Torque Transmitted By Shaft Given Polar Moment Of Inertia And Modulus Of Rigidity Calculator

Formula Used:

\[ \tau = \frac{C \times \theta \times J_{shaft}}{L} \]

Modulus of Rigidity (C):

Angle of Twist (θ):

rad

Polar Moment of Inertia (J_shaft):

m⁴

Length of Shaft (L):

Torque Exerted on Wheel (τ):

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1. What is Torque Transmitted by Shaft?

Torque transmitted by a shaft is the rotational force that causes torsion in the shaft. It is a crucial parameter in mechanical engineering that determines the shaft's ability to transmit power without excessive deformation or failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{C \times \theta \times J_{shaft}}{L} \]

Where:

\( \tau \) — Torque Exerted on Wheel (N·m)
\( C \) — Modulus of Rigidity (Pa)
\( \theta \) — Angle of Twist (rad)
\( J_{shaft} \) — Polar Moment of Inertia of shaft (m⁴)
\( L \) — Length of Shaft (m)

Explanation: This formula calculates the torque transmitted through a shaft based on its material properties (modulus of rigidity), geometric properties (polar moment of inertia and length), and the resulting angle of twist.

3. Importance of Torque Calculation

Details: Accurate torque calculation is essential for designing shafts that can safely transmit power without excessive twisting or failure. It helps engineers determine appropriate shaft dimensions and material selection for various mechanical applications.

4. Using the Calculator

Tips: Enter all values in the specified units. Modulus of Rigidity, Angle of Twist, Polar Moment of Inertia, and Length of Shaft must all be positive values greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Modulus of Rigidity?
A: Modulus of Rigidity (also known as shear modulus) is a material property that measures its resistance to shearing deformation. It's defined as the ratio of shear stress to shear strain.

Q2: What is Polar Moment of Inertia?
A: Polar Moment of Inertia is a geometrical property of a shaft's cross-section that measures its resistance to torsion. For circular shafts, it's calculated as \( J = \frac{\pi d^4}{32} \) where d is the diameter.

Q3: How does shaft length affect torque transmission?
A: Longer shafts experience greater angular deflection (twist) for the same torque, as torque is inversely proportional to shaft length in this formula.

Q4: What are typical values for Modulus of Rigidity?
A: For steel, it's approximately 80 GPa; for aluminum, about 26 GPa; and for copper, around 45 GPa.

Q5: When is this formula applicable?
A: This formula applies to shafts with circular cross-sections undergoing elastic deformation (within the proportional limit of the material).