Thickness Of Thin Cylindrical Vessel Given Longitudinal Strain Calculator

Formula Used:

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

Internal Pressure in thin shell:

Inner Diameter of Cylinder:

Longitudinal Strain:

Modulus of Elasticity Of Thin Shell:

Poisson's Ratio:

Thickness Of Thin Shell:

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1. What is Thickness Of Thin Cylindrical Vessel Given Longitudinal Strain?

The thickness of a thin cylindrical vessel given longitudinal strain is a calculation that determines the required wall thickness of a cylindrical pressure vessel based on the longitudinal strain experienced by the material under internal pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( t \) — Thickness of thin shell (m)
\( P_i \) — Internal pressure in thin shell (Pa)
\( D_i \) — Inner diameter of cylinder (m)
\( \varepsilon_{longitudinal} \) — Longitudinal strain
\( E \) — Modulus of elasticity of thin shell (Pa)
\( \nu \) — Poisson's ratio

Explanation: This formula calculates the required thickness of a thin-walled cylindrical vessel based on the material properties and applied internal pressure, considering the longitudinal strain.

3. Importance of Thickness Calculation

Details: Accurate thickness calculation is crucial for designing pressure vessels that can safely contain internal pressures without failure while optimizing material usage and cost.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "thin" cylindrical vessel?
A: A vessel is considered thin-walled when the wall thickness is less than about 1/10 of the radius.

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, which affects the 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 close to 0.5.

Q4: How does internal pressure affect the required thickness?
A: Higher internal pressure requires greater wall thickness to withstand the increased stress on the vessel walls.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors to account for material imperfections, unexpected pressure surges, and other uncertainties.