Max Shear Stress Calculator

Formula

The formula to calculate the maximum shear stress (τ) is:

\[ \tau = \frac{F \cdot r}{J} \]

Where:

\( \tau \) is the maximum shear stress
\( F \) is the force applied
\( r \) is the radius
\( J \) is the polar moment of inertia

Definition

Max Shear Stress: The maximum value of shear stress that a material can withstand before failing. Shear stress occurs when a force is applied parallel or tangential to the surface of a material. The maximum shear stress is a critical parameter in the design and analysis of mechanical components, as it helps engineers ensure that the material can handle the applied loads without experiencing shear failure.

Example

Let's say the force (F) is 500 newtons, the radius (r) is 0.05 meters, and the polar moment of inertia (J) is 0.0001 meters to the fourth power. Using the formula:

\[ \tau = \frac{500 \cdot 0.05}{0.0001} \]

We get:

\[ \tau = 250000 \, \text{N/m²} \]

So, the maximum shear stress is 250,000 N/m².