branches return the captured positive square-root solution when multiple signed stresses are possible.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

All stress components use the same units and sign convention. Two-dimensional mode assumes plane stress. Equivalent stress is nonnegative; inverse principal/component branches return the captured positive square-root solution when multiple signed stresses are possible.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Physical domain for real principal inverses and nonnegative equivalent stress. Pounds-force per square foot use the exact international pound and foot with standard gravity. Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor.

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