Modulus of Rigidity given Deflection in Spring Calculator

Formula Used:

\[ G = \frac{8 \times P \times D^3 \times N_a}{\delta \times d^4} \]

Axial Spring Force (P):

Mean Coil Diameter of Spring (D):

Active Coils in Spring (Na):

coils

Deflection of Spring (δ):

Diameter of Spring Wire (d):

Modulus of Rigidity (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:

\[ G = \frac{8 \times P \times D^3 \times N_a}{\delta \times d^4} \]

Where:

\( G \) — Modulus of rigidity of spring wire (Pa)
\( P \) — Axial Spring Force (N)
\( D \) — Mean Coil Diameter of Spring (m)
\( N_a \) — Active Coils in Spring
\( \delta \) — Deflection of Spring (m)
\( d \) — Diameter of spring wire (m)

Explanation: This formula calculates the modulus of rigidity based on spring geometry and applied force.

3. Importance of Modulus of Rigidity Calculation

Details: Accurate calculation of modulus of rigidity is crucial for spring design, material selection, and ensuring proper spring performance under load.

4. Using the Calculator

Tips: Enter all values in appropriate units. 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: The modulus of rigidity typically ranges from 70-80 GPa for steel springs and 40-45 GPa for brass springs.

Q2: How does wire diameter affect the modulus of rigidity?
A: The modulus of rigidity is a material property and is not affected by wire diameter. However, the calculation formula includes wire diameter to account for geometric factors.

Q3: What are active coils in a spring?
A: Active coils are the coils or turns of a spring that actually contribute to the load-bearing capacity, excluding the end coils that are typically ground flat.

Q4: Why is the mean coil diameter important in this calculation?
A: The mean coil diameter significantly affects the spring's stiffness and stress distribution, making it a critical parameter in the calculation.

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