Modulus Of Elasticity Given Radial Strain In Thick Cylindrical Shell Calculator

Formula Used:

\[ E = \frac{-\sigma_c - \nu \cdot (\sigma_\theta + \sigma_l)}{\varepsilon} \]

Compressive Stress Thick Shell (σc):

Poisson's Ratio (ν):

Hoop Stress on thick shell (σθ):

Longitudinal Stress Thick Shell (σl):

Strain (ε):

Modulus of Elasticity Of Thick Shell (E):

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1. What is the Modulus of Elasticity Formula?

The formula calculates the modulus of elasticity for thick cylindrical shells considering radial strain. It accounts for compressive stress, Poisson's ratio, hoop stress, longitudinal stress, and strain to determine the material's resistance to elastic deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{-\sigma_c - \nu \cdot (\sigma_\theta + \sigma_l)}{\varepsilon} \]

Where:

\( E \) — Modulus of Elasticity Of Thick Shell (Pa)
\( \sigma_c \) — Compressive Stress Thick Shell (Pa)
\( \nu \) — Poisson's Ratio
\( \sigma_\theta \) — Hoop Stress on thick shell (Pa)
\( \sigma_l \) — Longitudinal Stress Thick Shell (Pa)
\( \varepsilon \) — Strain

Explanation: The formula calculates the modulus of elasticity by considering the combined effects of various stresses and the material's Poisson ratio on the radial strain.

3. Importance of Modulus of Elasticity Calculation

Details: The modulus of elasticity is a fundamental material property that indicates how much a material will deform under stress. Accurate calculation is crucial for designing thick cylindrical shells that can withstand internal pressures and external loads without excessive deformation.

4. Using the Calculator

Tips: Enter all stress values in Pascals (Pa). Poisson's ratio should be between 0 and 0.5. Strain must be a non-zero value. Ensure all inputs are valid numerical values.

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, representing 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 strain that occurs when a material is stretched or compressed, which affects the overall deformation behavior.

Q3: What are typical values for modulus of elasticity?
A: Steel: 200 GPa, Aluminum: 69 GPa, Concrete: 20-30 GPa, Rubber: 0.01-0.1 GPa. Values vary significantly between materials.

Q4: How does this differ from thin shell calculations?
A: Thick shell calculations account for stress variations through the wall thickness, while thin shell assumptions consider uniform stress distribution.

Q5: When should this formula be used?
A: This formula is specifically designed for calculating modulus of elasticity in thick cylindrical shells under combined loading conditions with known radial strain.