Modulus Of Elasticity Given Longitudinal Strain In Thick Cylindrical Shell Calculator

Formula Used:

\[ E = \frac{\sigma_l - \nu (\sigma_{\theta} - \sigma_c)}{\varepsilon_{longitudinal}} \]

Longitudinal Stress Thick Shell (σl):

Poisson's Ratio (ν):

Hoop Stress on thick shell (σθ):

Compressive Stress Thick Shell (σc):

Longitudinal Strain (εlongitudinal):

Modulus of Elasticity (E):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Modulus of Elasticity Formula?

The formula calculates the modulus of elasticity (E) for a thick cylindrical shell using longitudinal stress, Poisson's ratio, hoop stress, compressive stress, and longitudinal strain. It provides a measure of the material's stiffness and resistance to deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{\sigma_l - \nu (\sigma_{\theta} - \sigma_c)}{\varepsilon_{longitudinal}} \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( \sigma_l \) — Longitudinal Stress (Pa)
\( \nu \) — Poisson's Ratio
\( \sigma_{\theta} \) — Hoop Stress (Pa)
\( \sigma_c \) — Compressive Stress (Pa)
\( \varepsilon_{longitudinal} \) — Longitudinal Strain

Explanation: The formula accounts for the relationship between various stresses and strain to determine the material's elastic modulus.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for material characterization, structural design, and predicting material behavior under load.

4. Using the Calculator

Tips: Enter all stress values in Pascals (Pa). Poisson's ratio and longitudinal strain are dimensionless. Ensure longitudinal strain is not zero.

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-strain relationship.

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

Q5: When is this formula most applicable?
A: This formula is particularly useful for thick-walled pressure vessels, pipes, and cylindrical structures where wall thickness is significant relative to diameter.