Hoop Stress On Thick Spherical Shell Given Compressive Radial Strain Calculator

Formula Used:

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

Modulus of Elasticity Of Thick Shell (E):

Pascal

Compressive Strain (ε):

unitless

Radial Pressure (P_v):

Pascal/m²

Mass Of Shell (M):

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:

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

Where:

\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pascal)
\( E \) — Modulus of Elasticity Of Thick Shell (Pascal)
\( \varepsilon_{compressive} \) — Compressive Strain (unitless)
\( P_v \) — Radial Pressure (Pascal per Square Meter)
\( M \) — Mass Of Shell (kg)

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

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 loads.

4. Using the Calculator

Tips: Enter all values in appropriate units. Modulus of Elasticity and Radial Pressure should be in Pascal units, Compressive Strain is unitless, and Mass should be in kilograms. 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.

Q2: How does wall thickness affect hoop stress in spherical shells?
A: In thick-walled spheres, hoop stress varies through the wall thickness, being maximum at the inner surface and minimum at the outer surface.

Q3: What safety factors should be considered in design?
A: Typical safety factors range from 2 to 4 depending on the application, material properties, and operating conditions.

Q4: Can this formula be used for thin-walled spherical shells?
A: For thin-walled spheres (where thickness is less than 1/10 of the radius), simplified formulas are typically used as stress distribution is more uniform.

Q5: What materials are commonly used for spherical pressure vessels?
A: Common materials include carbon steel, stainless steel, aluminum alloys, and composite materials, chosen based on strength, corrosion resistance, and application requirements.