Shear Stress Induced At Radius 'r' From Center Of Shaft Using Modulus Of Rigidity Calculator

Formula Used:

\[ \text{Shear Stress at Radius r} = \frac{\text{Radius from Center to Distance r} \times \text{Modulus of Rigidity} \times \text{Angle of Twist for Circular Shafts}}{\text{Shear Stress in Shaft}} \] \[ T_r = \frac{r \times G_{\text{Torsion}} \times \theta_{\text{Circular shafts}}}{\tau} \]

Radius from Center to Distance r:

Modulus of Rigidity:

Angle of Twist for Circular Shafts:

rad

Shear Stress in Shaft:

Shear Stress at Radius r:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Stress at Radius r?

Shear Stress at Radius r from shaft is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. It represents the internal resistance of a material to shear deformation at a specific radial distance from the center of a circular shaft.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_r = \frac{r \times G_{\text{Torsion}} \times \theta_{\text{Circular shafts}}}{\tau} \]

Where:

\( T_r \) — Shear Stress at Radius r (Pa)
\( r \) — Radius from Center to Distance r (m)
\( G_{\text{Torsion}} \) — Modulus of Rigidity (Pa)
\( \theta_{\text{Circular shafts}} \) — Angle of Twist for Circular Shafts (rad)
\( \tau \) — Shear Stress in Shaft (Pa)

Explanation: This formula calculates the shear stress at a specific radial distance from the center of a circular shaft subjected to torsion, using the modulus of rigidity and the angle of twist.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress at different radii is crucial for understanding stress distribution in circular shafts, designing mechanical components to withstand torsional loads, and ensuring structural integrity in engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for radius, Pascals for stress and modulus, radians for angle). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Modulus of Rigidity?
A: Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It represents a material's resistance to shearing deformation.

Q2: How does shear stress vary along the radius?
A: In circular shafts under torsion, shear stress varies linearly with radial distance, being zero at the center and maximum at the outer surface.

Q3: What units should be used for accurate calculation?
A: Use consistent SI units: meters for length, Pascals for stress and modulus, and radians for angular measurements.

Q4: When is this formula applicable?
A: This formula applies to circular shafts made of homogeneous, isotropic materials undergoing elastic deformation under pure torsion.

Q5: What are typical values for Modulus of Rigidity?
A: For steel: ~80 GPa, for aluminum: ~26 GPa, for copper: ~48 GPa. The exact value depends on the specific material composition and treatment.