Von Mises Stress Calculator

Formula

The formula to calculate the Von Mises Stress (V) is:

\[ V = \sqrt{\sigma_x^2 - (\sigma_x \cdot \sigma_y) + \sigma_y^2 + (3 \cdot \tau_{xy}^2)} \]

Where:

\( V \) is the Von Mises Stress (MPa)
\( \sigma_x \) is the Normal Stress x component (MPa)
\( \sigma_y \) is the Normal Stress y component (MPa)
\( \tau_{xy} \) is the Shear Stress (MPa)

Von Mises Stress Definition

A von Mises stress is a measure of the total overall stress acting on a material, including normal stress in the x and y directions as well as the shear stress. It is used to predict yielding of materials under complex loading conditions.

Example Calculation

Let's consider an example:

Normal Stress (σx): 50 MPa
Normal Stress (σy): 30 MPa
Shear Stress (τxy): 20 MPa

Using the formula to calculate the Von Mises Stress:

\[ V = \sqrt{50^2 - (50 \cdot 30) + 30^2 + (3 \cdot 20^2)} \approx 55.68 \, \text{MPa} \]

This demonstrates that with normal stresses of 50 MPa and 30 MPa, and a shear stress of 20 MPa, the von Mises stress would be approximately 55.68 MPa.