Compressive Stress Given Radial Strain In Thick Cylindrical Shell Calculator

Formula Used:

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

Strain (ε):

Modulus of Elasticity (E):

Pascal

Poisson's Ratio (ν):

Hoop Stress (σ_θ):

Pascal

Longitudinal Stress (σ_l):

Pascal

Compressive Stress (σ_c):

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1. What is Compressive Stress in Thick Cylindrical Shell?

Compressive Stress in Thick Cylindrical Shell is the force that is responsible for the deformation of the material such that the volume of the material reduces. It's calculated considering radial strain, material properties, and other stress components.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_c \) — Compressive Stress (Pascal)
\( \varepsilon \) — Strain
\( E \) — Modulus of Elasticity (Pascal)
\( \nu \) — Poisson's Ratio
\( \sigma_{\theta} \) — Hoop Stress (Pascal)
\( \sigma_l \) — Longitudinal Stress (Pascal)

Explanation: The formula accounts for the combined effect of elastic deformation and Poisson's ratio on compressive stress in thick cylindrical shells.

3. Importance of Compressive Stress Calculation

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

4. Using the Calculator

Tips: Enter all required values with appropriate units. Strain and Poisson's Ratio are dimensionless. Modulus of Elasticity, Hoop Stress, and Longitudinal Stress should be in Pascal units.

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: Why is the compressive stress negative in the formula?
A: The negative sign indicates that compressive stress acts in the opposite direction to tensile stress, reducing the volume of the material.

Q3: What materials is this formula applicable to?
A: This formula applies to isotropic materials that follow Hooke's law within their elastic limits.

Q4: How does thick shell differ from thin shell analysis?
A: Thick shell analysis considers radial stress variations through the wall thickness, while thin shell assumes constant stress through the thickness.

Q5: What are practical applications of this calculation?
A: This calculation is essential for designing pressure vessels, hydraulic cylinders, gun barrels, and other thick-walled cylindrical components.