Modulus Of Elasticity Using Hoop Stress Due To Temperature Fall Calculator

Young's Modulus Formula:

\[ E = \frac{\sigma_h \times d_{tyre}}{D_{wheel} - d_{tyre}} \]

Young's Modulus (E):

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1. What is Young's Modulus?

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain. It is a measure of the stiffness of a material.

2. How Does the Calculator Work?

The calculator uses the Young's Modulus formula:

\[ E = \frac{\sigma_h \times d_{tyre}}{D_{wheel} - d_{tyre}} \]

Where:

\( E \) — Young's Modulus (Pascal)
\( \sigma_h \) — Hoop Stress SOM (Pascal)
\( d_{tyre} \) — Diameter of Tyre (Meter)
\( D_{wheel} \) — Wheel Diameter (Meter)

Explanation: This formula calculates the modulus of elasticity using hoop stress due to temperature fall, considering the dimensional relationship between tyre and wheel diameters.

3. Importance of Young's Modulus Calculation

Details: Young's Modulus is crucial for understanding material behavior under stress, designing structural components, and predicting material deformation under various loading conditions.

4. Using the Calculator

Tips: Enter hoop stress in Pascal, tyre diameter and wheel diameter in meters. All values must be valid (positive values, wheel diameter must be greater than tyre diameter).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of hoop stress in this calculation?
A: Hoop stress represents the circumferential stress in cylindrical objects caused by internal or external pressure, which is essential for calculating Young's Modulus in this context.

Q2: Why is the difference between wheel and tyre diameters important?
A: The dimensional difference affects the stress distribution and strain characteristics, making it a critical factor in the modulus calculation.

Q3: What are typical Young's Modulus values for common materials?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~30 GPa, Rubber: ~0.01-0.1 GPa. Values vary based on material composition and treatment.

Q4: Can this formula be used for all materials?
A: This specific formula is designed for calculating Young's Modulus using hoop stress due to temperature fall in tyre-wheel systems and may not be universally applicable to all materials.

Q5: How does temperature affect Young's Modulus?
A: Generally, Young's Modulus decreases with increasing temperature as materials become less stiff at higher temperatures.