Calculator Input
Use one consistent length unit for radius, thickness, and shell length. The modulus unit changes automatically with the selected unit system.
Formula Used
This calculator uses a classical elastic buckling screening expression for a long, thin cylindrical shell under uniform external pressure.
Meaning of the outputs:
- Ideal critical pressure is the theoretical elastic buckling pressure.
- Reduced critical pressure applies the knockdown factor for imperfections.
- Allowable design pressure applies the selected safety factor.
- Utilization compares your applied pressure with the allowable pressure.
How to Use This Calculator
- Select metric or imperial units.
- Enter shell radius, thickness, and shell length using the same length unit.
- Enter elastic modulus, Poisson ratio, knockdown factor, and safety factor.
- Choose the pressure unit and enter the applied external pressure.
- Press Calculate Pressure to view the result card above the form, the pressure graph, and export options.
Example Data Table
| Case | Radius (mm) | Thickness (mm) | Length (mm) | E (GPa) | ν | η | SF | Applied (kPa) | Allowable (kPa) |
|---|---|---|---|---|---|---|---|---|---|
| Steel Shell A | 500 | 5 | 1500 | 200 | 0.30 | 0.85 | 1.50 | 10.000 | 17.148 |
| Aluminum Shell B | 300 | 4 | 900 | 70 | 0.33 | 0.90 | 1.40 | 12.000 | 16.310 |
| Steel Shell C | 750 | 8 | 2400 | 210 | 0.29 | 0.80 | 1.60 | 12.000 | 19.219 |
FAQs
1. What does this calculator estimate?
It estimates elastic buckling pressure for a thin cylindrical shell under uniform external pressure. It also applies an imperfection knockdown factor and a design safety factor.
2. Which formula is used here?
The calculator uses a classical long-shell screening equation: pcr = (2E / √(3(1-ν²))) × (t/D)3. Real shells can buckle earlier, so the knockdown factor matters.
3. Why is shell length included?
Length is shown for context through the L/D ratio. Very short or intermediate shells may show boundary effects that the simple long-shell formula does not capture fully.
4. What is the knockdown factor?
It reduces the ideal theoretical pressure to account for imperfections, fabrication tolerances, residual stresses, and real-world sensitivity. Lower values produce more conservative results.
5. Can I use mixed units?
Use one consistent length unit for radius, thickness, and length. Pressure can be entered in the selected pressure unit, and modulus must match the chosen unit system.
6. Does this replace code-based design checks?
No. This is a fast screening tool. Final design should follow the relevant pressure vessel, aerospace, or structural code and, when needed, detailed shell analysis.
7. Why does thickness change pressure so strongly?
The model uses a cubic thickness relation. Small thickness increases can raise buckling pressure sharply, which is why thin shells are especially sensitive to fabrication quality.
8. When should I avoid this model?
Avoid using it alone for thick shells, strong end constraints, large openings, stiffeners, nonlinear material behavior, plastic collapse, or highly imperfect geometries.