1. What is Hoop Stress?

Hoop Stress on thick shell is the circumferential stress in a cylinder that occurs due to internal or external pressure. It's a critical parameter in pressure vessel design and structural integrity analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sigma_{\theta} \) — Hoop Stress (Pa)
• \( R_i \) — Increase in radius (m)
• \( r^* \) — Radius at junction (m)
• \( E \) — Modulus of Elasticity (Pa)
• \( P_v \) — Radial Pressure (Pa/m²)
• \( M \) — Mass of Shell (kg)

Explanation: This formula calculates the circumferential stress in a thick-walled cylinder by considering the increase in radius, material properties, and applied pressures.

3. Importance of Hoop Stress Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all inputs. The calculator provides results in Pascals (Pa).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress and radial stress?
A: Hoop stress is circumferential stress acting tangentially, while radial stress acts perpendicular to the cylindrical surface.

Q2: When is this formula applicable?
A: This formula is specifically for thick-walled cylinders where wall thickness is significant compared to the radius.

Q3: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, for aluminum: ~70 GPa, for concrete: ~20-30 GPa, depending on the specific material.

Q4: How does temperature affect hoop stress?
A: Temperature changes can cause thermal expansion/contraction, which may induce additional hoop stresses in constrained cylinders.

Q5: What safety factors should be considered?
A: Typical safety factors range from 1.5 to 4.0 depending on the application, material properties, and consequences of failure.