Longitudinal Stress Given Longitudinal Strain In Thick Cylindrical Shell Calculator

Formula Used:

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

Longitudinal Strain (ε):

Modulus of Elasticity (E):

Poisson's Ratio (μ):

Hoop Stress (σ_θ):

Compressive Stress (σ_c):

Longitudinal Stress (σ_l):

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1. What is Longitudinal Stress in Thick Cylindrical Shell?

Longitudinal Stress in a thick cylindrical shell is the stress component acting parallel to the longitudinal axis of the cylinder. It is produced when the cylinder is subjected to internal pressure and other mechanical loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the longitudinal stress by considering both the direct elastic response and the effect of lateral stresses through Poisson's ratio.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for designing pressure vessels, pipelines, and other cylindrical structures to ensure structural integrity and prevent failure under internal pressure.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Poisson's Ratio?
A: For most engineering materials, Poisson's Ratio ranges between 0.1 and 0.5, with common metals typically around 0.3.

Q2: How does longitudinal stress differ from hoop stress?
A: Longitudinal stress acts parallel to the cylinder axis, while hoop stress acts circumferentially around the cylinder.

Q3: When is compressive stress significant in this calculation?
A: Compressive stress becomes significant when external compressive loads or thermal contraction effects are present in the cylindrical structure.

Q4: What materials is this formula applicable to?
A: This formula applies to isotropic, homogeneous materials that follow Hooke's law within their elastic limits.

Q5: How accurate is this calculation for real-world applications?
A: This provides a theoretical estimation. For critical applications, finite element analysis and experimental validation are recommended.