Hoop Stress On Thick Spherical Shell Given Tensile Radial Strain And Poisson's Ratio Calculator

Formula Used:

\[ \sigma_{\theta} = \frac{(E \times \varepsilon_{tensile}) - P_v}{2 \times \nu} \]

Modulus of Elasticity Of Thick Shell (E):

Pascal

Tensile Strain (ε_tensile):

unitless

Radial Pressure (P_v):

Pascal per m²

Poisson's Ratio (ν):

unitless

Hoop Stress on thick shell (σ_θ):

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1. What is Hoop Stress on Thick Spherical Shell?

Hoop Stress on thick spherical shell is the circumferential stress that develops in a thick-walled spherical pressure vessel when subjected to internal or external pressure. It represents the tensile stress acting tangentially to the circumference of the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{\theta} = \frac{(E \times \varepsilon_{tensile}) - P_v}{2 \times \nu} \]

Where:

\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pascal)
\( E \) — Modulus of Elasticity Of Thick Shell (Pascal)
\( \varepsilon_{tensile} \) — Tensile Strain (unitless)
\( P_v \) — Radial Pressure (Pascal per Square Meter)
\( \nu \) — Poisson's Ratio (unitless)

Explanation: This formula calculates the circumferential (hoop) stress in a thick spherical shell based on material properties and applied pressure conditions.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing pressure vessels, storage tanks, and other spherical containers to ensure structural integrity and prevent failure under pressure loading conditions.

4. Using the Calculator

Tips: Enter modulus of elasticity in Pascal, tensile strain (unitless), radial pressure in Pascal per square meter, and Poisson's ratio (typically between 0.1-0.5). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress in cylindrical and spherical shells?
A: In spherical shells, hoop stress is uniform in all directions, while in cylindrical shells, there are both circumferential (hoop) and longitudinal stresses with different magnitudes.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the material's tendency to contract in directions perpendicular to the applied stress, which affects the stress distribution in thick-walled vessels.

Q3: What are typical values for Poisson's ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.25-0.35. Rubber-like materials can have values close to 0.5, while cork has a value near 0.

Q4: When is this formula applicable?
A: This formula is valid for thick spherical shells where wall thickness is significant compared to the radius, and material behavior is linear elastic.

Q5: How does radial pressure affect hoop stress?
A: Internal pressure typically creates tensile hoop stress, while external pressure creates compressive hoop stress. The magnitude increases with pressure intensity.