Compressive Stress Given Change In Radius Of Thick Cylindrical Shell Calculator

Formula Used:

\[ \sigma_c = \sigma_l - \left( \frac{\sigma_\theta - \left( \frac{\Delta r \cdot E}{r_{\text{cylindrical shell}}} \right)}{\nu} \right) \]

Longitudinal Stress Thick Shell (σl):

Pascal

Hoop Stress on thick shell (σθ):

Pascal

Change in radius (Δr):

Meter

Modulus of Elasticity Of Thick Shell (E):

Pascal

Radius Of Cylindrical Shell (r):

Meter

Poisson's Ratio (ν):

Compressive Stress Thick Shell (σc):

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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 an important parameter in pressure vessel design and structural engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = \sigma_l - \left( \frac{\sigma_\theta - \left( \frac{\Delta r \cdot E}{r} \right)}{\nu} \right) \]

Where:

\( \sigma_c \) — Compressive Stress Thick Shell (Pascal)
\( \sigma_l \) — Longitudinal Stress Thick Shell (Pascal)
\( \sigma_\theta \) — Hoop Stress on thick shell (Pascal)
\( \Delta r \) — Change in radius (Meter)
\( E \) — Modulus of Elasticity Of Thick Shell (Pascal)
\( r \) — Radius Of Cylindrical Shell (Meter)
\( \nu \) — Poisson's Ratio

Explanation: The formula calculates compressive stress by considering the relationship between longitudinal stress, hoop stress, material properties, and geometric changes.

3. Importance of Compressive Stress Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Radius must be greater than zero. Poisson's Ratio typically ranges between 0.1 and 0.5 for most metals and alloys.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Poisson's Ratio in this calculation?
A: Poisson's Ratio relates the lateral strain to axial strain and is essential for understanding how materials deform under stress in multiple directions.

Q2: How does change in radius affect compressive stress?
A: The change in radius directly influences the stress distribution in the cylindrical shell, with larger changes typically indicating higher stress levels.

Q3: What are typical values for Modulus of Elasticity?
A: Modulus of Elasticity varies by material. For steel, it's approximately 200 GPa, for aluminum about 70 GPa, and for concrete around 30 GPa.

Q4: When is this formula most applicable?
A: This formula is particularly useful for thick-walled cylindrical pressure vessels where wall thickness is significant compared to the radius.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors of 1.5 to 4.0 depending on the application, material properties, and regulatory requirements.