1. What is Hoop Stress in Thin Cylindrical Vessels?

Hoop stress (circumferential stress) is the stress exerted circumferentially in both the wall of a cylinder when it is subjected to internal pressure. It is a critical parameter in pressure vessel design and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sigma_{\theta} \) — Hoop Stress (Pascal)
• \( \varepsilon_{longitudinal} \) — Longitudinal Strain (unitless)
• \( E \) — Modulus of Elasticity (Pascal)
• \( \sigma_{l} \) — Longitudinal Stress (Pascal)
• \( \nu \) — Poisson's Ratio (unitless)

Explanation: This formula calculates the hoop stress in thin cylindrical vessels based on the given longitudinal strain, material properties, and stress conditions.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is essential for pressure vessel design, ensuring structural integrity and safety under internal pressure conditions.

4. Using the Calculator

Tips: Enter longitudinal strain (unitless), modulus of elasticity (Pascal), longitudinal stress (Pascal), and Poisson's ratio (between 0.1-0.5). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress and longitudinal stress?
A: Hoop stress acts circumferentially around the cylinder, while longitudinal stress acts along the length of the cylinder.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the material's tendency to expand or contract in directions perpendicular to the applied stress.

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.

Q4: When is this formula applicable?
A: This formula is specifically for thin-walled cylindrical vessels where the wall thickness is much smaller than the diameter.

Q5: What units should be used for input values?
A: All stress values should be in Pascals, strains are unitless, and Poisson's ratio is also unitless.