1. What is Hoop Stress?

Hoop stress is the stress exerted circumferentially in both directions on a cylinder when it is subjected to internal or external pressure. It is a critical parameter in pressure vessel design and analysis.

2. How Does the Calculator Work?

The calculator uses the hoop stress formula:

Where:

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

Explanation: This formula calculates the circumferential stress in a thin-walled cylindrical pressure vessel. It assumes uniform internal pressure and a wall thickness much smaller than the radius.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing safe pressure vessels, piping systems, and other cylindrical structures subjected to internal pressure. It helps determine the required wall thickness to prevent 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 is the difference between hoop stress and longitudinal stress?
A: Hoop stress acts circumferentially around the cylinder, while longitudinal stress acts along the length of the cylinder. Hoop stress is typically twice the longitudinal stress in thin-walled cylinders.

Q2: When is this formula valid?
A: This formula is valid for thin-walled pressure vessels where the wall thickness is less than about one-tenth of the radius.

Q3: What units should I use?
A: Use consistent SI units: pressure in Pascals (Pa), dimensions in meters (m). The result will be in Pascals (Pa).

Q4: How does temperature affect hoop stress?
A: Temperature changes can cause thermal expansion, which may add to or subtract from the pressure-induced stress, depending on whether the vessel is heated or cooled.

Q5: What safety factors should be considered?
A: Engineering design typically includes safety factors to account for material imperfections, unexpected pressure surges, and other variables. Consult relevant design codes for appropriate safety factors.