Change In Radius Of Thick Cylindrical Shell Given Stresses And Poison's Ratio Calculator

Formula Used:

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

Radius Of Cylindrical Shell:

Hoop Stress on thick shell:

Poisson's Ratio:

Longitudinal Stress Thick Shell:

Compressive Stress Thick Shell:

Modulus of Elasticity Of Thick Shell:

Change in radius (Δr):

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1. What is Change in Radius of Thick Cylindrical Shell?

The change in radius of a thick cylindrical shell refers to the deformation or alteration in the radius when the shell is subjected to various stresses. This calculation is crucial in engineering to understand how materials behave under stress and to ensure structural integrity.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \Delta r \) — Change in radius (m)
\( r_{cylindrical\ shell} \) — Radius of cylindrical shell (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 calculates the radial deformation of a thick cylindrical shell by considering the combined effects of hoop stress, longitudinal stress, compressive stress, and material properties through Poisson's ratio and modulus of elasticity.

3. Importance of Radius Change Calculation

Details: Calculating the change in radius is essential for designing pressure vessels, pipelines, and other cylindrical structures to ensure they can withstand operational stresses without excessive deformation or failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for radius, Pascals for stresses). Ensure Poisson's ratio is between 0.1 and 0.5, and all stress values are accurate measurements from engineering analysis.

5. Frequently Asked Questions (FAQ)

Q1: What is Poisson's ratio and why is it important?
A: Poisson's ratio is a measure of the Poisson effect, which describes the expansion of material perpendicular to the direction of compression. It's crucial for understanding how materials deform under stress.

Q2: How does hoop stress differ from longitudinal stress?
A: Hoop stress acts circumferentially around the cylinder, while longitudinal stress acts along the length of the cylinder. Both contribute differently to the overall deformation.

Q3: What is the typical range for modulus of elasticity?
A: Modulus of elasticity varies by material. For steel, it's typically around 200 GPa, for aluminum about 70 GPa, and for concrete around 20-30 GPa.

Q4: When is this calculation most relevant?
A: This calculation is particularly important for thick-walled pressure vessels, hydraulic cylinders, and other engineering applications where cylindrical structures are subjected to internal or external pressure.

Q5: How accurate is this formula for real-world applications?
A: The formula provides a theoretical calculation based on elastic deformation. For precise engineering applications, additional factors like temperature effects, material imperfections, and safety factors should be considered.