Engineering task and calculation objective
The S36 module deals with vessel nozzles under additional loading in accordance with AD 2000-Merkblatt S 3/6, part of the German AD 2000 pressure vessel code. In practice, nozzles are never loaded by internal pressure alone: connected piping transfers forces and moments from thermal expansion, dead weight, and reaction forces onto the nozzle and the surrounding shell. Anyone who has to calculate or assess nozzle loads needs a measure of how much load-carrying reserve the pressure-loaded design still holds for these additional loads.
To this end, the program determines a fictitious spare strength for additional nozzle loads and at the same time checks the conditions under which stress determination by the methods provided in AD 2000 S 3/6, Section 4 is permissible in the first place. The input quantities are the inside diameters of the nozzle pipe and the basic shell, the as-built wall thicknesses without allowances, and derived characteristic values such as the stress intensification factor, the geometry factor, and the diameter ratio.
This makes it possible to decide early in the project whether the connection loads reported by the piping engineers can be accepted without detailed individual analyses (for example to WRC bulletins or by FEA) – a frequent checkpoint for pressure vessels designed to the AD 2000 code.
Standard and calculation basis: AD 2000 S3/6: 2001-09
Calculation workflow
- Record the geometry of the penetration: The inputs are the inside diameter of the nozzle pipe, the inside diameter of the header or basic shell, and the wall thicknesses at the outlet edge of the basic shell and at the nozzle, each without allowances. These actual values – not the minimum required wall thicknesses – determine the available reserve.
- Form the geometric characteristic values: From the dimensions, the diameter ratio of nozzle to basic shell and the geometry factor of the penetration are formed. They characterize how strongly the opening disturbs the membrane stress state of the shell.
- Check the limits of applicability: The module checks whether the ratios lie within the limits for which the simplified stress determination methods of AD 2000 S 3/6, Section 4 are validated. Outside these limits, a more accurate analysis is required.
- Determine stress intensification and spare strength: The stress intensification factor is used to evaluate the pressure-induced stress peak at the edge of the opening. The portion of the allowable stress not consumed by pressure yields the fictitious spare strength available for forces and moments from the piping.
- Assess the additional loads: The reported nozzle loads are compared with the determined reserve. If the reserve is insufficient, design measures (a thicker shell, a reinforcing pad, a modified pipe routing) or a detailed individual analysis are required.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inside diameter of the nozzle pipe | di | mm |
| Inside diameter of the header | Di | mm |
| Wall thickness at the outlet edge of the basic shell without allowances | eA | mm |
| Wall thickness of the nozzle without allowances | eS | mm |
| Stress intensification factor | α | – |
| Geometric Factor | ψ | – |
| Ratio | eS / eA | – |
| Value | a(eS / eA) | – |
| Value | b(eS / eA) | – |
| Design pressure | p | bar |
| Allowable pressure | pall | bar |
| Utilization of the strength by pressure | ρ | – |
| Fictitious strength reserve for additional nozzle loads | Kquer | N/mm² |
| Header diameter | Da | mm |
| Wall thickness allowance | c1 | mm |
| Corrosion / wear allowances | c2 | mm |
| Nominal design strength of the material | K | N/mm² |
Frequently asked questions
What does "fictitious spare strength" mean in concrete terms?
The pressure design to the B series usually does not fully exhaust the allowable stress at the nozzle, because the as-built wall thicknesses exceed the required ones. This difference is interpreted as a fictitious reserve that can absorb additional loading from piping forces and moments. It is called "fictitious" because it does not come from an exact stress analysis of the additional loads, but from a conservative estimate based on the degree of utilization in the pressure load case.
Why do the wall thicknesses enter the calculation without allowances?
Corrosion and manufacturing allowances are no longer available as load-bearing cross-section at the end of the service life. For the strength verification, therefore, the wall thickness minus the allowances c1 and c2 counts – both at the basic shell and at the nozzle. Anyone who mistakenly uses the nominal wall thickness overestimates the reserve and thus the allowable connection loads.
When is the method to S 3/6 no longer sufficient?
The simplified methods apply only within the geometry limits defined in Section 4, for example for the ratio of nozzle to shell diameter and the wall thickness ratios. For large openings, hillside or angled nozzles, closely spaced openings, or very high connection loads, more accurate procedures must be used, such as influence-surface methods or an FEA with stress categorization.
Does the calculation to S 3/6 replace the pressure design of the nozzle to AD 2000 B 9?
No. B 9 provides the required reinforcement of the opening for the internal pressure load case; S 3/6 additionally assesses the externally applied forces and moments. The two verifications belong together: first the pressure design, then the check of whether the remaining reserve covers the additional loads.