Engineering task and calculation objective
The LOBO module calculates the required plate thickness of highly perforated flat heads to AD 2000-Merkblatt B5 of the German AD 2000 pressure vessel code. Such perforated plates appear throughout apparatus engineering wherever a flat plate is penetrated by many holes – typically tubesheets of heat exchangers, distributor plates, sieve plates or base plates with a regular hole pattern. The holes weaken the plate, so the wall thickness has to be increased considerably compared with a solid head.
The special strength of LOBO lies in its treatment of supports: the plate can be unstayed, or supported regularly or irregularly by legs or anchors. Anchorages reduce the size of the governing plate panels and thereby cut the required plate thickness substantially – an economically important effect at large diameters. The calculation method is mainly derived from AD-Merkblatt B5 for flat heads and plates.
Inputs are the design pressure, the operating temperature, the material with its nominal design strength and safety factor, the allowances for wall thickness undertolerance and corrosion, and the hole-field geometry given by hole diameter and hole pitch. As a result, the module delivers the required wall thickness of the perforated plate – including openings without a nozzle and regions with several openings – and compares it with the actual wall thickness.
Standard and calculation basis: AD Merkblatt B5
Calculation workflow
- Define loading and material: The design pressure and the operating temperature are entered; for the selected material, the nominal design strength and the safety factor are determined, supplemented by the allowances for wall thickness undertolerance and corrosion/wear.
- Assess plate geometry and edge restraint: The design diameter of the governing plate panel and the shape factor C are established. The factor captures the boundary condition of the plate (type of clamping or edge support) and – for stayed plates – the subdivision of the plate into panels by legs or anchors.
- Account for the weakening from the hole field: The ligament efficiency of the hole field follows from the hole diameter and the hole pitch. The closer the pitch relative to the hole diameter, the smaller the load-bearing ligament cross-section and the thicker the plate has to be.
- Calculate the required plate thickness: Following the method of AD-Merkblatt B5, the required wall thickness of the perforated plate is determined from the design diameter, the shape factor, the pressure, the allowable stress and the ligament efficiency, and the allowances are added.
- Verify openings and supports: In addition, the required wall thicknesses are calculated for individual openings without a nozzle and for regions with several openings. For anchored plates, the effect of the regular or irregular support arrangement on the panel sizes is taken into account.
- Compare with the actual wall thickness: The governing required wall thickness – the maximum from the hole-field, single-opening and multiple-opening checks – is compared with the actual wall thickness and evaluated.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Material | Wk | – |
| Nominal design strength | K | N/mm² |
| Safety factor | S | – |
| Modulus of elasticity | E | N/mm² |
| Design pressure | p | bar |
| Shape factor | CAa | – |
| Shape factor | C | – |
| Shape factor | c1 | – |
| Shape factor | c2 | – |
| Shape factor | C3 | – |
| Shape factor | Cz | – |
| Inside stay diameter | di | mm |
| Outside stay diameter | da | mm |
| Mean gasket diameter | dD | mm |
| Gasket pitch diameter | dt | mm |
| Hole diameter | di | mm |
| Tube hole pitch | t | mm |
| Design diameter | D1 | mm |
| Design diameter | d1 | mm |
| Auxiliary value | δ | – |
| Characteristic gasket value | k1 | mm |
| Leak safety factor | SD | – |
| Free buckling length | lk | mm |
| Pitch 2 | t2 | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Required wall thickness | s | mm |
| Axial load | FA | N |
| Buckling rigidity | FK | N |
| Required wall thickness of opening without nozzle | s' | mm |
| Second moment of area | J | mm^4 |
| Slenderness ratio | λ | – |
| Required wall thickness (uniformly spaced stays) | sg | mm |
| Required wall thickness (not uniformly spaced stays) | su | mm |
| Final wall thickness | se | mm |
| Required wall thickness of opening with several openings | s'' | mm |
| Required wall thickness (unsupported) | su | mm |
Frequently asked questions
How does the perforated-plate verification differ from that of a solid flat head?
For a solid head to AD 2000 B5, the design diameter, the shape factor C and the allowable stress determine the thickness. For a perforated plate, the ligament efficiency derived from hole diameter and hole pitch is added: only the ligaments between the holes carry load, so the required thickness grows markedly as the pitch becomes tighter. With very heavy perforation, the ligament stresses dominate the design.
What do anchors or support legs underneath the plate achieve?
The required thickness of a flat plate grows roughly linearly with the diameter of the free plate panel. Supports subdivide the plate into smaller panels, so that only the governing panel or anchor spacing enters the calculation instead of the overall diameter. For large plates, the thickness can often be reduced to a fraction of the unstayed value; irregular arrangements require assessment of the most unfavourable panel.
Does the method also apply to tubesheets of heat exchangers?
The method treats the plate as a weakened flat head under pressure. For tubesheets of fixed tubesheet heat exchangers, where the tubes act as stays and temperature differences between shell and tube bundle generate restraint forces, further-reaching codes must be applied (e.g. AD 2000 B5 in conjunction with the relevant heat exchanger rules, or EN 13445-3 Clause 13). LOBO covers the flat, perforated, optionally anchored plate.
What role does the corrosion allowance play for plates wetted on both sides?
The corrosion/wear allowance must be applied on every side in contact with the medium. For perforated plates, note that the hole walls are also exposed to the medium – the hole diameter grows in service, which increases the weakening. A conservative approach therefore uses the hole diameter enlarged by the allowance.