Engineering task and calculation objective
The EN16.05 module calculates local loads on nozzles in cylindrical shells to DIN EN 13445-3, Clause 16.5. In service, piping connections transmit not only pressure but also axial forces, shear forces in the longitudinal and circumferential directions of the shell, bending moments about both axes, and torsional moments. These nozzle loads generate local membrane and bending stresses in the region of the opening that must be checked separately when verifying a pressure vessel.
Unlike the spherical shell, the loading on a cylinder is direction-dependent: a longitudinal moment acts differently from a circumferential moment, and the shear forces are likewise recorded separately for the longitudinal and circumferential directions. The module determines the allowable individual loads from pressure, axial force and moments, forms the resultant bending moment and performs the interaction check for the combined loading – optionally with a reinforcing plate.
The calculation is linked to the opening reinforcement check per Clause 9 (module EN09), whose allowable design pressure enters the interaction, and to the global limit loads for nozzles per Clause 16.14. This makes it possible to calculate nozzle loads on cylindrical shells consistently to the European pressure vessel code.
Standard and calculation basis: DIN EN 13445-3/16.5: 2018-12
Calculation workflow
- Define effective wall thickness and nominal design stress: The corrosion allowance and the wall thinning allowance are deducted from the nominal wall thickness; the nominal design stress is obtained from the material strength value and the safety factor. Together with the diameter ratios of nozzle and shell, these quantities determine the load-bearing capacity of the connection.
- Record the nozzle loads separately by direction: The inputs are the axial force (tension positive), the shear forces in the longitudinal and circumferential directions of the shell, the circumferential and longitudinal moments, and the torsional moment. From the two bending moments, the resultant bending moment is formed.
- Calculate the allowable individual loads per Clause 16.5: For the nozzle in the cylindrical shell, the allowable pressure (taking into account the opening reinforcement check per module EN09), the allowable axial force, and the allowable moments in the circumferential and longitudinal directions are determined. A credited reinforcing plate increases the load-bearing capacity within the conditions of the standard.
- Perform the interaction check: The simultaneously acting loads are related to their allowable values and combined via the interaction relationships of the standard. Shear and torsional loading are checked in addition. The verification is satisfied if all usage factors remain below the limit values.
- Compare with the global limit loads: Finally, the loads are compared with the maximum allowable global values for moment and force at the nozzle per Clause 16.14 (module EN16.14), to ensure that the nozzle pipe itself and its attachment are also adequately dimensioned. The equations used can be displayed in the module for documentation.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Load case | case | – |
| Reinforcing plate | plate | – |
| Calculation temprature | t | °C |
| Calculation pressure | P | MPa(p) |
| Shell outside diameter | De | mm |
| Nominal shell thickness | en | mm |
| Outside nozzle diameter | de | mm |
| Nominal wall thickness Nozzle | enb | mm |
| Outside diameter of a reinforcing plate | d2 | mm |
| Nominal thickness reinforcement | en2 | mm |
| Material | Material | – |
| Wall thinning allowance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Material strength | Ks | N/mm² |
| Safety factor | Ss | - |
| Nominal desgin stress | f | N/mm² |
| Material | Material | – |
| Wall thinning allowance | c1ST | mm |
| Corrosion allowance | c2ST | mm |
| Material strength | KN | N/mm² |
| Safety factor | SN | - |
| Nominal desgin stress | fb | N/mm² |
| Material | Material | – |
| Wall thinning allowance | c1RT | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Allowable design pressure (Module EN09) | Pmax | MPa(p) |
| Allowable global nozzle moment (Module EN16.14) | Mmax | N·mm |
| Allowable global nozzle force (Module EN16.14) | Fmax | N |
| 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 |
| Thickness of a reinforcing plate | e2 | mm |
| Width of the reinforcing plate | L | mm |
| Conditions of length | length | – |
| Combined thickness of shell and reinforcment | ec | mm |
| Equivalent shell thickness | eeq | mm |
| Ratio | ea/D | - |
| Conditions of Ratio | Ratio | – |
| Ratio | ea/eb | - |
| Ratio | D/ec | - |
| Ratio | eb/ec | - |
| Parameter for nozzle | λc | - |
| Check the ratio ea/R | ea/R | – |
| Factor for axial Load | C1 | - |
| Factor for circumferential moment | C2 | - |
| Factor for longitudinal moment | C3 | - |
Calculation options
Load case
operation · test
Reinforcing plate
Yes · No
Are there other local loads ?
Yes · No
Frequently asked questions
Why are the longitudinal and circumferential moments treated separately on a cylinder?
The cylindrical shell responds direction-dependently: the stiffness and the stress distribution around the opening differ markedly between the longitudinal and circumferential directions, which is why the standard provides separate allowable moments for the two directions. Only in the interaction check are the contributions combined via the resultant bending moment or the interaction relationship. For the spherical shell (Clause 16.4) this distinction is unnecessary because of rotational symmetry.
Does the verification also apply to openings with a set-on nozzle without a set-through pipe?
Clause 16.5 applies to nozzles in cylindrical shells within the geometric limits of the standard, in particular for the ratio of nozzle to shell diameter and the wall thickness ratios. Set-on and set-through nozzles are covered, provided the welded connection can fully transmit the loads. Outside the limits (very large openings, hillside nozzles), more accurate methods such as verification by FEM per Annex C are required.
What is a typical source of error when entering the nozzle loads?
Loads are frequently handed over in the wrong coordinate system: the piping stress analysis often delivers internal forces in the global plant system, whereas the verification needs the components referred to the shell (longitudinal/circumferential). The sign convention for the axial force (tension positive, pointing away from the vessel) and the question of whether the loads apply at the nozzle end or at the shell junction must also be consistent – moments grow with the lever arm of the nozzle length.
Is an additional fatigue assessment required?
If the nozzle loads or the pressure fluctuate cyclically (start-up/shutdown, batch operation), the range of the local stresses must be assessed. DIN EN 13445-3 provides the simplified assessment per Clause 17 and the detailed assessment per Clause 18 for this purpose; the local stresses from Clause 16.5 are the input quantity.