Thickness Of Thin Cylindrical Vessel Given Circumferential Strain Calculator

Formula Used:

\[ t = \frac{P_i \cdot D_i}{2 \cdot e_1 \cdot E} \cdot \left(\frac{1}{2} - \mu\right) \]

Internal Pressure (P_i):

Inner Diameter (D_i):

Circumferential Strain (e₁):

Modulus of Elasticity (E):

Poisson's Ratio (μ):

Thickness Of Thin Shell (t):

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1. What is the Thickness Of Thin Cylindrical Vessel Formula?

The thickness of thin cylindrical vessel formula calculates the required wall thickness of a cylindrical pressure vessel based on internal pressure, dimensions, material properties, and circumferential strain. This is essential for ensuring structural integrity and safety in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{P_i \cdot D_i}{2 \cdot e_1 \cdot E} \cdot \left(\frac{1}{2} - \mu\right) \]

Where:

\( t \) — Thickness of thin shell (m)
\( P_i \) — Internal pressure (Pa)
\( D_i \) — Inner diameter of cylinder (m)
\( e_1 \) — Circumferential strain
\( E \) — Modulus of elasticity (Pa)
\( \mu \) — Poisson's ratio

Explanation: The formula accounts for the relationship between internal pressure, vessel dimensions, material properties, and the resulting circumferential strain to determine the appropriate wall thickness.

3. Importance of Thickness Calculation

Details: Accurate thickness calculation is crucial for pressure vessel design to prevent failure under internal pressure, ensure safety, and optimize material usage while maintaining structural integrity.

4. Using the Calculator

Tips: Enter internal pressure in Pascals, inner diameter in meters, circumferential strain (dimensionless), modulus of elasticity in Pascals, and Poisson's ratio (between 0-0.5). All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "thin" cylindrical vessel?
A: A vessel is considered thin when the wall thickness is less than about 1/10 of the inner radius. For thicker vessels, more complex formulas are required.

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 and stress distribution.

Q3: What are typical values for Poisson's ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.25 and 0.35. Rubber-like materials can have values接近 0.5, while cork is around 0.0.

Q4: How does circumferential strain affect thickness calculation?
A: Higher circumferential strain typically requires thicker walls to contain the same internal pressure, as the material experiences greater deformation.

Q5: When should this formula not be used?
A: This formula should not be used for thick-walled vessels, vessels with complex geometries, or when plastic deformation occurs. It's primarily for elastic deformation in thin-walled cylindrical vessels.