Radius Of Shaft Given Total Strain Energy Stored In Shaft Calculator

Formula Used:

\[ r_{shaft} = \sqrt{\frac{(\tau^2) \times L \times J_{shaft}}{2 \times G \times U}} \]

Shear Stress On Surface Of Shaft (τ):

Length Of Shaft (L):

Polar Moment Of Inertia Of Shaft (J_shaft):

m⁴

Modulus Of Rigidity Of Shaft (G):

Strain Energy In Body (U):

Radius Of Shaft (r_shaft):

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1. What is Radius Of Shaft Given Total Strain Energy Stored In Shaft?

This calculation determines the radius of a shaft when the total strain energy stored in the shaft is known, along with other mechanical properties such as shear stress, length, polar moment of inertia, and modulus of rigidity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{shaft} = \sqrt{\frac{(\tau^2) \times L \times J_{shaft}}{2 \times G \times U}} \]

Where:

\( r_{shaft} \) — Radius of Shaft (m)
\( \tau \) — Shear stress on surface of shaft (Pa)
\( L \) — Length of Shaft (m)
\( J_{shaft} \) — Polar Moment of Inertia of shaft (m⁴)
\( G \) — Modulus of rigidity of Shaft (Pa)
\( U \) — Strain Energy in body (J)

Explanation: This formula calculates the radius of a shaft based on the relationship between strain energy and the shaft's mechanical properties under torsional loading.

3. Importance of Radius Calculation

Details: Calculating the radius of a shaft is crucial for mechanical design and analysis, ensuring proper sizing for strength requirements and energy storage capacity in torsional applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. All input values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of strain energy in shaft design?
A: Strain energy represents the energy stored in a shaft due to deformation under torsional load, which is important for understanding the shaft's energy absorption capacity and potential failure modes.

Q2: How does modulus of rigidity affect the radius calculation?
A: Higher modulus of rigidity (stiffer material) generally requires a smaller radius to achieve the same strain energy storage, as stiffer materials deform less under the same stress.

Q3: What are typical applications of this calculation?
A: This calculation is used in mechanical engineering for designing shafts in power transmission systems, automotive applications, and industrial machinery where torsional energy storage is a consideration.

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material behavior and linear elastic deformation. It may not accurately predict behavior for materials with non-linear properties or under extreme loading conditions.

Q5: How does shear stress relate to shaft radius?
A: Shear stress is inversely proportional to the cube of the radius for a given torque, meaning small changes in radius can significantly affect the stress levels in the shaft.