1. What is Hoop Stress?

Hoop stress is the stress exerted circumferentially in both directions on a particle in the wall of a cylinder or sphere when it is subjected to internal pressure. For spherical vessels, the stress is uniform in all directions.

2. How Does the Calculator Work?

The calculator uses the hoop stress formula for spheres:

Where:

• \( \sigma \) — Hoop stress (Pa)
• \( P \) — Internal pressure (Pa)
• \( r \) — Radius of the sphere (m)
• \( t \) — Wall thickness (m)

Explanation: The formula calculates the stress in the wall of a 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 safely withstand internal pressures without failure.

4. Using the Calculator

Tips: Enter pressure in Pascals (Pa), radius in meters (m), and thickness in meters (m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between hoop stress in spheres vs cylinders?
A: For spheres, hoop stress is uniform in all directions and calculated as Pr/2t. For cylinders, hoop stress is Pr/t and longitudinal stress is Pr/2t.

Q2: What are typical safety factors for pressure vessels?
A: Safety factors typically range from 2 to 4, depending on the application, material, and regulatory requirements.

Q3: How does temperature affect hoop stress calculations?
A: Temperature affects material properties (like yield strength) and may cause thermal expansion, which should be considered in design calculations.

Q4: What units should I use for accurate calculations?
A: Use consistent SI units: Pascals for pressure, meters for dimensions. Ensure all inputs use the same unit system.

Q5: When is this formula not applicable?
A: This formula assumes thin-walled vessels (t < r/10), uniform material properties, and static internal pressure. For thick-walled vessels, more complex formulas are needed.