Longitudinal Stress Given Circumferential Strain Calculator

Formula Used:

\[ \text{Longitudinal Stress Thick Shell} = \frac{\text{Hoop Stress in Thin shell} - (\text{Circumferential strain Thin Shell} \times \text{Modulus of Elasticity Of Thin Shell})}{\text{Poisson's Ratio}} \]

Hoop Stress in Thin shell (σθ):

Pascal

Circumferential strain Thin Shell (e1):

(dimensionless)

Modulus of Elasticity Of Thin Shell (E):

Pascal

Poisson's Ratio (ν):

(dimensionless)

Longitudinal Stress Thick Shell (σl):

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1. What is Longitudinal Stress?

Longitudinal Stress in a thick shell is the stress produced along the length of a pipe or cylinder when subjected to internal pressure. It works in conjunction with hoop stress to determine the structural integrity of pressurized vessels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_l = \frac{\sigma_\theta - (e_1 \times E)}{\nu} \]

Where:

\( \sigma_l \) — Longitudinal Stress Thick Shell (Pascal)
\( \sigma_\theta \) — Hoop Stress in Thin shell (Pascal)
\( e_1 \) — Circumferential strain Thin Shell (dimensionless)
\( E \) — Modulus of Elasticity Of Thin Shell (Pascal)
\( \nu \) — Poisson's Ratio (dimensionless, typically 0.1-0.5)

Explanation: This formula calculates the longitudinal stress in thick-walled pressure vessels by accounting for the relationship between hoop stress, material properties, and strain.

3. Importance of Longitudinal Stress Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Hoop stress and modulus of elasticity should be in Pascals. Poisson's ratio must be between 0.1 and 0.5. Circumferential strain is dimensionless.

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. Both are important for pressure vessel design.

Q2: When is this formula applicable?
A: This formula is used for thick-walled pressure vessels where wall thickness is significant compared to the diameter.

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, with common values around 0.3 for steel.

Q4: How does circumferential strain affect longitudinal stress?
A: Higher circumferential strain typically reduces the longitudinal stress, as shown in the formula where strain is subtracted from the hoop stress component.

Q5: What units should be used for input values?
A: Stress values (hoop stress and modulus) should be in Pascals. Strain and Poisson's ratio are dimensionless. Ensure consistent units for accurate results.