Shear Stress Due To Torsion At Radius 'r' From Center Calculator

Shear Stress Formula:

\[ \text{Shear stress at radius 'r' from shaft} = \left( \frac{\text{Radius 'r' from Center Of Shaft}}{\text{Radius of Shaft}} \right) \times \text{Shear stress on surface of shaft} \]

Shear stress at radius 'r' from shaft:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Stress Due To Torsion?

Shear stress due to torsion is the stress that develops in a shaft when it is subjected to a twisting moment. The stress varies linearly from zero at the center to maximum at the outer surface of the shaft.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \text{Shear stress at radius 'r' from shaft} = \left( \frac{\text{Radius 'r' from Center Of Shaft}}{\text{Radius of Shaft}} \right) \times \text{Shear stress on surface of shaft} \]

Where:

Radius 'r' from Center Of Shaft — Distance from the center of the shaft to the point where stress is being calculated (m)
Radius of Shaft — Outer radius of the shaft (m)
Shear stress on surface of shaft — Maximum shear stress at the outer surface of the shaft (Pa)

Explanation: The formula shows that shear stress in a shaft under torsion varies linearly with the radial distance from the center.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial for designing shafts and other rotating components to ensure they can withstand torsional loads without failure. It helps determine the appropriate shaft dimensions and material selection.

4. Using the Calculator

Tips: Enter the radius from center of shaft, radius of shaft, and shear stress on surface of shaft. All values must be positive numbers with appropriate units.

5. Frequently Asked Questions (FAQ)

Q1: Why does shear stress vary with radius?
A: In torsion, shear stress varies linearly from zero at the center to maximum at the outer surface due to the distribution of deformation across the cross-section.

Q2: What is the maximum shear stress in a shaft?
A: The maximum shear stress occurs at the outer surface of the shaft where the radius is maximum.

Q3: Does this formula apply to all shaft materials?
A: This formula applies to homogeneous, isotropic materials that obey Hooke's law within the elastic range.

Q4: What are typical units for shear stress?
A: Shear stress is typically measured in Pascals (Pa) or Megapascals (MPa) in the SI system.

Q5: How does shaft diameter affect shear stress?
A: For a given torque, larger diameter shafts experience lower maximum shear stress due to the increased cross-sectional area resisting the torsional load.