Longitudinal Stress Given Radial Strain In Thick Cylindrical Shell Calculator

Formula Used:

\[ \text{Longitudinal Stress Thick Shell} = \frac{(-\text{Compressive Stress Thick Shell} - (\text{Strain} \times \text{Modulus of Elasticity Of Thick Shell}))}{\text{Poisson's Ratio}} - \text{Hoop Stress on thick shell} \] \[ \sigma_l = \frac{(-\sigma_c - (\varepsilon \times E))}{\mu} - \sigma_{\theta} \]

Compressive Stress Thick Shell:

Strain:

Modulus of Elasticity Of Thick Shell:

Poisson's Ratio:

Hoop Stress on thick shell:

Longitudinal Stress Thick Shell:

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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 axis of the cylinder. It's an important parameter in pressure vessel design and analysis, particularly when considering combined loading conditions and material behavior under internal or external pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates longitudinal stress by considering the combined effects of compressive stress, material strain, elastic properties, and hoop stress in a thick-walled cylindrical shell.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for pressure vessel design, pipeline engineering, and structural analysis where cylindrical components are subjected to internal pressure and other loading conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (Pa for stresses and modulus, dimensionless for strain and Poisson's ratio). Ensure Poisson's ratio is not zero to avoid division by zero.

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 0.3 being a common value for many metals.

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 this formula particularly important?
A: This calculation is critical in pressure vessel design, pipeline engineering, and any application involving thick-walled cylindrical structures under pressure.

Q4: What are the limitations of this formula?
A: The formula assumes linear elastic material behavior and may not accurately represent stress states in materials with nonlinear behavior or under extreme conditions.

Q5: How does wall thickness affect longitudinal stress?
A: In thick-walled cylinders, stress distribution varies through the wall thickness, making accurate stress calculation more complex than in thin-walled vessels.