1. What Is Hoop Stress In Thin Spherical Shell?

Hoop stress is the circumferential stress that develops in a thin-walled spherical shell when subjected to internal pressure. It represents the tensile stress acting tangentially to the circumference of the shell.

2. How Does The Calculator Work?

The calculator uses the hoop stress formula:

Where:

• \( \sigma_{\theta} \) — Hoop stress (Pa)
• \( P_i \) — Internal pressure (Pa)
• \( D_i \) — Inner diameter of the vessel (m)
• \( t \) — Thickness of the thin shell (m)

Explanation: This formula calculates the circumferential stress in a thin-walled spherical pressure vessel subjected to internal pressure.

3. Importance Of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing pressure vessels, piping systems, and containment structures to ensure they can withstand internal pressures without failure.

4. Using The Calculator

Tips: Enter internal pressure in Pascals, inner diameter in meters, and thickness in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress and longitudinal stress?
A: Hoop stress acts circumferentially around the vessel, while longitudinal stress acts along the length of the vessel. In spherical shells, hoop stress is uniform in all directions.

Q2: When is the thin shell assumption valid?
A: The thin shell assumption is generally valid when the thickness is less than 1/10 of the radius of the vessel.

Q3: What are typical units for these calculations?
A: While Pascals and meters are used here, engineers often work with MPa for stress, MPa for pressure, and mm for dimensions.

Q4: How does material properties affect hoop stress?
A: Material properties determine the allowable stress limits, but the calculated hoop stress depends only on geometry and pressure loading.

Q5: What safety factors are typically used?
A: Safety factors vary by application and material, but typically range from 2.0 to 4.0 for pressure vessel design.