Modulus Of Elasticity Given Change In Radius Of Thick Cylindrical Shell Calculator

Formula Used:

\[ E = r_{\text{cylindrical shell}} \times \frac{\sigma_{\theta} - (\nu \times (\sigma_l - \sigma_c))}{\Delta r} \]

Radius Of Cylindrical Shell:

Hoop Stress On Thick Shell:

Poisson's Ratio:

Longitudinal Stress Thick Shell:

Compressive Stress Thick Shell:

Change In Radius:

Modulus Of Elasticity Of Thick Shell:

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1. What Is The Modulus Of Elasticity Formula?

The modulus of elasticity formula calculates the elastic modulus of a thick cylindrical shell based on radius, stresses, Poisson's ratio, and change in radius. It provides a measure of the material's stiffness and resistance to deformation under stress.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ E = r_{\text{cylindrical shell}} \times \frac{\sigma_{\theta} - (\nu \times (\sigma_l - \sigma_c))}{\Delta r} \]

Where:

\( E \) — Modulus of Elasticity Of Thick Shell (Pa)
\( r_{\text{cylindrical shell}} \) — Radius Of Cylindrical Shell (m)
\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pa)
\( \nu \) — Poisson's Ratio
\( \sigma_l \) — Longitudinal Stress Thick Shell (Pa)
\( \sigma_c \) — Compressive Stress Thick Shell (Pa)
\( \Delta r \) — Change in radius (m)

Explanation: The formula accounts for the relationship between various stresses and the resulting deformation in a thick cylindrical shell.

3. Importance Of Modulus Of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for material characterization, structural design, and predicting how materials will behave under different loading conditions.

4. Using The Calculator

Tips: Enter all values in appropriate units (meters for lengths, Pascals for stresses). Ensure radius and change in radius are positive values. Poisson's ratio should be between 0 and 0.5.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of elasticity?
A: Modulus of elasticity (Young's modulus) is a measure of a material's stiffness, defined as the ratio of stress to strain in the elastic deformation region.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the lateral deformation that occurs when a material is stretched or compressed, affecting the overall stress distribution.

Q3: What are typical values for modulus of elasticity?
A: Values vary by material: steel ~200 GPa, aluminum ~70 GPa, concrete ~20-30 GPa, rubber ~0.01-0.1 GPa.

Q4: When is this formula particularly useful?
A: This formula is especially valuable for analyzing thick-walled pressure vessels, pipes, and cylindrical structures under internal or external pressure.

Q5: What are the limitations of this calculation?
A: The formula assumes linear elastic behavior, homogeneous material properties, and may not account for temperature effects or material anisotropy.