Calculator
Example Data Table
| Case | Pressure (MPa) | Inner Diameter (mm) | Thickness (mm) | Corrosion Allowance (mm) | Allowable Stress (MPa) | Joint Efficiency |
|---|---|---|---|---|---|---|
| Example 1 | 3.50 | 1600 | 45 | 2 | 140 | 1.00 |
| Example 2 | 5.00 | 1800 | 60 | 3 | 150 | 0.95 |
| Example 3 | 2.20 | 1200 | 32 | 1.5 | 125 | 0.90 |
Formula Used
This calculator reports both thin-wall and thick-wall cylindrical stress estimates. Thin-wall formulas are convenient when the diameter-to-thickness ratio is large. Thick-wall formulas are more reliable when the wall is relatively heavy.
1) Thin-Wall Hoop Stress
σh = (P × D) / (2 × t × E)
Where σh is hoop stress, P is net internal pressure, D is inner diameter, t is effective thickness, and E is joint efficiency.
2) Thin-Wall Longitudinal Stress
σL = (P × D) / (4 × t × E)
This estimates the axial membrane stress in the drum shell due to end loading from pressure.
3) Thick-Wall Lamé Equations
σr = A − B / r²
σθ = A + B / r²
A = (Piri² − Poro²) / (ro² − ri²)
B = ri²ro²(Pi − Po) / (ro² − ri²)
σr is radial stress, σθ is hoop stress, r is the evaluation radius, ri is inner radius, and ro is outer radius.
4) Required Thickness Estimate
treq = (P × D) / (2 × S × E)
This gives a quick required net thickness estimate using allowable stress S. Gross required thickness is net required thickness plus corrosion allowance.
How to Use This Calculator
- Enter the internal pressure and choose the matching pressure unit.
- Enter any external pressure if it applies. Leave zero otherwise.
- Provide the inner drum diameter and wall thickness.
- Enter the corrosion allowance to obtain effective thickness.
- Type the allowable material stress in MPa.
- Enter the weld or joint efficiency value between 0 and 1.
- Press Calculate Stress to show results above the form.
- Review hoop stress, longitudinal stress, thickness requirement, safety factor, and the plotted stress distribution.
- Use the CSV and PDF buttons to export the result set.
Engineering note: This tool is useful for quick screening and education. Final vessel design should still be checked against the governing pressure vessel code and detailed stress requirements.
Frequently Asked Questions
1) What stress is usually highest in a pressurized boiler drum?
Hoop stress is usually the highest membrane stress in a cylindrical drum under internal pressure. That is why it often controls shell thickness during preliminary checks.
2) Why does corrosion allowance matter?
Corrosion allowance reduces the effective metal thickness available to resist pressure. A larger allowance means higher computed stress and a smaller remaining thickness margin.
3) When should thick-wall equations be preferred?
Thick-wall equations are preferred when wall thickness is not small relative to drum diameter. They show stress variation across the wall instead of assuming uniform membrane stress.
4) What does joint efficiency do in this calculator?
Joint efficiency adjusts the effective load-carrying capability of the shell. Lower efficiency increases calculated thin-wall stress and can raise the required thickness estimate.
5) Why are thin-wall and thick-wall results different?
Thin-wall formulas assume stress is nearly uniform through the shell thickness. Thick-wall analysis accounts for changing radial and hoop stresses from the inner surface to the outer surface.
6) Is the safety factor here a code acceptance value?
No. It is a simple ratio of allowable stress to the controlling computed stress. Actual code acceptance may require different limits, load cases, and material adjustments.
7) Can I use this for design approval?
This calculator helps with fast estimation, comparison, and learning. It should not replace a full code-based design package, fabrication review, or certified engineering assessment.
8) What unit system does the calculator use internally?
The calculator converts pressure to MPa and geometry to millimeters internally. That keeps the equations consistent and makes the displayed stress results easy to compare.
Content Checks
- Meta description word count: 20 words
- Tag line word count: 20 words
- Result appears above the form after submission.
- CSV and PDF export options are included.
- Plotly graph is included.
- FAQs use plain HTML with no accordion.