Shear Stress Induced At Surface Of Shaft Calculator

Shear Stress in Shaft Formula:

\[ \tau = \frac{R \times G_{Torsion} \times \theta_{Torsion}}{L_{shaft}} \]

Radius of Shaft (R):

Modulus of Rigidity (G):

Angle of Twist (θ):

rad

Length of Shaft (L):

Shear Stress in Shaft (τ):

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1. What is Shear Stress in Shaft?

Shear stress in a shaft is the stress component parallel to the cross-section of the shaft that occurs when the shaft is subjected to torque or twisting moments. It represents the internal resistance of the material to shear deformation.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \tau = \frac{R \times G_{Torsion} \times \theta_{Torsion}}{L_{shaft}} \]

Where:

\( \tau \) — Shear stress in shaft (Pa)
\( R \) — Radius of shaft (m)
\( G_{Torsion} \) — Modulus of rigidity (Pa)
\( \theta_{Torsion} \) — Angle of twist (rad)
\( L_{shaft} \) — Length of shaft (m)

Explanation: This formula calculates the maximum shear stress at the surface of a circular shaft subjected to torsion, based on the material properties and geometric parameters.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial for designing shafts in mechanical systems to ensure they can withstand applied torques without failure. It helps determine if the shaft material and dimensions are adequate for the intended application.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length dimensions, pascals for 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 (G) is a material property that measures its resistance to shear deformation. It's the ratio of shear stress to shear strain.

Q2: Why does shear stress vary across the shaft cross-section?
A: Shear stress varies linearly from zero at the center to maximum at the outer surface in a circular shaft under torsion.

Q3: What are typical values of modulus of rigidity?
A: For steel: ~80 GPa, for aluminum: ~26 GPa, for copper: ~48 GPa. Values vary depending on the specific alloy and treatment.

Q4: When is this formula applicable?
A: This formula applies to circular shafts made of homogeneous, isotropic materials undergoing elastic deformation within the proportional limit.

Q5: How does shaft length affect shear stress?
A: For a given angle of twist, longer shafts experience lower shear stress, while shorter shafts experience higher shear stress under the same torque.