Modulus Of Elasticity Given Increase In Inner Radius Of Outer Cylinder Calculator

Formula Used:

\[ E = \frac{r^*}{R_i} \times \left( \sigma_\theta + \frac{P_v}{M} \right) \]

Radius at Junction (r*):

Increase in Radius (Ri):

Hoop Stress on Thick Shell (σθ):

Radial Pressure (Pv):

Pa/m²

Mass Of Shell (M):

Modulus of Elasticity (E):

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1. What is Modulus of Elasticity?

Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. It's a fundamental property in material science and engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{r^*}{R_i} \times \left( \sigma_\theta + \frac{P_v}{M} \right) \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( r^* \) — Radius at Junction (m)
\( R_i \) — Increase in Radius (m)
\( \sigma_\theta \) — Hoop Stress on Thick Shell (Pa)
\( P_v \) — Radial Pressure (Pa/m²)
\( M \) — Mass Of Shell (kg)

Explanation: This formula calculates the modulus of elasticity based on the geometric and mechanical properties of a thick-walled cylindrical shell.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for material selection, structural design, and predicting how materials will behave under various loading conditions in engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Radius values must be in meters, stress in Pascals, pressure in Pascals per square meter, and mass in kilograms. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of modulus of elasticity?
A: Modulus of elasticity indicates the stiffness of a material - how much it will deform under a given load. Higher values mean stiffer materials.

Q2: How does this differ from Young's modulus?
A: Modulus of elasticity is often used interchangeably with Young's modulus, which specifically refers to the ratio of tensile stress to tensile strain.

Q3: What are typical modulus values for common materials?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~30 GPa, Wood: ~10 GPa, Rubber: ~0.01-0.1 GPa.

Q4: Why is this calculation important for thick shells?
A: Thick shells experience complex stress distributions, and accurate modulus calculation helps predict deformation and failure under pressure loads.

Q5: Can this formula be used for all materials?
A: This formula is specifically derived for thick-walled cylindrical shells and assumes linear elastic material behavior.