Longitudinal Stress In Thin Cylindrical Vessel Given Longitudinal Strain Calculator

Formula Used:

\[ \sigma_l = (\varepsilon_{longitudinal} \times E) + (\mu \times \sigma_{\theta}) \]

Longitudinal Strain (ε_longitudinal):

Modulus of Elasticity (E):

Pascal

Poisson's Ratio (μ):

Hoop Stress (σ_θ):

Pascal

Longitudinal Stress (σ_l):

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1. What is Longitudinal Stress in Thin Cylindrical Vessel?

Longitudinal Stress in Thin Cylindrical Vessel is defined as the stress produced when a pipe or cylindrical vessel is subjected to internal pressure along its longitudinal axis. It's an important parameter in pressure vessel design and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_l = (\varepsilon_{longitudinal} \times E) + (\mu \times \sigma_{\theta}) \]

Where:

\( \sigma_l \) — Longitudinal Stress (Pascal)
\( \varepsilon_{longitudinal} \) — Longitudinal Strain
\( E \) — Modulus of Elasticity (Pascal)
\( \mu \) — Poisson's Ratio
\( \sigma_{\theta} \) — Hoop Stress (Pascal)

Explanation: The formula calculates longitudinal stress by considering both the elastic deformation component and the effect of Poisson's ratio on hoop stress.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for pressure vessel design, structural integrity assessment, and ensuring safe operation under internal pressure conditions.

4. Using the Calculator

Tips: Enter longitudinal strain, modulus of elasticity, Poisson's ratio (typically between 0.1-0.5 for metals), and hoop stress. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Poisson's ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.1 and 0.5.

Q2: How does longitudinal stress differ from hoop stress?
A: Longitudinal stress acts along the length of the cylinder, while hoop stress acts circumferentially around the cylinder.

Q3: When is this formula most applicable?
A: This formula is most accurate for thin-walled cylindrical vessels where wall thickness is small compared to the diameter.

Q4: What are the units for these parameters?
A: Stress values are typically in Pascals, strain is dimensionless, and modulus of elasticity is in Pascals.

Q5: How does temperature affect these calculations?
A: Temperature changes can affect material properties like modulus of elasticity, which should be considered for accurate calculations.