Radial Strain Given Stresses On Thick Cylinder And Poisson's Ratio Calculator

Formula Used:

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

Compressive Stress Thick Shell (σc):

Poisson's Ratio (μ):

Hoop Stress on thick shell (σθ):

Longitudinal Stress Thick Shell (σl):

Modulus of Elasticity Of Thick Shell (E):

Radial Strain (ε):

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1. What is Radial Strain in Thick Cylinders?

Radial strain in thick cylinders refers to the deformation or change in dimension along the radial direction when subjected to internal or external pressures. It is a crucial parameter in pressure vessel design and mechanical engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \varepsilon \) — Radial strain (dimensionless)
\( \sigma_c \) — Compressive stress (Pa)
\( \mu \) — Poisson's ratio (dimensionless)
\( \sigma_\theta \) — Hoop stress (Pa)
\( \sigma_l \) — Longitudinal stress (Pa)
\( E \) — Modulus of elasticity (Pa)

Explanation: This formula calculates the radial strain by considering the combined effects of compressive stress, hoop stress, longitudinal stress, and material properties through Poisson's ratio and modulus of elasticity.

3. Importance of Radial Strain Calculation

Details: Accurate calculation of radial strain is essential for designing pressure vessels, piping systems, and cylindrical structures to ensure they can withstand internal pressures without excessive deformation or failure.

4. Using the Calculator

Tips: Enter all stress values in Pascals (Pa). Poisson's ratio should be between 0.1 and 0.5 for most metals and alloys. Modulus of elasticity must be a positive non-zero value.

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, with common values around 0.3 for steel and 0.33 for aluminum.

Q2: How does radial strain differ from hoop strain?
A: Radial strain measures deformation in the radial direction (thickness change), while hoop strain measures circumferential deformation (diameter change).

Q3: When is this formula most applicable?
A: This formula is particularly useful for thick-walled cylinders where stress distribution is not uniform across the wall thickness.

Q4: What are the limitations of this calculation?
A: The formula assumes linear elastic material behavior and may not be accurate for materials with significant plastic deformation or non-linear behavior.

Q5: How does temperature affect the calculation?
A: Temperature changes can affect material properties (E and μ) and induce thermal stresses, which should be considered separately in the analysis.