Engineering task and calculation objective
The EN16.04 module verifies nozzles in spherical shells and dished ends under local loads to DIN EN 13445-3, Clause 16.4. In addition to internal pressure, connected piping transmits forces and moments to the nozzle: axial forces from pipe thermal expansion, shear forces, bending moments in the circumferential and longitudinal directions, and torsional moments. These nozzle loads generate local membrane and bending stresses at the shell opening that a plain opening reinforcement check does not capture.
To calculate nozzle loads on a spherical shell you need, besides the geometry, the nominal design stress of the shell, obtained from the material strength value and the safety factor, and the effective wall thickness after deducting the corrosion allowance and the wall thinning allowance. From these, the module determines the allowable individual loads (pressure, axial force, bending moment) and performs the interaction check for the combined loading. A reinforcing plate can be taken into account.
In addition, the module checks the longitudinal stress in the nozzle pipe itself, including the stability usage factor against local buckling, as well as the ranges of pressure, axial force and moments for classification under the simplified fatigue assessment. The link to the allowable design pressure from the opening reinforcement check (module EN09) and to the global limit loads per Clause 16.14 is built in.
Standard and calculation basis: DIN EN 13445-3/16.4: 2021-12
Calculation workflow
- Determine effective wall thickness and nominal design stress: The corrosion allowance and the wall thinning allowance are deducted from the as-built wall thickness. From the material strength value of the shell and the safety factor, the nominal design stress f is obtained – the reference quantity for all admissibility checks.
- Compile the loads acting on the nozzle: Pressure, axial force (tension positive), shear force, circumferential and longitudinal moments, and the torsional moment are recorded. From the two bending moments, the resultant bending moment is formed, which together with the axial force and the pressure determines the governing local loading.
- Determine the allowable individual loads: According to Clause 16.4, the allowable pressure (in conjunction with the opening reinforcement check per module EN09), the allowable axial force and the allowable bending moment for the nozzle in the spherical shell are calculated – depending on the ratio of nozzle diameter to shell diameter, the wall thickness, and any reinforcing plate.
- Perform the interaction check for combined loading: The simultaneously acting loads are related to their allowable individual values and combined via the interaction relationship of the standard. The check is satisfied if the interaction sum does not exceed the limit value.
- Check nozzle longitudinal stress and stability: In the nozzle pipe, the longitudinal stress from pressure, axial force and the resultant bending moment is calculated and compared with the allowable stress. Under compressive loading, the stability usage factor against local buckling of the nozzle is additionally verified.
- Evaluate the load ranges: For fluctuating loads, the ranges of pressure, axial nozzle force and moments are evaluated. They serve as input to the simplified fatigue assessment per DIN EN 13445-3 and limit the allowable number of load cycles.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Load case | case | – |
| Reinforcing plate | plate | – |
| Calculation temperature | t | °C |
| Calculation pressure | P | MPa(p) |
| Shell outside diameter | De | mm |
| Nominal wall shell thickness | en | mm |
| Outside diameter nozzle | de | mm |
| Nominal wall thickness Nozzle | enb | mm |
| Outside diameter of a reinforcing plate | d2 | mm |
| Nominal thickness reinforcement | en2 | mm |
| Type of Nozzle | Nozzle | – |
| Material | Material | – |
| Wall thinning allowance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Material strength shell | Ks | N/mm² |
| Safety factor shell | Ss | - |
| Nominal desgin stress | f | N/mm² |
| Material | Material | – |
| Wall thinning allowance | c1ST | mm |
| Corrosion allowance | c2ST | mm |
| Material strength shell | KN | N/mm² |
| Safety factor shell | SN | - |
| Nominal desgin stress | fb | N/mm² |
| Material | Material | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Allowable design pressure (Module EN09) | Pmax | MPa(p) |
| Allowable global moment (Module EN16.14) | Mmax | N·mm |
| Allowable global Nozzle force (Module EN16.14) | Fmax | N |
| Spherical shell thickness | ea | mm |
| Shell inside diameter | Di | mm |
| Mean shell diameter | D | mm |
| Mean shell radius at the nozzle | R | mm |
| Analysis wall thickness, Nozzle | eb | mm |
| inside nozzle diameter | di | mm |
| Mean nozzle diameter | d | mm |
| Thickness of a reinforcing plate | e2 | mm |
| Width of the reinforcing plate | L | mm |
| Conditions of length | length | – |
| Combined thickness of shell and reinforcement | ec | mm |
| Equivalent shell thickness | eeq | mm |
| Ratio | ea/eb | - |
| Ratio | D/ec | - |
| Ratio | eb/ec | - |
| Reinforcement rate factor | k | - |
| Parameter for nozzle | λs | - |
| Allowable axial force | Fzmax | N |
| Allowable bending moment | MBmax | N·mm |
| Shear stress in shell caused by shear force | τF | N/mm² |
| Shear stress caused by torsional moment | τZ | N/mm² |
Calculation options
Load case
Operation · Test
Reinforcing plate
Yes · No
Type of Nozzle
Set-on · Protruding
Are there other local loads ?
Yes · No
Frequently asked questions
When is the opening reinforcement check per EN 13445-3 Clause 9 sufficient, and when do I need Clause 16.4?
Clause 9 verifies the reinforcement of the opening for pressure loading only. As soon as the connected piping transmits significant forces or moments to the nozzle – for example from thermal expansion, dead weight or reaction forces – the resulting local stresses must additionally be verified per Clause 16.4 (spherical shells) or 16.5 (cylindrical shells). The two checks belong together: the allowable design pressure from the opening reinforcement check enters the interaction check.
How does a reinforcing plate affect the allowable nozzle loads?
A reinforcing plate welded to the shell increases the effective wall thickness in the load introduction zone and thereby raises the allowable individual loads from pressure, force and moment. The standard ties this credit to conditions on the width and thickness of the plate and on the welded connection; outside these limits the plate must not be fully credited.
Which sign convention applies to the axial force?
In the module, the axial force is defined positive in tension, i.e. a force pulling the nozzle outward away from the shell. Compressive forces (negative) act unfavourably on the stability of the nozzle pipe together with the internal pressure, which is why the stability usage factor against buckling is then additionally checked.
Where do I obtain realistic nozzle loads for the verification?
The governing values are the internal forces and moments from the piping stress analysis at the nozzle connection; alternatively, manufacturer data or project-specific standard load tables can be used. Overly conservative blanket loads frequently lead to unnecessarily thick shells or large reinforcements – a coordinated piping stress analysis pays off immediately here.