Strain Energy In Rod When It Is Subjected To External Torque Calculator

Formula Used:

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

Torque on Rod or Shaft (τ):

N·m

Length of Rod or Shaft (L):

Polar Moment of Inertia (J):

m⁴

Modulus of Rigidity (G):

Strain Energy in Rod or Shaft (U):

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1. What is Strain Energy in Rod or Shaft?

Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation when subjected to external torque. It represents the work done by the applied torque to twist the shaft.

2. How Does the Calculator Work?

The calculator uses the strain energy formula:

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

Where:

\( U \) — Strain Energy in Rod or Shaft (Joules)
\( \tau \) — Torque on Rod or Shaft (N·m)
\( L \) — Length of Rod or Shaft (meters)
\( J \) — Polar Moment of Inertia (m⁴)
\( G \) — Modulus of Rigidity (Pascal)

Explanation: The formula calculates the energy stored in a shaft when it is twisted by an external torque, considering the shaft's material properties and geometry.

3. Importance of Strain Energy Calculation

Details: Calculating strain energy is crucial for understanding the energy absorption capacity of shafts, designing mechanical systems for torsion, and analyzing the behavior of shafts under torsional loading.

4. Using the Calculator

Tips: Enter torque in N·m, length in meters, polar moment of inertia in m⁴, and modulus of rigidity in Pascal. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of polar moment of inertia?
A: Polar moment of inertia measures a shaft's resistance to torsional deformation. Larger values indicate greater resistance to twisting.

Q2: How does modulus of rigidity affect strain energy?
A: Higher modulus of rigidity (shear modulus) means the material is stiffer, resulting in less deformation and lower strain energy for the same torque.

Q3: Can this formula be used for any shaft material?
A: Yes, as long as the material behaves elastically and the appropriate modulus of rigidity value is used for that specific material.

Q4: What are typical units for these parameters?
A: Torque in N·m, length in m, polar moment of inertia in m⁴, modulus of rigidity in Pa, and strain energy in Joules.

Q5: When is this calculation particularly important?
A: This calculation is essential in mechanical design, automotive engineering, and any application where shafts transmit torque and energy absorption is a concern.