1. What is Hoop Stress?

Hoop stress (also known as circumferential stress) is the stress exerted circumferentially in both directions on a cylinder wall when pressure is applied. It's a critical factor in designing pressure vessels, pipes, and other cylindrical structures.

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: The formula calculates the tensile stress in the circumferential direction of a cylindrical pressure vessel. This stress is twice the longitudinal stress in a thin-walled cylinder.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing safe pressure vessels, pipelines, and storage tanks. It helps engineers determine the appropriate wall thickness to prevent failure under internal pressure.

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. In thin-walled cylinders, hoop stress is approximately twice the longitudinal stress.

Q2: When is the hoop stress formula valid?
A: The formula is most accurate for thin-walled cylinders where the wall thickness is less than about 1/10 of the radius.

Q3: What are typical units for hoop stress?
A: While we use Pascals (Pa) in this calculator, hoop stress is often expressed in MPa (megaPascals) or psi (pounds per square inch) in engineering applications.

Q4: How does material strength relate to hoop stress?
A: The calculated hoop stress must be less than the yield strength of the material (with an appropriate safety factor) to prevent permanent deformation or failure.

Q5: Does this formula work for concrete structures?
A: Yes, the formula applies to cylindrical concrete structures like silos, water tanks, and pipes, though additional factors like concrete's tensile strength limitations must be considered.