Modulus Of Rigidity Given Deflection For Close-Coiled Helical Spring Calculator

Formula Used:

\[ G = \frac{64 \times W \times R^3 \times N}{\delta \times d^4} \]

Spring Load (W):

Mean Radius (R):

Number of Coils (N):

Deflection of Spring (δ):

Diameter of Spring (d):

Modulus of Rigidity (G):

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1. What is the Modulus of Rigidity Formula?

The Modulus of Rigidity (also known as shear modulus) is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. For close-coiled helical springs, it can be calculated using the deflection formula.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{64 \times W \times R^3 \times N}{\delta \times d^4} \]

Where:

\( G \) — Modulus of Rigidity (Pa)
\( W \) — Spring Load (N)
\( R \) — Mean Radius of spring coil (m)
\( N \) — Number of Coils in spring
\( \delta \) — Deflection of Spring (m)
\( d \) — Diameter of Spring wire (m)

Explanation: This formula calculates the modulus of rigidity based on the spring's physical characteristics and its response to applied load.

3. Importance of Modulus of Rigidity Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units (N for load, m for dimensions). 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 common materials?
A: For steel: 75-80 GPa, for aluminum: 24-28 GPa, for rubber: 0.0001-0.001 GPa.

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

Q3: Why is this formula specific to close-coiled helical springs?
A: Close-coiled springs have specific geometric assumptions that simplify the calculation of shear stress and strain.

Q4: What factors can affect the accuracy of this calculation?
A: Material homogeneity, temperature effects, and manufacturing tolerances can affect accuracy.

Q5: Can this formula be used for open-coiled springs?
A: No, open-coiled springs have different stress distributions and require more complex formulas.