Hoop Stress On Thick Spherical Shell Given Tensile Radial Strain Calculator

Formula Used:

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

Modulus of Elasticity (E):

Pascal

Tensile Strain (ε):

Radial Pressure (Pv):

Pascal/m²

Mass of Shell (M):

Hoop Stress (σθ):

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1. What is Hoop Stress?

Hoop stress is the circumferential stress in a thick-walled spherical shell, which is a critical parameter in pressure vessel design and structural analysis. It represents the stress acting tangentially to the circumference of the shell.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_{\theta} \) — Hoop stress (Pascal)
\( E \) — Modulus of elasticity (Pascal)
\( \varepsilon_{tensile} \) — Tensile strain
\( P_v \) — Radial pressure (Pascal/m²)
\( M \) — Mass of shell (kg)

Explanation: This formula calculates the hoop stress in a thick spherical shell by considering the material properties, strain conditions, radial pressure, and mass of the shell.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing pressure vessels, piping systems, and spherical containers to ensure structural integrity and prevent failure under internal or external pressure.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Ensure positive values for modulus of elasticity, tensile strain, and mass. Radial pressure can be zero or positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress and radial stress?
A: Hoop stress acts circumferentially around the shell, while radial stress acts perpendicular to the surface of the shell.

Q2: When is this formula applicable?
A: This formula is specifically designed for thick spherical shells under tensile radial strain conditions.

Q3: What are typical values for modulus of elasticity?
A: Modulus of elasticity varies by material. For steel: ~200 GPa, aluminum: ~70 GPa, concrete: ~30 GPa.

Q4: How does shell thickness affect hoop stress?
A: In thick shells, hoop stress varies through the thickness, with maximum stress typically occurring at the inner surface.

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