Estimate drum hoop and axial stress accurately. Choose units, wall model, and safety metrics easily. Download tables, validate inputs, and document maintenance actions clearly.
This tool estimates stress in a cylindrical boiler drum due to pressure. Choose the model that best matches your thickness ratio.
For comparison and reporting, the calculator also reports von Mises equivalent stress: sigma_vm = sqrt(0.5*((sh-sz)^2 + (sz-sr)^2 + (sr-sh)^2)).
| Model | Internal (bar) | External (bar) | Inner diameter (mm) | Thickness (mm) | Hoop stress (MPa) | Axial stress (MPa) |
|---|---|---|---|---|---|---|
| Thin-wall | 120 | 0 | 1600 | 90 | 106.667 | 53.333 |
| Thick-wall | 120 | 0 | 1600 | 150 | 165.517 | 72.414 |
| Thin-wall | 80 | 1 | 1200 | 70 | 67.714 | 33.857 |
Example values are illustrative. Confirm design allowables and applicable codes for your project.
A boiler drum behaves like a cylindrical pressure vessel holding a steam–water mixture. Internal pressure generates membrane forces in the shell, producing hoop and axial stresses. These baseline stresses support quick screening of operating conditions and integrity reporting.
The driving load is net pressure: internal pressure minus external pressure. Net pressure controls stress magnitude directly, so pressure basis must be consistent. If you enter gauge internal pressure, keep external pressure at zero. If you enter absolute values, use absolute external values too.
For thin shells, hoop stress is approximated by (P·D)/(2t), and axial stress by (P·D)/(4t). Hoop stress is usually larger because the circumference carries most of the pressure load. Thin-wall results are fast for preliminary checks when thickness is small compared with diameter.
The ratio t/D helps decide whether through-thickness variation is important. When t/D is small, hoop stress is nearly uniform across the wall. As t/D increases, the inner surface carries a higher peak hoop stress, so thick-wall analysis becomes preferable.
Thick-wall theory captures the stress gradient using the Lamé equations. Hoop stress is highest at the inner radius and decreases toward the outside. Radial stress is compressive at the bore and relaxes toward the external pressure at the outer wall. This calculator reports inner-surface values for conservative screening.
Closed ends cause axial stress from pressure acting on the end area. Under thin-wall conditions, axial stress is about half the hoop stress. Under thick-wall conditions, the axial component is treated as uniform for the closed-end case. Different boundary conditions may change the axial result.
Multiaxial stress is important for thick walls where radial stress is non-negligible. Von Mises equivalent stress combines hoop, axial, and radial components into one comparison value. If you provide yield strength, the calculator estimates factor of safety as yield divided by von Mises stress.
Pair operating pressure with measured wall thickness from inspection. Recalculate after thickness updates, pressure uprates, or hydrotest changes. Export CSV for trends and PDF for documentation. High calculated stress suggests targeted NDE, thickness mapping, and engineering review under applicable codes.
Use gauge pressure when the outside is atmospheric, and set external pressure to zero. Use absolute pressures only if you also enter the matching absolute external pressure so net pressure stays correct.
Thin-wall estimates are commonly reasonable when t/D is small, often at or below 0.05. If your ratio is higher, thick-wall inner-surface stresses typically provide a better peak-stress estimate.
Pressure loads the shell around its entire circumference, creating a larger membrane force than the end-cap force. For closed ends in thin-wall theory, axial stress is approximately half of hoop stress.
Radial stress is the pressure stress through the thickness. At the inner surface it equals negative internal pressure, and it approaches the external pressure at the outside. It is most relevant for thick walls.
If yield strength is provided, the tool computes yield strength divided by von Mises equivalent stress. Treat it as a screening metric; design allowables and temperature effects must follow your governing code.
Thick-wall theory resolves the stress gradient and reports peak hoop stress at the bore. Thin-wall equations effectively average the stress through the wall, so they can underpredict the maximum inner-surface hoop stress.
No. The calculator reports ideal shell stresses from pressure. Openings, attachments, weld geometry, and local thinning can raise stress. Use detailed analysis or code-based methods for concentration and reinforcement checks.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.