Torsional Moment Given Angle of Twist on Basis of Torsional Rigidity Calculator

Formula Used:

\[ Torsional\ Moment\ in\ Hollow\ Shaft = \frac{Angle\ of\ Twist\ of\ Hollow\ Shaft \times (Modulus\ of\ Rigidity\ of\ Hollow\ Shaft \times Outer\ Diameter\ of\ Hollow\ Shaft^4 \times (1 - Ratio\ of\ Inner\ to\ Outer\ Diameter\ of\ Hollow\ Shaft^4))}{584 \times Length\ of\ Hollow\ Shaft} \]

Angle of Twist of Hollow Shaft:

rad

Modulus of Rigidity of Hollow Shaft:

Outer Diameter of Hollow Shaft:

Ratio of Inner to Outer Diameter of Hollow Shaft:

Length of Hollow Shaft:

Torsional Moment in Hollow Shaft:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Torsional Moment in Hollow Shaft?

The Torsional Moment in a Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist. It represents the internal resistance of the shaft to torsional deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Torsional\ Moment = \frac{\theta \times (G \times d_o^4 \times (1 - C^4))}{584 \times L} \]

Where:

\( \theta \) — Angle of Twist of Hollow Shaft (rad)
\( G \) — Modulus of Rigidity of Hollow Shaft (Pa)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( L \) — Length of Hollow Shaft (m)

Explanation: This formula calculates the torsional moment based on the angle of twist and the torsional rigidity properties of the hollow shaft.

3. Importance of Torsional Moment Calculation

Details: Accurate calculation of torsional moment is crucial for designing shafts in mechanical systems, ensuring structural integrity, and preventing failure due to excessive twisting.

4. Using the Calculator

Tips: Enter all values in appropriate units. Angle of twist in radians, modulus of rigidity in Pascals, diameters in meters, and length in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 584 constant in the formula?
A: The constant 584 is derived from the conversion factors and geometric properties specific to the torsional rigidity calculation for hollow circular shafts.

Q2: How does the diameter ratio affect the torsional moment?
A: The term (1-C⁴) accounts for the hollow section's reduced material compared to a solid shaft, where C is the ratio of inner to outer diameter.

Q3: What is the typical range for modulus of rigidity?
A: For most metals, modulus of rigidity ranges from 25-80 GPa. Steel typically has around 79.3 GPa, while aluminum has about 26 GPa.

Q4: When is this formula applicable?
A: This formula applies to hollow circular shafts with uniform cross-section undergoing elastic deformation within the material's proportional limit.

Q5: How does length affect the torsional moment?
A: Longer shafts will experience greater angular deflection for the same applied torque, resulting in a different torsional moment calculation.