Engineering task and calculation objective
The S30 module performs the general safety verification for pressure vessels to AD 2000-Merkblatt S3/0 of the German AD 2000 pressure vessel code. This Merkblatt sets out the principles by which additional loadings – weight loads, nozzle loads, moments from attachments, wind and connection forces – are assessed together with the internal pressure when the component Merkblätter of the B series alone are not sufficient. The verification is based on given equivalent stresses, which may come from a hand calculation or from a detailed analysis.
The core of the method is the comparison of the equivalent stresses with the allowable values, which may be set at different levels depending on the stress category and load case: membrane stresses are limited more strictly than local bending or peak stresses. The module contains a material database for determining the nominal design strength and the safety factor at design temperature, and provides selection criteria for the application of the limit load method or the shakedown method, by which locally limited exceedances of the elastic limits can be assessed as acceptable.
In practice, S3/0 acts as the umbrella over the specific stability Merkblätter S3/1 to S3/4: whoever has to verify additional loads on vessels that do not match any of the standard situations (skirt support, saddles, legs, brackets) carries out the strength verification according to the principles of this Merkblatt.
Standard and calculation basis: AD 2000 S3/0: 2016-09
Calculation workflow
- Compile load cases and actions: For operation, testing and erection, all simultaneously acting loads are recorded: internal or external pressure, dead weight and filling, forces and moments from nozzles, supports, anchorages and attachments, including torsion.
- Determine the equivalent stresses: For the governing cross-sections, the stresses from the superposed loads are calculated and combined into equivalent stresses – according to the distortion energy (von Mises) or maximum shear stress (Tresca) hypothesis, separated into membrane, bending and total components.
- Establish the allowable stresses: The nominal design strength K and the safety factor S at design temperature are determined from the material database. Depending on the stress category and load case (operation, test, erection), different allowable multiples of K/S apply.
- Check the strength condition: The existing equivalent stresses are compared with the allowable values. Membrane stresses must not exceed the basic strength; elevated limits apply to locally confined bending and peak stresses.
- Apply the limit load or shakedown method: If the elastic verification is not sufficient, the selection criteria of the Merkblatt indicate whether the limit load method (verification against plastic collapse with a global safety factor) or the shakedown method (verification that the component settles into purely elastic behaviour after a few cycles) may be applied.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Specification: Exposed area of attachment | An | m² |
| Nominal design strength of material | K | N/mm² |
| Safety factor (operating) | S | – |
| Allowable design stress | f | N/mm² |
| Safety factor (test) | S' | – |
| Allowable design stress (test) | fP | N/mm² |
| Safety factor (installed) | SM | – |
| Allowable design stress (installed) | fM | N/mm² |
| Safety factor (special case) | SS | – |
| Allowable design stress (special case) | fS | N/mm² |
| Reduction factor | r | – |
| Allowable design stress (operating) | fT | N/mm² |
| Allowable design stress (operating) | fa | N/mm² |
| Total moment in the sectional plane | M | N·mm |
| Number of supports | n | – |
| Maximum vessel weight (operation) | Gd | N |
| Minimum vessel weight (operation) | Gz | N |
| Pitch circle diameter of the supports | dF | mm |
| Pressure force on each support | NFd | N |
| Maximum tensile force on each support | NFz | N |
| L5 | > | N |
| R5 | > | N |
| Factor | a | – |
| Material | WNr | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Aerodynamic force factor of the attachment | cf | – |
| Consideration of adjacent vessels (Y/N) (Y/N) | flg1 | – |
| Distance between adjacent vessels or vessels and buildings (w<d) | w | m |
| Outside vessel diameter including insulation | da | m |
| Number of attachments of the selected type | n | – |
| Type of attachment (1...8) | (1...8) | – |
| Platform outside diameter | db | m |
| Platform width | bb | m |
| Rectangular platform, diagonal dimension | dm | m |
| Gangway, length | sl | m |
| Ladder, vertical heigth | shl | m |
| Corrected aerodynamic force factor | cfkorr | – |
| Specification: Exposed area of attachment | An | m² |
| Total exposed area of all attachments | Ang | m² |
| Wind velocity (according to DIN EN 1991-1-4) | v | m/s |
| Dynamic wind pressure | q | KN/m² |
| Total wind load | W | kN |
| Wind load on the attachments | WA | kN |
| Wind load on vessel | WB | kN |
| Vessel height | hB | m |
| Wind exposed area of the vessel | AB | m² |
| Aerodynamic form factor of vessel | cfB | – |
| Wind moment | M | kN·m |
Frequently asked questions
When is S3/0 needed in addition to the B-series Merkblätter?
The B-series Merkblätter size components for pressure as the principal load. As soon as significant additional loads act – large nozzle forces from piping, moments from agitators, wind and seismic loads, support reactions outside the standard cases S3/1 to S3/4 – their superposition with the pressure must be verified separately. S3/0 provides the principles, stress limits and safety factors for this.
What distinguishes the limit load method from the shakedown method?
The limit load method demonstrates that the load lies with a sufficient safety margin below the plastic limit capacity of the component – suitable for predominantly static loading. The shakedown method demonstrates that, under repeated loading, the component behaves purely elastically after initial local yielding, i.e. no progressive plastic deformation (ratcheting) occurs – decisive for cyclic loading. The Merkblatt states selection criteria for which method is admissible.
Why are membrane stresses limited more strictly than bending stresses?
A membrane stress acting through the entire wall thickness causes the whole cross-section to plastify immediately when the yield limit is reached – there is no redistribution reserve. Bending stresses initially plastify only the outer fibres; the cross-section continues to carry load until a plastic hinge forms. Local peak stresses are relevant only for fatigue. The different allowable multiples of K/S reflect this graded severity.