Modulus of Rigidity Given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Calculator

Formula Used:

\[ G_h = \frac{584 \times M_{t_{hollowshaft}} \times L_h}{\theta_{hollow} \times d_o^4 \times (1 - C^4)} \]

Torsional Moment in Hollow Shaft (M_{t_hollowshaft}):

N·m

Length of Hollow Shaft (L_h):

Angle of Twist of Hollow Shaft (θ_hollow):

rad

Outer Diameter of Hollow Shaft (d_o):

Ratio of Inner to Outer Diameter of Hollow Shaft (C):

Modulus of Rigidity of Hollow Shaft (G_h):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Modulus of Rigidity?

The Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G_h = \frac{584 \times M_{t_{hollowshaft}} \times L_h}{\theta_{hollow} \times d_o^4 \times (1 - C^4)} \]

Where:

\( G_h \) — Modulus of Rigidity of Hollow Shaft (Pa)
\( M_{t_{hollowshaft}} \) — Torsional Moment in Hollow Shaft (N·m)
\( L_h \) — Length of Hollow Shaft (m)
\( \theta_{hollow} \) — Angle of Twist of Hollow Shaft (rad)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft

Explanation: This formula calculates the modulus of rigidity based on torsional rigidity principles for hollow shafts.

3. Importance of Modulus of Rigidity Calculation

Details: Accurate calculation of modulus of rigidity is crucial for designing mechanical components, analyzing structural integrity, and ensuring proper performance under torsional loads.

4. Using the Calculator

Tips: Enter all values in appropriate units. Torsional moment in N·m, length in meters, angle in radians, diameter in meters, and ratio as a dimensionless value between 0 and 1.

5. Frequently Asked Questions (FAQ)

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

Q2: What are typical values for modulus of rigidity?
A: For most metals, modulus of rigidity ranges from 20-80 GPa, depending on the material composition and treatment.

Q3: Why is the ratio C important in this calculation?
A: The ratio C accounts for the hollow nature of the shaft and significantly affects the torsional stiffness and rigidity calculations.

Q4: What units should be used for input values?
A: All dimensional inputs should be in SI units: meters for length, Newton-meters for moment, and radians for angle.

Q5: Can this formula be used for solid shafts?
A: For solid shafts, set C = 0 (inner diameter = 0), which simplifies the formula by eliminating the (1-C⁴) term.