Engineering task and calculation objective
The NOLS module verifies a nozzle in a cylindrical shell under combined loads: internal pressure plus external axial force and bending moments from the connected piping. From the moments in the X and Y directions, the resultant moment at the nozzle is formed and compared, together with the axial force, against the allowable values – the allowable design pressure from the opening reinforcement check (module EN09, i.e. EN 13445-3 Clause 9) as well as the allowable global moment and the allowable global nozzle force (module EN16.14 according to EN 13445-3 Clause 16).
In practice, this verification is indispensable because nozzles rarely see pressure alone: thermal expansion, dead weight and piping reaction forces generate forces and moments that produce local membrane and bending stresses in the shell and nozzle. Anyone who wants to calculate nozzle loads to EN 13445 or define allowable piping loads at a vessel nozzle obtains with this module the interaction check for the operating and test load cases, each with the associated nominal design stresses of shell and nozzle.
Calculation workflow
- Select load case and design conditions: First, the load case (operation or test) is defined, along with the design temperature and design pressure. In the test load case, higher nominal design stresses apply, but the test conditions govern.
- Record geometry and effective wall thicknesses: From the outside diameter and nominal wall thickness of shell and nozzle – after deducting the wall thinning and corrosion allowances – the analysis wall thicknesses as well as the inside and mean diameters are determined; the type of nozzle (set-on or set-through) enters the coefficients.
- Form material parameters and nominal design stresses: For shell and nozzle, the nominal design stresses of the respective load case are determined from the material strength value and the safety factor; reinforcements are accounted for via the combined thickness of shell plus reinforcement and the equivalent wall thickness.
- Determine the allowable individual loads: The allowable design pressure follows from the opening reinforcement check according to Clause 9 (EN09); the allowable global moment and the allowable global nozzle force follow from the procedure of Clause 16 (EN16.14). The dimensionless ratios with their conditions of validity limit the range of application.
- Verify the load interaction: Axial force, resultant moment and design pressure are each referred to their respective allowable values and combined in the interaction relationship; the verification is fulfilled if the combination does not exceed the allowable limit.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Load case operation = 1 / test = 2 | Lastfall | – |
| Load case | Lastfall | – |
| Calculation temperature | t | °C |
| Calculation pressure | P | MPa(p) |
| Shell material | Schale | – |
| Material strength | R | MPa |
| Safety factor | S | – |
| Nominal design stress | f | MPa |
| Nozzle material | Stutzen | – |
| Material strength | R | MPa |
| Safety factor | S | – |
| Nominal design stress | f | MPa |
| Shell outside diameter | De | mm |
| Nominal wall thickness shell | en | mm |
| Nozzle outside diameter | de | mm |
| Nominal wall thickness nozzle | enb | mm |
| Nominal design stress | f | MPa |
| Reinforcement outside diameter | d2 | mm |
| Reinforcement width | L | mm |
| Axial force on the nozzle (tension>0) | FZ | N |
| Moment in X direction on nozzle | MX | Nm |
| Longitudinal moment on nozzle | MY | Nm |
| Resultant moment | √(MX²+MY²) MB | Nm |
| Combined thickness of shell and reinforcement | ec | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Analysis wall thickness, shell | ea | mm |
| Shell inside diameter | Di | mm |
| Mean shell diameter | D | mm |
| Analysis wall thickness, nozzle | eb | mm |
| Inside nozzle diameter | di | mm |
| Mean nozzle diameter | d | mm |
| Reinforcement analysis thickness | e2 | mm |
| Reinforcement width | L | mm |
| Combined thickness of shell and reinforcement | ec | mm |
| Equivalent wall thickness | eeq | mm |
| Ratio | eb/ec | – |
| Ratio | D/ec | – |
| Parameter for nozzle | λs | – |
| Allowable design pressure (Module EN09) | Pmax | MPa(p) |
| Allowable global moment (Module EN16.14) | Mmax | Nm |
| Allowable global nozzle force (Module EN16.14) | Fmax | N |
| Allowable axial force | FZ,max | N |
| Allowable bending moment | MB,max | Nm |
| Condition | ΦP ≤ 1 | – |
| Load Ratio Condition | ΦZ ≤ 1 | – |
| Load Ratio Condition | ΦB ≤ 1 | – |
| Interaction condition | ≤ 1 | – |
| Reinforcement rate factor | κ = min( ; 1,0) = | – |
| Reinforcement rate factor | κ = min( ; 1,0) = | – |
Frequently asked questions
Why is the opening reinforcement check according to Clause 9 alone not sufficient?
The opening reinforcement check covers only the pressure loading. External forces and moments from the piping generate additional local stresses at the nozzle attachment that interact with the pressure stresses. Only the combined assessment – pressure contribution plus force and moment contributions in the interaction relationship – fully verifies the connection.
How is the resultant moment formed from Mx and My?
The bending moments about the two transverse axes are combined vectorially into the resultant moment (square root of the sum of squares), since for the rotationally symmetric nozzle geometry only the magnitude of the bending moment is decisive. Torsional moments and shear forces must be assessed separately.
What difference does it make whether the nozzle is set-on or set-through?
A set-through nozzle contributes to the reinforcement of the opening with its inward protrusion and stiffens the attachment; the code coefficients therefore distinguish between the two designs. The choice influences both the allowable pressure and the allowable external loads.
Where do the axial force and the moments at the nozzle come from?
Usually from the piping analysis (pipe stress analysis): thermal expansion, weight, friction and start-up forces generate reaction loads at the connection point. In early project phases, allowable nozzle loads are often specified instead as a requirement for the piping engineer – the verification can also be used for this by solving the interaction equation for the loads.