Modulus Of Elasticity Of Vessel Given Circumferential Strain Calculator

Formula Used:

\[ E = \frac{P_i \cdot D_i}{2 \cdot t \cdot \varepsilon_1} \cdot \left( \frac{1}{2} - \nu \right) \]

Internal Pressure (P_i):

Inner Diameter (D_i):

Thickness (t):

Circumferential Strain (ε₁):

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 for a thin-walled vessel under internal pressure, considering circumferential strain and Poisson's ratio. It provides a measure of the material's stiffness and resistance to deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{P_i \cdot D_i}{2 \cdot t \cdot \varepsilon_1} \cdot \left( \frac{1}{2} - \nu \right) \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( P_i \) — Internal Pressure (Pa)
\( D_i \) — Inner Diameter (m)
\( t \) — Thickness (m)
\( \varepsilon_1 \) — Circumferential Strain
\( \nu \) — Poisson's Ratio

Explanation: The formula accounts for the relationship between internal pressure, vessel dimensions, material deformation, and Poisson's effect on the modulus of elasticity.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for designing pressure vessels, predicting material behavior under stress, and ensuring structural integrity in engineering applications.

4. Using the Calculator

Tips: Enter all values in consistent units (Pa for pressure, meters for dimensions). Ensure circumferential strain is not zero, and Poisson's ratio is between 0 and 0.5.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of elasticity?
A: Modulus of elasticity is a measure of a material's stiffness and its resistance to elastic deformation under stress.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the lateral contraction/expansion that occurs when a material is stretched/compressed, 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, concrete ≈ 30 GPa, rubber ≈ 0.01-0.1 GPa.

Q4: When is this formula applicable?
A: This formula is specifically for thin-walled pressure vessels under internal pressure with known circumferential strain.

Q5: What are the limitations of this calculation?
A: The formula assumes homogeneous, isotropic material behavior and is most accurate for small deformations within the elastic limit.