Modulus Of Elasticity Of Vessel Material Given Internal Pressure Calculator

Formula Used:

\[ E = \frac{P_i \cdot D_i}{2 \cdot t \cdot \varepsilon_{\text{longitudinal}}}} \cdot \left(\frac{1}{2} - \nu\right) \]

Internal Pressure (P_i):

Inner Diameter (D_i):

Thickness (t):

Longitudinal Strain (ε_longitudinal):

Poisson's Ratio (ν):

Modulus of Elasticity (E):

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1. What is the Modulus of Elasticity Formula?

The formula calculates the modulus of elasticity of vessel material given internal pressure, inner diameter, thickness, longitudinal strain, and Poisson's ratio. It provides a measure of the material's stiffness and resistance to deformation under pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{P_i \cdot D_i}{2 \cdot t \cdot \varepsilon_{\text{longitudinal}}}} \cdot \left(\frac{1}{2} - \nu\right) \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( P_i \) — Internal Pressure (Pa)
\( D_i \) — Inner Diameter (m)
\( t \) — Thickness (m)
\( \varepsilon_{\text{longitudinal}} \) — Longitudinal Strain
\( \nu \) — Poisson's Ratio

Explanation: The formula calculates the material's elastic modulus by considering the pressure-induced stress, geometric parameters, and material properties.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate modulus of elasticity calculation is crucial for designing pressure vessels, predicting material behavior under load, and ensuring structural integrity and safety.

4. Using the Calculator

Tips: Enter internal pressure in Pascals, inner diameter and thickness in meters, longitudinal strain (dimensionless), and Poisson's ratio (between 0-0.5). All values must be valid and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of elasticity?
A: Modulus of elasticity measures a material's resistance to elastic deformation under stress. It indicates how stiff a material is.

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

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

Q4: When should this formula be used?
A: This formula is specifically for calculating modulus of elasticity in thin-walled pressure vessels under internal pressure.

Q5: Are there limitations to this equation?
A: This formula assumes thin-walled vessels, homogeneous material properties, and linear elastic behavior. It may not be accurate for thick-walled vessels or materials with non-linear behavior.