Shear Strain Energy Calculator

Formula Used:

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

Shear Stress on Surface of Shaft (τ):

Pascal

Volume of Shaft (V):

m³

Modulus of Rigidity of Shaft (G):

Pascal

Strain Energy in Body (U):

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1. What is Shear Strain Energy?

Strain Energy in body is defined as the energy stored in a body due to deformation. In the context of shear, it represents the energy stored in a shaft or material when subjected to shear stress.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( U \) — Strain Energy in body (Joule)
\( \tau \) — Shear stress on surface of shaft (Pascal)
\( V \) — Volume of Shaft (m³)
\( G \) — Modulus of rigidity of Shaft (Pascal)

Explanation: The formula calculates the energy stored in a material due to shear deformation, which is proportional to the square of the shear stress and the volume, and inversely proportional to twice the modulus of rigidity.

3. Importance of Strain Energy Calculation

Details: Calculating strain energy is crucial for understanding material behavior under stress, designing structural components, and analyzing energy absorption capacity in mechanical systems.

4. Using the Calculator

Tips: Enter shear stress in Pascal, volume in cubic meters, and modulus of rigidity in Pascal. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of strain energy?
A: Strain energy represents the work done by external forces that is stored as potential energy within the material due to deformation.

Q2: How does modulus of rigidity affect strain energy?
A: Higher modulus of rigidity means the material is stiffer, resulting in lower strain energy for the same applied stress and volume.

Q3: Can this formula be used for all materials?
A: This formula applies to materials that follow Hooke's law in shear and have linear elastic behavior.

Q4: What are typical units for these measurements?
A: Shear stress and modulus of rigidity are typically measured in Pascal (Pa), volume in cubic meters (m³), and strain energy in Joules (J).

Q5: How is this different from other forms of strain energy?
A: This specifically calculates energy due to shear deformation. Other forms include tensile strain energy and compressive strain energy, which have different formulas.