Length of Shaft Subjected to Torsional Moment given Angle of Twist Calculator

Formula Used:

\[ L = \frac{\theta \times (G \times d_{torl}^4)}{584 \times M_{tshaft}} \]

Angle of Twist in Shaft (θ):

rad

Modulus of Rigidity of Shaft (G):

Diameter of Shaft from Torsional Rigidity (d_torl):

Torsional Moment in Shaft (M_tshaft):

N·m

Length of Shaft from Torsional Rigidity (L):

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1. What is the Length of Shaft from Torsional Rigidity?

The Length of Shaft from Torsional Rigidity is the length of the shaft calculated based on torsional rigidity, which determines how much a shaft will twist under a given torsional moment.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{\theta \times (G \times d_{torl}^4)}{584 \times M_{tshaft}} \]

Where:

\( L \) — Length of Shaft from Torsional Rigidity (m)
\( \theta \) — Angle of Twist in Shaft (rad)
\( G \) — Modulus of Rigidity of Shaft (Pa)
\( d_{torl} \) — Diameter of Shaft from Torsional Rigidity (m)
\( M_{tshaft} \) — Torsional Moment in Shaft (N·m)

Explanation: This formula calculates the length of a shaft based on its torsional properties, including the angle of twist, modulus of rigidity, diameter, and applied torsional moment.

3. Importance of Length Calculation

Details: Accurate calculation of shaft length from torsional rigidity is crucial for mechanical design, ensuring shafts can withstand torsional loads without excessive twisting that could affect performance.

4. Using the Calculator

Tips: Enter all values in appropriate units (radians for angle, Pascals for modulus, meters for diameter and length, Newton-meters for moment). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is torsional rigidity?
A: Torsional rigidity is a measure of a shaft's resistance to twisting under applied torque, determined by the material properties and cross-sectional geometry.

Q2: Why is the diameter raised to the fourth power?
A: The diameter appears to the fourth power because torsional stiffness is proportional to the polar moment of inertia, which for circular shafts is proportional to diameter^4.

Q3: What is modulus of rigidity?
A: Modulus of rigidity (shear modulus) is a material property that measures the ratio of shear stress to shear strain, indicating the material's resistance to shearing deformation.

Q4: When is this calculation most important?
A: This calculation is critical in applications where precise angular positioning is required, such as in drive shafts, machine tool spindles, and precision mechanical systems.

Q5: What are typical values for modulus of rigidity?
A: For steel, G ≈ 79.3 GPa; for aluminum, G ≈ 26 GPa; for brass, G ≈ 40 GPa. The exact value depends on the specific alloy and treatment.