Circumferential Stress Given Longitudinal Strain In Thick Cylindrical Shell Calculator

Formula Used:

\[ \sigma_{\theta} = \frac{\sigma_l - (\varepsilon_{longitudinal} \times E)}{\nu} + \sigma_c \]

Longitudinal Stress Thick Shell (σl):

Longitudinal Strain (εlongitudinal):

Modulus of Elasticity (E):

Poisson's Ratio (ν):

Compressive Stress Thick Shell (σc):

Hoop Stress on thick shell (σθ):

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1. What is Circumferential Stress?

Circumferential stress (hoop stress) is the stress experienced by the walls of a cylindrical pressure vessel when subjected to internal pressure. It acts tangentially to the circumference of the cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{\theta} = \frac{\sigma_l - (\varepsilon_{longitudinal} \times E)}{\nu} + \sigma_c \]

Where:

\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pa)
\( \sigma_l \) — Longitudinal Stress Thick Shell (Pa)
\( \varepsilon_{longitudinal} \) — Longitudinal Strain
\( E \) — Modulus of Elasticity (Pa)
\( \nu \) — Poisson's Ratio
\( \sigma_c \) — Compressive Stress Thick Shell (Pa)

Explanation: This formula calculates the circumferential stress in a thick cylindrical shell based on longitudinal strain and other material properties.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing pressure vessels, pipes, and cylindrical structures to ensure they can withstand internal pressures without failure.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Poisson's ratio must be between 0 and 0.5. All stress values should be in Pascals (Pa).

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 0.1 and 0.5.

Q4: When is this formula applicable?
A: This formula is specifically for thick cylindrical shells where wall thickness is significant compared to the radius.

Q5: What units should be used for input values?
A: All stress values should be in Pascals (Pa), strain is dimensionless, and modulus of elasticity should be in Pascals (Pa).