Torsional Moment Given Torsional Shear Stress In Hollow Shaft Calculator

Formula Used:

\[ Torsional\ Moment\ in\ Hollow\ Shaft = \frac{Torsional\ Shear\ Stress\ in\ Hollow\ Shaft \times \pi \times Outer\ Diameter\ of\ Hollow\ Shaft^3 \times (1 - Ratio\ of\ Inner\ to\ Outer\ Diameter\ of\ Hollow\ Shaft^4)}{16} \]

Torsional Moment in Hollow Shaft:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Torsional Moment in Hollow Shaft?

Torsional Moment in 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:

\[ Torsional\ Moment = \frac{\tau \times \pi \times d_o^3 \times (1 - C^4)}{16} \]

Where:

\( \tau \) — Torsional Shear Stress in Hollow Shaft (Pa)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the torsional moment that a hollow shaft can withstand based on the given shear stress and geometric properties.

3. Importance of Torsional Moment Calculation

Details: Accurate calculation of torsional moment is crucial for designing shafts in mechanical systems, ensuring they can withstand applied torques without failure, and optimizing material usage in engineering applications.

4. Using the Calculator

Tips: Enter torsional shear stress in Pascals (Pa), outer diameter in meters (m), and the diameter ratio (0 ≤ C < 1). All values must be positive, with the diameter ratio between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the diameter ratio in the formula?
A: The diameter ratio (C) accounts for the hollow nature of the shaft. As C increases (approaching 1), the shaft becomes thinner-walled, reducing its torsional capacity.

Q2: How does this formula differ from solid shaft calculations?
A: For solid shafts, C = 0, and the formula simplifies to \( \frac{\tau \times \pi \times d^3}{16} \). The hollow shaft formula includes the (1-C⁴) term to account for the missing inner material.

Q3: What are typical values for torsional shear stress?
A: Allowable torsional shear stress depends on the material. For steel, it's typically 40-60 MPa, while for aluminum it's around 20-30 MPa.

Q4: Why use hollow shafts instead of solid ones?
A: Hollow shafts provide better strength-to-weight ratio, reducing material usage and weight while maintaining good torsional resistance.

Q5: What are the limitations of this formula?
A: This formula assumes homogeneous, isotropic material, linear elastic behavior, and applies to circular cross-sections only. It may not be accurate for very thin-walled tubes or under plastic deformation.