Engineering task and calculation objective
The TST module calculates tees with a perpendicular branch under internal pressure according to AD 2000-Merkblatt B9 (a sheet of the German AD 2000 pressure vessel code) and DIN 2413 — that is, internally pressurized cylindrical run pipes into which a nozzle connects at right angles, optionally with a gusset (crotch) or additional reinforcement. Such branch connections are found in piping systems, on headers and manifolds, and on vessel nozzles in apparatus engineering.
Opening reinforcement is the critical verification of every branch: the opening weakens the load-bearing cross-section of the run, and the membrane stresses concentrate at the edge of the opening. According to the area-compensation (pressure area) principle anchored in AD 2000 B9, the contributing wall cross-sections of run and branch must compensate the area loaded by the pressure. The module performs this verification for both run and branch and determines the required minimum wall thicknesses of both components.
To calculate a tee to the AD 2000 code, you specify the design pressure and design temperature, the materials with their strength values and safety factors for run and branch, and the geometry (diameters, as-built wall thicknesses, transition radius); allowances for wall thickness undertolerance and corrosion are taken into account separately for both components.
Standard and calculation basis: AD2000 B9 & DIN 2413
Calculation workflow
- Define design data and materials: The design pressure and design temperature are specified. For run and branch, the materials are selected separately with their strength values K at design temperature and their safety factors S; from these follow the allowable stresses of both components.
- Record the tee geometry: The inputs are the outside diameter and as-built wall thickness of run and branch as well as the radius of the branch transition. From these, the module forms the corroded inside diameters used in the verifications.
- Apply the allowances: The allowances c1 for wall thickness undertolerance and c2 for corrosion/wear are applied separately for run and branch and subtracted from the as-built wall thicknesses before the analysis wall thicknesses enter the weakening verification.
- Weakening verification at the branch: According to AD 2000 B9, the opening reinforcement is checked: the contributing cross-sectional areas of run wall and branch wall within the contributing lengths must compensate the pressure-loaded area at the opening. With different materials, the lower strength of the branch is weighted accordingly; optionally, additional reinforcement (pad/gusset) is included.
- Report the minimum wall thicknesses: As a result, the module delivers the required minimum wall thicknesses (without allowances) for run and branch and compares them with the as-built wall thicknesses. If the as-built wall thickness minus the allowances is greater than the minimum wall thickness, the verification is satisfied.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Design excess pressure | p | bar |
| Design excess pressure | p | N/mm² |
| Design temperature | T | °C |
| Outside diameter of the basic body | Da ≤ 1.2∙D1 | mm |
| Inside diameter of the basic body (corroded) | D1 | mm |
| Actual wall thickness of the basic body | sg | mm |
| Outside nozzle diameter | da | mm |
| Inside nozzle diameter (corroded) | d2 | mm |
| Actual wall thickness of the nozzle | ss | mm |
| Material of the basic body | Grundkörper | – |
| Nominal design strength of the basic body | K1 | N/mm² |
| Safety factor of the basic body | S | – |
| Nozzle material | Stutzen | – |
| Nominal design strength of the nozzle | K2 ≤ K1 | N/mm² |
| Radius of the nozzle transition | R ≤ s1 | mm |
| Wall thickness allowance of the basic body | c1 | mm |
| Corrosion / wear allowance of the basic body | c2 | mm |
| Joint efficiency factor | v | – |
| Effective length of the basic body | a1' | mm |
| Effective nozzle length | a2' | mm |
| Pressure loaded area | Ap | mm² |
| Bearing cross-sectional area | (Aσ = Aσ1 + Aσ2 + AσV) Aσ | mm² |
| Minimum wall thickness of basic body (without allowances) | s1 | mm |
| Minimum wall thickness of the nozzle (without allowances) | s2 | mm |
Frequently asked questions
How does the calculation to AD 2000 B9 differ from that to DIN 2413?
AD 2000 B9 is the code sheet for openings in pressure vessel walls and works with the weakening or area-compensation method, whereas DIN 2413 governs the calculation of steel piping under internal pressure and contains its own rules for branches. The module combines both codes: piping tees are treated with the boundary conditions of DIN 2413, vessel branches with those of the AD 2000 code. The underlying mechanics — compensation of the opening weakening by contributing wall cross-sections — is identical.
Up to which diameter ratio may a perpendicular branch be calculated this way?
The pressure-area method applies to branches whose diameter ratio di/DI stays within the limits of the code; for very large branches (diameter ratio close to 1, the classic wye or breeches piece), the area compensation fails because hardly any contributing run cross-section remains. Such designs require additional verifications via gusset reinforcements or an analysis with an equivalent model — the module covers the gusset case separately.
Why are allowances and safety factors entered separately for run and branch?
Run and branch are often made of different materials with different tolerance fields (e.g. seamless pipe with 12.5% minus tolerance versus plate with a fixed lower limit). The corrosion attack may also differ. For the weakening verification, what counts is the actually load-bearing, corroded cross-section of each component — which is why c1, c2, K, and S are handled per component. If the branch material has a lower allowable stress than the run, its area may only be credited proportionally.
What role does the radius of the branch transition play?
The transition radius mitigates the notch effect at the junction of the branch. Radii that are too small increase the local stress peaks and are particularly critical under pulsating loading (pressure cycling); the codes require minimum radii depending on the wall thicknesses. For the fatigue analysis to AD 2000 S1/S2, the transition geometry enters directly into the stress concentration factor.