Modulus Of Rigidity Using Deflection Of Square Section Wire Spring Calculator

Formula Used:

\[ G = \frac{44.7 \times W_{load} \times R^3 \times N}{\delta \times d^4} \]

Spring Load (W_load):

Mean Radius (R):

Number of Coils (N):

Deflection of Spring (δ):

Diameter of Spring (d):

Modulus of Rigidity (G):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Modulus of Rigidity?

The Modulus of Rigidity (also known as shear modulus) is the measure of the rigidity of a body, given by the ratio of shear stress to shear strain. It is often denoted by G and is an important property in materials science and engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{44.7 \times W_{load} \times R^3 \times N}{\delta \times d^4} \]

Where:

\( G \) — Modulus of Rigidity (Pa)
\( W_{load} \) — 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 for a spring with square section wire based on its geometric properties and deflection under load.

3. Importance of Modulus of Rigidity Calculation

Details: Calculating the modulus of rigidity is crucial for understanding material behavior under shear stress, designing mechanical components, and ensuring structural integrity in engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (N for load, m for dimensions). Ensure all values are positive and within reasonable ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of rigidity for common materials?
A: The modulus of rigidity varies by material. For steel, it's typically around 79 GPa, for aluminum about 26 GPa, and for rubber it can be as low as 0.0003 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 the constant 44.7 used in this formula?
A: The constant 44.7 is derived from the geometry and material properties specific to square section wire springs and ensures dimensional consistency in the formula.

Q4: Can this formula be used for springs with circular cross-section wire?
A: No, this specific formula is designed for square section wire springs. Circular wire springs use a different formula with different constants.

Q5: What factors can affect the accuracy of this calculation?
A: Measurement accuracy of input parameters, material homogeneity, temperature effects, and manufacturing tolerances can all affect the calculation accuracy.