Hoop Stress Calculation Formula

Hoop Stress Formula:

\[ \sigma_h = \frac{P D}{2 t} \]

Hoop Stress (σₕ):

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1. What is Hoop Stress?

Hoop stress (also called circumferential stress) is the stress in a pipe or cylindrical vessel wall acting circumferentially in a plane perpendicular to the longitudinal axis. It arises from internal pressure and is a crucial factor in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the hoop stress formula:

\[ \sigma_h = \frac{P D}{2 t} \]

Where:

\( \sigma_h \) — Hoop stress (Pa)
\( P \) — Internal pressure (Pa)
\( D \) — Diameter of the cylinder (m)
\( t \) — Wall thickness (m)

Explanation: The formula shows that hoop stress is directly proportional to the internal pressure and diameter, and inversely proportional to the wall thickness.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is essential for designing safe pressure vessels, pipes, and cylindrical containers. It helps prevent structural failure due to excessive stress.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the calculation?
A: The calculator uses SI units: Pascals (Pa) for pressure and meters (m) for dimensions. Make sure all inputs are in consistent units.

Q2: Does this formula work for thin-walled cylinders only?
A: Yes, this formula is most accurate for thin-walled cylinders where D/t > 20. For thick-walled cylinders, more complex formulas are needed.

Q3: What is the typical safety factor for hoop stress?
A: Safety factors vary by application but typically range from 2.5 to 4 for pressure vessels, depending on material and regulations.

Q4: How does hoop stress compare to longitudinal stress?
A: Hoop stress is typically twice the longitudinal stress in a cylindrical pressure vessel under internal pressure.

Q5: What materials are commonly used to withstand high hoop stress?
A: Common materials include carbon steel, stainless steel, and high-strength alloys, chosen based on their yield strength and corrosion resistance.