Length of Shaft when Strain Energy in Shaft Subjected to External Torque Calculator

Formula Used:

\[ L = \frac{2 \times U \times J \times G}{\tau^2} \]

Strain Energy in Rod or Shaft (U):

Polar Moment of Inertia of rod or shaft (J):

m⁴

Modulus of rigidity of rod or shaft (G):

Torque on Rod or Shaft (τ):

N·m

Length of Rod or Shaft (L):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

This calculation determines the length of a rod or shaft based on the strain energy stored when subjected to an external torque, using Castigliano's theorem. It's essential in mechanical engineering for designing shafts that can withstand torsional loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{2 \times U \times J \times G}{\tau^2} \]

Where:

\( L \) — Length of Rod or Shaft (m)
\( U \) — Strain Energy in Rod or Shaft (J)
\( J \) — Polar Moment of Inertia of rod or shaft (m⁴)
\( G \) — Modulus of rigidity of rod or shaft (Pa)
\( \tau \) — Torque on Rod or Shaft (N·m)

Explanation: This formula calculates the length of a shaft based on the strain energy stored when subjected to torsional loading, derived from Castigliano's theorem.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for designing mechanical systems, ensuring shafts can withstand torsional stresses without excessive deformation or failure.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Strain energy (J), polar moment of inertia (m⁴), modulus of rigidity (Pa), and torque (N·m) must all be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in a shaft?
A: Strain energy is the energy stored in a shaft due to deformation when subjected to torsional loading.

Q2: What is polar moment of inertia?
A: Polar moment of inertia is a measure of a shaft's resistance to torsional deformation, depending on its cross-sectional shape and size.

Q3: What is modulus of rigidity?
A: Modulus of rigidity (shear modulus) is a material property that measures its resistance to shearing deformation.

Q4: When is this calculation most useful?
A: This calculation is particularly useful in mechanical design and analysis of drive shafts, axles, and other torsionally loaded components.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material and applies to shafts with uniform cross-section subjected to pure torsion.