Engineering task and calculation objective
The K10A module belongs to the module series for calculating shell boilers to DIN EN 12953-3 and, following the chapter structure of this series, covers Section 10: the design of furnace tubes and reversal chambers. Furnace tubes are the combustion-chamber tubes of a shell boiler loaded externally by the boiler pressure; the governing criterion is therefore not tensile strength under internal pressure, but the load-bearing capacity under external pressure, including stability against elastic and plastic buckling.
In practice, this calculation is needed for the design and re-rating of three-pass and smoke-tube boilers: plain and corrugated furnace tubes whose allowable pressure depends on wall thickness, diameter, unsupported length and out-of-roundness. DIN EN 12953-3 (shell boilers, Part 3: design and calculation for pressure parts) lays down the calculation rules, the allowable stresses and the design limits for this purpose.
The module determines the required wall thickness or the allowable pressure of the externally pressurized component and checks the geometric boundary conditions of the code, so that the furnace tube design can be calculated and documented without having to evaluate the standard by hand.
Calculation workflow
- Define geometry and design type: First the geometry of the externally pressurized component is defined: diameter, wall thickness, unsupported length between effective stiffeners, and the design type (plain or corrugated furnace tube). The permissible out-of-roundness also enters the calculation as an imperfection measure.
- Enter material and loading data: The design pressure and design temperature are specified; from the selected boiler steel follow the strength values and the modulus of elasticity at temperature, from which the standard derives the allowable stress.
- Verify load-bearing capacity under external pressure: For externally pressurized cylinders, the standard requires verification both against plastic collapse and against elastic buckling. The module evaluates the corresponding design equations with the prescribed safety factors.
- Check design limits: The geometric limits of application of the chapter are then checked, such as minimum and maximum wall thicknesses and permissible length-to-diameter ratios that the code prescribes for furnace tubes.
- Document the result: The result is the required wall thickness or the allowable pressure together with the utilization of the individual checks; the strength verification to DIN EN 12953-3 is thus documented in a traceable form.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| load case | case | – |
| Subjected to heat transfer | transfer | – |
| Gas entery temperature | tG | – |
| Nominal shell thickness | e | mm |
| Heating by | by | – |
| Calculation pressure | pc | MPa(p) |
| Saturation temperature | ts | °C |
| Additional temperature | tz | °C |
| Calculation temperature | tc | °C |
| Rectangular area | area | – |
| Elliptical area | area | – |
| Number of shape factor acc. to table 4 | 4 | – |
| Shell | Shell | – |
| Material strength | Ks | N/mm² |
| Material strength (Test) | Ks(Test) | N/mm² |
| Yield strength (Test) | Rp0.2 | N/mm² |
| Safety factor | Ss | - |
| Safety factor | Ss | - |
| design stress | fs | N/mm² |
| Wall thinning allawance | C1 | mm |
| Corrosion allawance | C2 | mm |
| Plate | Plate | – |
| Material strength | Kp | N/mm² |
| Material strength (Test) | Kp(Test) | N/mm² |
Calculation options
load case
operation · test
Subjected to heat transfer
Yes · No
Gas entery temperature
≤ 400 · 400-800 · > 800
Heating by
radiation · convection
Rectangular area
0 · 1 · 2 · 3 · 4 · 5
Elliptical area
0 · 1 · 2 · 3 · 4 · 5
Number of shape factor acc. to table 4
1 · 2 · 3 · 4
Wet back reversal chambers
Yes · No
Frequently asked questions
How does the calculation of a furnace tube differ from that of a normal boiler shell?
The boiler shell is under internal pressure and is designed against plastic collapse using the boiler formula. The furnace tube, in contrast, is loaded with external pressure from the water side; here, in addition to limiting the stress, stability against buckling is the governing criterion. This is why the modulus of elasticity, the unsupported length and the out-of-roundness enter the calculation, none of which play a role in internal-pressure design.
Why are furnace tubes often corrugated?
Corrugated tubes increase the buckling stiffness compared with a plain tube of the same wall thickness and additionally absorb thermal expansion between furnace tube and shell elastically. This allows larger unsupported lengths and higher pressures; the standard treats plain and corrugated furnace tubes with different rules.
What role does the out-of-roundness of the furnace tube play?
For externally pressurized cylinders, any deviation from the ideal circular shape acts as an initial imperfection and significantly reduces the critical buckling pressure. The standard therefore limits the permissible out-of-roundness and accounts for it in the verification; when re-rating existing boilers, the actually measured out-of-roundness should be used.