Modulus Of Rigidity Given Strain Energy Stored By Spring Calculator

Formula Used:

\[ G = \frac{32 \times P^2 \times R^3 \times N}{U \times d^4} \]

Axial Load (P):

Mean Radius Spring Coil (R):

Number of Coils (N):

Strain Energy (U):

Diameter of Spring Wire (d):

Modulus of Rigidity of Spring (G):

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1. What is the Modulus of Rigidity Formula?

The Modulus of Rigidity formula calculates the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a spring material is under axial loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{32 \times P^2 \times R^3 \times N}{U \times d^4} \]

Where:

\( G \) — Modulus of Rigidity of Spring (Pa)
\( P \) — Axial Load (N)
\( R \) — Mean Radius Spring Coil (m)
\( N \) — Number of Coils
\( U \) — Strain Energy (J)
\( d \) — Diameter of Spring Wire (m)

Explanation: The formula relates the modulus of rigidity to the spring's geometric properties, applied load, and stored strain energy.

3. Importance of Modulus of Rigidity Calculation

Details: Calculating the modulus of rigidity is essential for spring design and analysis, helping engineers determine the material's stiffness and predict spring behavior under various loading conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (Newtons for load, meters for dimensions, Joules for energy). All values must be positive and non-zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is Modulus of Rigidity?
A: Modulus of Rigidity (Shear Modulus) is the ratio of shear stress to shear strain, measuring a material's resistance to shearing deformation.

Q2: How does spring geometry affect rigidity?
A: Wire diameter has the strongest effect (d^4 term), followed by coil radius (R^3). More coils generally reduce overall stiffness.

Q3: What are typical values for modulus of rigidity?
A: For spring steel, typical values range from 75-80 GPa. The exact value depends on the specific alloy and heat treatment.

Q4: Can this formula be used for all spring types?
A: This formula is specifically for helical compression/tension springs with circular wire cross-section under axial loading.

Q5: What if I get an unrealistically high or low value?
A: Double-check your input units and values. Ensure all measurements are in consistent units (preferably SI units).