Radius Of Thick Cylindrical Shell Given Stress On Cylindrical Shell And Poisson's Ratio Calculator

Formula Used:

\[ r_{cylindrical\ shell} = \frac{\Delta r}{\frac{\sigma_{\theta} - (\nu \cdot (\sigma_{l} - \sigma_{c}))}{E}} \]

Change In Radius (Δr):

Hoop Stress On Thick Shell (σ_θ):

Poisson's Ratio (ν):

Longitudinal Stress Thick Shell (σ_l):

Compressive Stress Thick Shell (σ_c):

Modulus Of Elasticity Of Thick Shell (E):

Radius Of Cylindrical Shell (r):

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1. What Is The Radius Of Thick Cylindrical Shell Formula?

The formula calculates the radius of a thick cylindrical shell given the change in radius, various stress components, Poisson's ratio, and modulus of elasticity. It's derived from the relationship between stress, strain, and material properties in cylindrical structures.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ r_{cylindrical\ shell} = \frac{\Delta r}{\frac{\sigma_{\theta} - (\nu \cdot (\sigma_{l} - \sigma_{c}))}{E}} \]

Where:

\( r_{cylindrical\ shell} \) — Radius of cylindrical shell (m)
\( \Delta r \) — Change in radius (m)
\( \sigma_{\theta} \) — Hoop stress on thick shell (Pa)
\( \nu \) — Poisson's ratio
\( \sigma_{l} \) — Longitudinal stress thick shell (Pa)
\( \sigma_{c} \) — Compressive stress thick shell (Pa)
\( E \) — Modulus of elasticity of thick shell (Pa)

Explanation: This formula accounts for the complex stress-strain relationships in thick-walled cylindrical structures under various loading conditions.

3. Importance Of Radius Calculation

Details: Accurate radius calculation is crucial for designing pressure vessels, piping systems, and cylindrical structures to ensure they can withstand internal and external pressures without failure.

4. Using The Calculator

Tips: Enter all stress values in Pascals (Pa), change in radius in meters (m), and ensure Poisson's ratio is between 0.1 and 0.5 for most metals and alloys.

5. Frequently Asked Questions (FAQ)

Q1: What is Poisson's ratio and why is it important?
A: Poisson's ratio is the ratio of transverse strain to axial strain. It's important because it describes how materials deform in multiple directions when stressed.

Q2: What are typical values for modulus of elasticity?
A: For steel: 200-210 GPa, aluminum: 69-79 GPa, concrete: 20-40 GPa, rubber: 0.01-0.1 GPa.

Q3: When is this formula most applicable?
A: This formula is most applicable for thick-walled cylinders where wall thickness is significant compared to the radius, typically when the ratio of outer to inner radius exceeds 1.1.

Q4: What are the limitations of this calculation?
A: The calculation assumes homogeneous, isotropic material behavior and may not account for temperature effects, creep, or anisotropic material properties.

Q5: How does this differ from thin-walled cylinder calculations?
A: Thin-walled formulas assume uniform stress distribution through the wall thickness, while thick-walled formulas account for stress variations through the wall.