Torque Given Strain Energy In Rod Subjected To External Torque Calculator

Formula Used:

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

Strain Energy in Rod or Shaft (U):

Joule

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

m⁴

Modulus of rigidity of rod or shaft (G):

Pascal

Length of Rod or Shaft (L):

Meter

Torque on Rod or Shaft (τ):

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1. What is Torque Given Strain Energy in Rod Subjected to External Torque?

This calculation determines the torque applied to a rod or shaft based on the strain energy stored in the material when subjected to external torque. It's derived from Castigliano's theorem and is essential in mechanical engineering for analyzing torsional systems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the torque required to produce a specific amount of strain energy in a rod or shaft, considering its material properties and dimensions.

3. Importance of Torque Calculation

Details: Accurate torque calculation is crucial for designing mechanical systems, ensuring structural integrity, preventing material failure, and optimizing energy efficiency in rotating machinery.

4. Using the Calculator

Tips: Enter strain energy in joules, polar moment of inertia in m⁴, modulus of rigidity in pascals, and length in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in torsional systems?
A: Strain energy is the energy stored in a material when it undergoes deformation due to applied torque. It represents the work done by the external torque.

Q2: How does polar moment of inertia affect torque calculation?
A: Polar moment of inertia measures a shaft's resistance to torsion. Higher values indicate greater resistance to twisting under applied torque.

Q3: What is modulus of rigidity?
A: Modulus of rigidity (shear modulus) is a material property that measures its resistance to shearing forces. It relates shear stress to shear strain.

Q4: When is this formula most applicable?
A: This formula is most accurate for homogeneous, isotropic materials undergoing elastic deformation within their proportional limit.

Q5: Are there limitations to this calculation?
A: This calculation assumes uniform cross-section, linear elastic material behavior, and pure torsion without bending or axial loads.