Shaft Length For Given Polar MOI, Twisting Moment, Modulus Of Rigidity, And Twist Angle Calculator

Formula Used:

\[ L_{shaft} = \frac{G_{Torsion} \times \theta \times J}{T} \]

Modulus of Rigidity (G):

Angle of Twist (θ):

rad

Polar Moment of Inertia (J):

m⁴

Torque (T):

N·m

Length of Shaft (Lshaft):

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1. What is the Shaft Length Formula?

The shaft length formula calculates the length of a shaft based on its material properties and applied torque. It's derived from the torsion formula that relates torque, angle of twist, and material properties in mechanical engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{shaft} = \frac{G_{Torsion} \times \theta \times J}{T} \]

Where:

\( G_{Torsion} \) — Modulus of Rigidity (Pa)
\( \theta \) — Angle of Twist (radians)
\( J \) — Polar Moment of Inertia (m⁴)
\( T \) — Torque (N·m)

Explanation: This formula calculates the length of a shaft that will produce a specific angle of twist when subjected to a given torque, based on the material's rigidity and the shaft's cross-sectional properties.

3. Importance of Shaft Length Calculation

Details: Accurate shaft length calculation is crucial for mechanical design, ensuring proper torque transmission, preventing excessive twisting, and maintaining structural integrity in rotating machinery and drive systems.

4. Using the Calculator

Tips: Enter modulus of rigidity in Pascals, angle of twist in radians, polar moment of inertia in meters to the fourth power, and torque in Newton-meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of rigidity?
A: Modulus of rigidity (G) is a material property that measures its resistance to shear deformation. It's the ratio of shear stress to shear strain.

Q2: How is polar moment of inertia different from area moment of inertia?
A: Polar moment of inertia (J) relates to torsion and is used for circular cross-sections, while area moment of inertia (I) relates to bending and is used for various cross-sectional shapes.

Q3: What factors affect the angle of twist in a shaft?
A: The angle of twist depends on the applied torque, shaft length, modulus of rigidity, and polar moment of inertia of the cross-section.

Q4: When is this formula applicable?
A: This formula applies to circular shafts experiencing pure torsion within the elastic limit of the material (Hooke's law applies).

Q5: What are typical units for these calculations?
A: SI units are typically used: Pascals for modulus of rigidity, radians for angle, meters⁴ for polar moment, Newton-meters for torque, and meters for length.