Modulus of Rigidity given Rate of Spring Calculator

Formula Used:

\[ G = \frac{k \times (8 \times D^3 \times N_a)}{d^4} \]

Stiffness of Spring (k):

N/m

Mean Coil Diameter of Spring (D):

Active Coils in Spring (Na):

Diameter of spring wire (d):

Modulus of rigidity of spring wire (G):

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1. What is Modulus of Rigidity?

Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{k \times (8 \times D^3 \times N_a)}{d^4} \]

Where:

\( G \) — Modulus of rigidity of spring wire (Pa)
\( k \) — Stiffness of Spring (N/m)
\( D \) — Mean Coil Diameter of Spring (m)
\( N_a \) — Active Coils in Spring
\( d \) — Diameter of spring wire (m)

Explanation: This formula calculates the modulus of rigidity based on the spring's physical characteristics and stiffness.

3. Importance of Modulus of Rigidity

Details: The modulus of rigidity is a fundamental material property that determines how a material will deform under shear stress. It's crucial for spring design and material selection in mechanical engineering applications.

4. Using the Calculator

Tips: Enter stiffness in N/m, diameters in meters, and number of active coils. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of rigidity for spring materials?
A: For common spring materials like steel, the modulus of rigidity typically ranges from 75-85 GPa, while for materials like phosphor bronze it's around 41-45 GPa.

Q2: How does modulus of rigidity differ from Young's modulus?
A: Young's modulus measures resistance to linear deformation under tension/compression, while modulus of rigidity measures resistance to shear deformation.

Q3: Why is this calculation important for spring design?
A: Knowing the modulus of rigidity helps engineers predict spring behavior, calculate deflection under load, and ensure the spring will perform as intended.

Q4: What factors can affect the accuracy of this calculation?
A: Material homogeneity, temperature variations, manufacturing tolerances, and measurement accuracy can all affect the precision of the result.

Q5: Can this formula be used for all types of springs?
A: This formula is primarily designed for helical compression and extension springs. Other spring types may require different calculations.