Engineering task and calculation objective
Nozzles, manholes and instrument connections interrupt the flow of forces in the pressure-bearing wall — every opening must therefore be reinforced and verified. This module calculates openings and opening reinforcements to DIN EN 13445-3, clause 9, supplemented by the requirements of DIN EN 14025 for tanks for dangerous goods. Covered are circular, elliptical and obround openings in cylindrical, conical and spherical shells as well as in dished ends, each under internal and external pressure.
The basis is the pressure-area method of EN 13445: the pressure-loaded areas are balanced against the stress-bearing cross-sectional areas of shell, nozzle and reinforcement within the contributing lengths. The available reinforcement variants are set-on, set-in and set-through nozzles, reinforcing pads, extruded openings and forged ring inserts. For nozzles in the knuckle region of dished ends — a zone with inherently increased loading — the module offers a dedicated calculation option.
Besides single openings, multiple openings are also treated: if openings lie so close together that their reinforcement zones overlap, the ligament between them is assessed in a joint verification. If you want to calculate nozzle reinforcement to EN 13445, this is the complete opening verification.
Standard and calculation basis: DIN EN 13445-3/9: 2021-12 & DIN EN 14025: 2018-09
Calculation scope
- Isolated openings in spherical and cylindrical shells
- Multiple openings in spherical and cylindrical shells
Calculation workflow
- Define the base shell: First, the load-bearing shell is described: cylindrical, conical or spherical shell, or dished end (Klöpper or Korbbogen type), with diameter, wall thickness minus allowances, material and design pressure — optionally internal or external pressure. The position of the opening (crown or knuckle region) decides which procedure is applied.
- Define opening and nozzle: The inputs are the shape and size of the opening (circular, elliptical, obround), the nozzle configuration (set-on, set-in or set-through), nozzle diameter and wall thickness, external and internal projections, and any reinforcing pad or forged ring insert with their dimensions.
- Determine the contributing lengths: The code limits how much material of shell and nozzle may act as reinforcement: the contributing lengths along the shell and along the nozzle are calculated from diameter and wall thickness. Only cross-sectional areas within these lengths enter the verification as load-bearing areas.
- Perform the pressure-area comparison: For each governing section, the pressure-loaded areas Ap and the load-bearing cross-sectional areas Af of shell, nozzle and reinforcement are balanced with their respective allowable stresses. The strength condition is satisfied if the load-bearing areas can carry the pressure loading with the required safety margins; with dissimilar materials, the lower strength of the attached part is taken into account.
- Check multiple openings and spacings: For several openings, the module checks the distance criterion: if the reinforcement zones overlap, the ligament verification is carried out for the web between the openings. In addition, minimum distances to welds and to discontinuities such as the knuckle are checked.
- Assess the result: The utilization ratios of all sections are reported as well as — if required — the maximum allowable pressure of the reinforced opening. If the reinforcement is insufficient, nozzle wall thickness, pad dimensions or the opening position can be varied and the verification repeated immediately.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Load case | Lastfall | – |
| Calculation temperature | t | °C |
| Calculation pressure | P | MPa |
| Material designation | Schale | – |
| Thickness allowance | δe | mm |
| Corrosion allowance | c | mm |
| Manufacturing allow. | δm | mm |
| Total allowance | ∑(δ) | mm |
| Schalenwerkstoff | Schalenwerkstoff | MPa |
| factor | factor | – |
| The strength condition is Utilization | ≤1 | – |
| Strength | Re, Rp, Rm K | MPa |
| Safety factor | S | – |
| Strength | Re, Rp, Rm K | MPa |
| Safety factor | S | – |
| Type of nozzle | nozzle | – |
| Shell without nozzle or with reinforcement pad | 9.4.5 d/(2 · ris) = ≤ 1 | – |
| Cylinder / Cone with nozzle | 9.4.5 dib/(2 · ris) = ≤ 1 | – |
| Nominal design stress | f=Min[Rm20/2,Rpe · 3/4]= | MPa |
| Outside diameter (spherical region, cone) of the shell at the larger opening 1 | De1 | mm |
| Outside diameter of opening, nozzle or ring | d1,deb1 | mm |
| Inside diameter of nozzle (or ring: dir) | dib1 | mm |
| Spheres+domed heads | 9.4.5 d/De = ≤ 0.6 | – |
| Spheres+domed heads | 9.4.5 dib/De = ≤ 0.6 | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Calculation pressure | P | MPa |
| The strength condition is Utilization | ≤1 | – |
| Nominal design stress | f=Min[Rm20/2,Rpe · 3/4]= | MPa |
| with a connection diameter | Dc | mm |
| Inside diameter of nozzle (or ring: dir) | dib1 | mm |
| and a thickness e1 (or e2 acc. Fig. 9.7-10) | junction | mm |
| Analysis thickness | eab1 | mm |
| Analysis thickness | eap1 | mm |
| Reduced thickness Min. (eap1,eas) | ep1 | mm |
| Nominal design stress | f=Min[Rm20/2,Rpe · 3/4]= | MPa |
| Nominal design stress | f=Min[Rm20/2,Rpe · 3/4]= | MPa |
| Reduced nozzle length outside shell | Min(lb;lbo) l'b1 | mm |
| Reduced nozzle length inside shell | Min(lbi;lbo/2) l'bi1 | mm |
| Max. supporting length of nozzle outside shell | lbo1 | mm |
| Max. supporting length of nozzle inside shell | lbo1/2 | mm |
| Supporting length of cylindrical connection | lcyl | mm |
| Effective supporting length | Min(ls;lso) l's | mm |
| Reduced width Min. (lp1,k · lso1) | l'p1 | mm |
| Maximum supporting length | lso1 | mm |
| (or e.g.:w | = ≤0) | mm |
| Cross-sectional area of nozzle material | Afb1 | mm² |
| Cross-sectional area | Afp | mm² |
| Cross-sectional area of shell | Afs | mm² |
| Cross-sectional area of fillet weld | Afw | mm² |
Calculation options
Type of nozzle
without nozzle · set-in · set-on · reinforcement ring · extruded · 6
Orientation of section
axial · 2
Shell type
Cylinder · sphere+semi-sphere+torispherical · elliptical · cone
Application case
Fatigue endurable and evaluation acc. chapter 17 · creep range · Other
Regulation
EN 13445-3: Unfired pressure vessels · EN 14025: Tanks for the transport of dangerous goods
Shell type
Torispherical head (Kloepper type) · Torispherical head (Korbbogen type) · Hemispherical head
Option
Isolated openings in spherical and cylindrical shells · Multiple openings in spherical and cylindrical shells
Frequently asked questions
What do set-on, set-in and set-through nozzles mean for the verification?
With a set-on nozzle, the nozzle pipe sits on the outside of the shell and only the external projection contributes. With a set-in nozzle, the pipe is welded into the opening; with a set-through nozzle it additionally protrudes inward, so that the internal projection within its contributing length may also be credited as reinforcement area. The configuration additionally affects weld type, inspectability and fatigue behaviour.
Why is the knuckle region of dished ends critical for nozzles?
In the knuckle, high bending stresses from the change in curvature between crown and cylindrical skirt superimpose even without an opening. A nozzle in this zone weakens precisely the most highly loaded region. The code provides more stringent rules for this; the module offers its own calculation option for nozzles in the knuckle region. As a design measure, openings should be placed in the crown wherever possible.
Reinforcing pad or thick-walled nozzle — which reinforcement is better?
A thick-walled or extruded nozzle reinforces directly at the location of highest loading, is more favourable for fatigue and is fully inspectable. Reinforcing pads are simple and economical to fabricate, but have limits: they act only via shear transfer through the fillet welds, are unfavourable at high temperatures and severe thermal transients (gap between pad and shell), and EN 13445 limits their thickness and width. For cyclic loading, integral reinforcement is preferable.
When does DIN EN 14025 additionally apply?
EN 14025 applies to tanks for the transport of dangerous goods (road tankers, rail tank wagons, tank containers). For the opening calculation it largely refers to EN 13445-3, but imposes its own minimum wall thicknesses, material requirements and dynamic load assumptions from transport. The module takes these additional requirements into account when a tank has to be verified to ADR/RID.