Hoop Stress Calculator
Calculate circumferential stress in pressure vessels
Inner radius of the cylindrical vessel
Wall thickness of the pressure vessel
How to Use This Calculator
Enter Internal Pressure
Input the internal pressure (P) that the vessel will experience. This is the gauge pressure inside the vessel. Use consistent units (MPa, psi, etc.).
Enter Inner Radius
Input the inner radius (r) of the cylindrical pressure vessel. This is half the inner diameter. Ensure units match your thickness and pressure units.
Enter Wall Thickness
Input the wall thickness (t) of the vessel. For thin-walled vessels, the thickness should be much less than the radius (t < r/10).
Calculate and Verify
Click "Calculate" to get the hoop stress. Compare this value to the material's yield strength to ensure the design is safe with appropriate factor of safety.
Formula
Hoop Stress = (Pressure × Radius) ÷ Thickness
σ_h = (P × r) / t
Where:
- σ_h = Hoop stress (circumferential stress)
- P = Internal pressure
- r = Inner radius
- t = Wall thickness
Example:
For a pressure vessel with:
- Pressure: 2.5 MPa
- Inner radius: 500 mm
- Wall thickness: 10 mm
Hoop Stress = (2.5 × 500) ÷ 10 = 125 MPa
Note: This formula is for thin-walled pressure vessels (t < r/10).
About Hoop Stress Calculator
The Hoop Stress Calculator is an essential engineering tool for analyzing the circumferential stress in cylindrical pressure vessels. Hoop stress, also called circumferential stress, is the stress that acts tangentially around the circumference of the vessel and is typically the critical stress component in pressure vessel design.
When to Use This Calculator
- Pressure Vessel Design: Determine wall thickness requirements for cylindrical vessels
- Safety Analysis: Verify that hoop stress is within acceptable limits
- Material Selection: Choose appropriate materials based on stress calculations
- Process Equipment: Design boilers, tanks, pipes, and reactors
- Quality Control: Verify manufacturing meets design specifications
Why Use Our Calculator?
- ✅ Quick Analysis: Instant hoop stress calculations for design verification
- ✅ Design Optimization: Determine optimal wall thickness for given pressure
- ✅ Safety Compliance: Ensure designs meet pressure vessel codes (ASME, etc.)
- ✅ Educational Tool: Learn pressure vessel stress analysis principles
- ✅ Error Prevention: Reduce calculation errors in critical designs
Common Applications
Chemical Processing: Design pressure vessels for chemical reactors, storage tanks, and process equipment. Hoop stress is typically the limiting factor in cylindrical vessel design.
Power Generation: Calculate stresses in boilers, steam drums, and heat exchangers. These components operate under high pressure and temperature, making accurate stress analysis critical.
Petroleum Industry: Design oil and gas storage tanks, pipelines, and pressure vessels. Hoop stress analysis ensures safe operation under various pressure conditions.
Important Notes
- This formula is valid for thin-walled pressure vessels (thickness < radius/10)
- For thick-walled vessels, use Lame's equations instead
- Hoop stress is typically twice the longitudinal (axial) stress in cylindrical vessels
- Always apply appropriate factor of safety (typically 2-3) in actual designs
- Consider temperature effects and material properties at operating conditions
Frequently Asked Questions
What is hoop stress?
Hoop stress (circumferential stress) is the stress acting tangentially around the circumference of a cylindrical pressure vessel. It's caused by internal pressure trying to expand the vessel radially. It's typically the highest stress component in cylindrical vessels.
Why is hoop stress higher than longitudinal stress?
Hoop stress is approximately twice the longitudinal stress in thin-walled cylindrical vessels because the circumference is twice the diameter. The hoop stress resists the pressure trying to split the vessel lengthwise, while longitudinal stress resists pressure pushing the ends apart.
What's the difference between thin-walled and thick-walled vessels?
Thin-walled vessels have thickness much less than the radius (t < r/10), allowing the simplified formula. Thick-walled vessels (t ≥ r/10) require Lame's equations which account for stress variation through the wall thickness.
Can I use this for spherical pressure vessels?
No, this formula is specifically for cylindrical vessels. For spherical vessels, the stress is uniform in all directions and uses the formula: σ = (P × r) / (2 × t).
How do I ensure my pressure vessel is safe?
Calculate the hoop stress and ensure it's less than the material's yield strength divided by an appropriate factor of safety (typically 2-3). Also consider fatigue, corrosion, and temperature effects. Follow applicable pressure vessel codes (ASME Boiler and Pressure Vessel Code, etc.).