Angle Of Twist With Known Shear Stress In Shaft Calculator

Angle of Twist Formula:

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

Shear Stress in Shaft (τ):

Length of Shaft (L):

Radius of Shaft (R):

Modulus of Rigidity (G):

Angle of Twist (θ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Angle of Twist Formula?

The Angle of Twist formula calculates the angular displacement of a shaft when subjected to torsional loading. It relates the shear stress, shaft length, radius, and material's modulus of rigidity to determine the twist angle in radians.

2. How Does the Calculator Work?

The calculator uses the Angle of Twist formula:

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

Where:

\( \tau \) — Shear Stress in Shaft (Pa)
\( L_{shaft} \) — Length of Shaft (m)
\( R \) — Radius of Shaft (m)
\( G_{Torsion} \) — Modulus of Rigidity (Pa)
\( \theta_{Torsion} \) — Angle of Twist (rad)

Explanation: The formula calculates the angular deformation of a shaft under torsional stress, considering the material's resistance to shear deformation.

3. Importance of Angle of Twist Calculation

Details: Calculating angle of twist is crucial for designing shafts and rotating elements in mechanical systems to ensure they operate within acceptable deformation limits and prevent failure.

4. Using the Calculator

Tips: Enter shear stress in Pascals, length and radius in meters, and modulus of rigidity in Pascals. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of angle of twist in shaft design?
A: Angle of twist helps determine if a shaft will experience excessive deformation under torsional loads, which could affect performance and lead to failure.

Q2: How does modulus of rigidity affect the angle of twist?
A: Higher modulus of rigidity (stiffer material) results in smaller angle of twist for the same applied torque and shaft dimensions.

Q3: Can this formula be used for non-circular shafts?
A: This specific formula is derived for circular shafts. Non-circular cross-sections require different formulas accounting for their specific geometry.

Q4: What are typical values for modulus of rigidity?
A: For steel: ~79 GPa, aluminum: ~26 GPa, brass: ~40 GPa. Values vary depending on the specific alloy and treatment.

Q5: How does shaft length affect the angle of twist?
A: Longer shafts experience greater angle of twist for the same applied torque and material properties, as twist accumulates along the length.