Engineering task and calculation objective
For openings and nozzles in pressure-loaded shells, the German codes offer two related approaches: the pressure-area method of AD 2000-Merkblatt B9 and the opening calculation of TRD 301/303 for steam boilers. The B9N module combines both and presents the balance of pressure force and pressure retaining force directly: the force generated by the pressure on the pressure-loaded areas is compared with the retaining force of the stress-loaded cross-sections, and the utilization is obtained as the ratio of existing to allowable force.
The scope is deliberately broad: single nozzles in cylindrical shells with and without reinforcing plates, single nozzles in spherical shells, oblique branches in spherical or cylindrical shells, set-on and set-in block flanges, and adjacent openings in the longitudinal and circumferential directions of a cylindrical shell as well as in the spherical shell. For the circumferential direction, the applicable reduction factors are applied; for oblique branches, the angle between the nozzle axes is used.
The module is thus suited to nozzle calculations on vessels and boiler-adjacent components alike — wherever welded-on or set-through nozzles, oval openings or closely spaced branches need to be verified. The basis is AD 2000 B9 in the corrected 2016-09 edition in combination with TRD 301/303.
Standard and calculation basis: AD 2000 B9: 2010-02, berichtigte Fassung 2016-09
Calculation scope
- Adjacent openings in spherical shell
- Oblique branch in spherical or cylindrical shell
- Single nozzle in cylindrical shell without reinforcement plate
- Single nozzle in cylindrical shell with reinforcement plate
- Single nozzle in spherical shell
- Set-on reinforcement ring (block flange) on cylindrical shell
- Set-in reinforcement ring (block flange) in cylindrical shell
- Adjacent openings in longitudinal direction of a cylindrical shell
- Adjacent openings in circumferential direction of a cylindrical shell
Calculation workflow
- Select the configuration: The verification case is defined via the type selection: single nozzle in a cylindrical or spherical shell, with or without a reinforcing plate, oblique branch, set-on or set-in block flange, or adjacent openings in the longitudinal or circumferential direction.
- Enter the geometry of shell and nozzle: Required are the outside diameters and as-built thicknesses of the base shell and the nozzle, the internal and external protrusions and, for adjacent openings, the axis spacing and the angle between the nozzle axes. Corrosion allowances lead to corrected inside diameters and net inside diameters.
- Determine effective lengths and creditable protrusions: For the shell and the nozzle, the effective lengths are calculated; of the internal nozzle protrusion, only the creditable portion is taken into account. These quantities limit the cross-sectional areas that may act as retaining-force cross-sections.
- Balance pressure force and retaining force: The pressure force results from the design pressure on the pressure-loaded areas, the retaining force from the stress-loaded cross-sections times the allowable stress K/S. For openings in the circumferential direction and for oblique branches, the reduction factors of the code are applied.
- Evaluate the utilization: The module reports the utilization as the ratio of existing to allowable force. If it is exceeded, the design is adjusted — a thicker nozzle, a reinforcing plate, a larger opening spacing — and the verification is repeated.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Design temperature | T | °C |
| Design pressure | p | bar |
| Designation | Grundkörper | – |
| Designation | Stutzen1 | – |
| Designation | 2 | – |
| Nominal design strength | K | MPa |
| Nominal design strength | K K1 K2 | MPa |
| Nominal design strength | K K1 K2 | MPa |
| Safety factor | S | - |
| Safety factor | S S1 S2 | - |
| Safety factor | S S1 S2 | - |
| Wall thickness manufacturing tolerance | c1 | mm |
| Allowance | c1 c11 c12 | mm |
| Allowance | c1 c11 c12 | mm |
| Corrosion/erosion allowance | c2 | mm |
| Corrosion/erosion allowance | c2 c21 c22 | mm |
| Corrosion/erosion allowance | c2 c21 c22 | mm |
| Allowable stress | K/S | MPa |
| Allowable stress | σ σ1 σ2 | MPa |
| Allowable stress | σ σ1 σ2 | MPa |
| Final shell wall thickness | se | mm |
| Shell outside diameter | Da | mm |
| Inside shell diameter (corroded state) | Di | mm |
| Nozzle inside diameter (corroded) | di | mm |
Calculation options
Type
Single nozzle with tubular and optional pad reinforcement (cylinders) acc. to AD B9 · Single nozzle with tubular and pad reinforcement (cylinders) acc. to AD B9 · Single nozzle (spheres) according to AD B9 · Set-on reinforcement ring (cylinders) according to AD B9 · Set-in pad-type flange (cylinders) according to AD B9 · Adjacent openings in longitudinal direction (cylinders) acc. to AD B9 · Adjacent openings in circumferential direction (cylinders) acc. to AD B9 · Adjacent openings (spheres) acc. to AD B9 · Oblique branch in cylinders and spheres acc. AD-B9/4.7
Frequently asked questions
When should B9N be used instead of B9?
B9N offers the presentation combined with TRD 301/303 in terms of pressure force, retaining force and utilization, and explicitly covers additional cases such as oblique branches and block flanges in set-in or set-on configurations. For components in the context of the steam boiler rules or for re-checking existing TRD designs, B9N is the appropriate choice; for the pure implementation of the current Merkblatt B9, the B9 module is available.
Why do reduction factors apply to openings in the circumferential direction?
In a cylindrical shell, the circumferential (hoop) stress is twice the longitudinal stress. The ligament between two circumferentially adjacent openings only appears to be favorably positioned across the larger stress — the code captures the actual loading situation through reduction factors that lower the allowable force contribution of the ligament. Forgetting them leads to unsafe results.
How does the angle of an oblique branch enter the calculation?
An obliquely cut nozzle produces an oval opening in the shell whose governing dimension grows as the angle becomes flatter. The pressure-loaded area increases accordingly, while the load-bearing cross-section barely grows — so the utilization increases with the obliqueness. The angle between the nozzle axes is therefore a direct input quantity of the verification.
What does the creditable internal nozzle protrusion mean?
A nozzle protruding into the vessel contributes to the reinforcement with its internal protrusion, but only up to the length limited in the code — material extending beyond it lies outside the effective zone and is moreover exposed to corrosion. The module automatically takes only the creditable portion into account.