Engineering task and calculation objective
Module BEIN calculates vertical vessels on support legs. It performs the stress check in the vessel wall at the load introduction point and the stability verification to AD 2000-Merkblatt S3/0, a sheet of the German AD 2000 pressure vessel code; if the maximum normal force per AD S3/3 is exceeded, a buckling check of the legs to DIN 18800 Part 2 follows. An integrated section database to DIN 1024 through 1029 provides the section properties of common rolled profiles (T, channel, I/H sections and others) — cross-sectional area, minimum section modulus and minimum moment of inertia are adopted automatically.
As loads, weight forces G (vessel, contents, attachments) and lateral forces Q — such as wind loads or seismic equivalent loads — can be specified. From their distribution over the legs follow the normal force and bending moment per leg as well as the local loading of the vessel shell at the attachment point.
This verification is needed in pressure equipment engineering for every vessel on legs: storage tanks, agitated vessels, heat exchangers and columns of moderate height frequently stand on three or four profile legs whose load-bearing capacity and buckling resistance must be verified just like the shell loading at the leg attachment.
Standard and calculation basis: AD/S 3, DIN 18800-2, DIN 1024 - 1029
Calculation workflow
- Define vessel and leg geometry: The vessel dimensions, the number and length of the support legs and their attachment to the shell are entered. For the legs, a profile type is chosen from the database to DIN 1024 through 1029; cross-sectional area, minimum section modulus and moment of inertia are set automatically.
- Specify the loads: The weight force G from dead weight, contents and attachments as well as horizontal lateral forces Q such as wind or seismic loads with their point of application are applied. From the vertical load and the overturning moment follows the non-uniform distribution of the normal forces over the individual legs — the most heavily loaded leg governs.
- Verify the stresses in the vessel wall: At the load introduction point of the legs, the local loading of the shell is checked to AD S3/0: the concentrated support force produces local bending and membrane stresses in the vessel wall, which are compared with the allowable values of the vessel material. Reinforcing pads may need to be provided.
- Check the load-bearing capacity of the legs: For the governing leg, the normal force and bending moment are compared with the profile cross-section. If the normal force remains below the limit per AD S3/3, the stress check is sufficient; otherwise the stability verification follows.
- Perform the buckling check to DIN 18800-2: From the buckling length, the minimum moment of inertia and the material, the slenderness ratio is formed; via the parameter of the applicable buckling curve, the reduction factor kappa results. With the moment coefficient for flexural buckling, the interaction of compressive force and bending moment is checked and it is reported whether the stability verification is satisfied.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| L-section leg length | aL | mm |
| Cross sectional area | A | mm² |
| Width | B | mm |
| Wall thickness allowance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Bolt circle diameter of supports | dF | mm |
| Distance = Support - Vessel | eG | mm |
| Modulus of elasticity (operation) | Ebe | N/mm² |
| Modulus of elasticity (test) | Epr | N/mm² |
| Center of gravity x | Ex | mm |
| Center of gravity y | Ey | mm |
| Weight | G | kg/m |
| Maximum total weight at operation | Gd | N |
| Minimum total weight at operation | Gz | N |
| Profile height | H | mm |
| Lever arm of lateral force | hQ | mm |
| Moment of inertia x | Jx | mm^4 |
| Moment of inertia y | Jy | mm^4 |
| Strength at operation | Kbe | N/mm² |
| Strength at testing | Kpr | N/mm² |
| Total profile length | hF | mm |
| Buckling length of profile (e.g.: 2*hF) | lK | mm |
| for | n | - |
| Load case | Lastfall | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Euler's buckling force | Fk | N |
| Total moment | M | Nm |
| Compressive normal force (pressure > 0) | NFd | N |
| Tensile normal force (tension > 0) | NFz | N |
| Normal stress (Transverse force=0) | σ0 | N/mm² |
| Compressive normal stress | σD | N/mm² |
| Tensile normal stress | σZ | N/mm² |
| Max. equivalent stress | σV | N/mm² |
| Equivalent stress in compression | σV1 | N/mm² |
| Equivalent stress in tension | σV2 | N/mm² |
| Equivalent stress dead weight (Q=0) | σV3 | N/mm² |
| Shear stress (Transverse force=0) | τ0 | N/mm² |
| Shear stress in compression | τD | N/mm² |
| Shear stress in Tension | τZ | N/mm² |
| Minimum section modulus | W | mm³ |
| Strength condition for selected load case | Festigkeitstext | – |
| Remark | Anzeigetext | – |
| Allowable stress (operation) | fBe | N/mm² |
| Allowable stress (test) | fPr | N/mm² |
| Strength condition dead weight (Q=0) | Eigengewicht | – |
| Minimum moment of inertia | Jmin | mm^4 |
| Lowest normal force for DIN18800-2 | NK | N |
| Stability proof according to DIN 18800 part 2 is | DIN18800-2 | – |
| Gross yield normal force | A·σall Fdpl | N |
Calculation options
Load case
Operation · Test
Frequently asked questions
When is the stress check sufficient, and when is the buckling check required?
Short, stocky legs fail by reaching the material strength — here the stress check is sufficient. Slender compression members, however, buckle well below the yield strength. AD S3/3 specifies a maximum normal force; if it is exceeded or the leg is slender, the code requires the stability verification to DIN 18800-2 with the reduction factor kappa, which reduces the load-bearing capacity as a function of slenderness.
How are the loads distributed over the individual legs?
With a symmetric arrangement, the weight force is distributed uniformly. A lateral force (wind), however, produces an overturning moment that additionally compresses the legs on the leeward side and relieves those on the windward side — up to tensile forces that require anchoring. Governing for the verification is the most heavily loaded leg under the most unfavorable wind direction; with three legs the non-uniformity is more pronounced than with four.
Why must the vessel wall at the leg attachment be verified separately?
The support force is introduced locally into the thin-walled shell over a small attachment area. Local bending stresses arise there that can far exceed the membrane stresses from the internal pressure — the shell can dimple or crack even though the legs and the pressure design are in order. Remedies are larger attachment areas, reinforcing pads, or placing the legs under the head knuckle region.
What do the reduction factor kappa and the moment coefficient mean?
Kappa is the buckling reduction factor of DIN 18800-2: it indicates what share of the plastic normal-force capacity may still be utilized at a given slenderness ratio and buckling curve (depending on profile shape and buckling direction). The moment coefficient for flexural buckling captures the shape of the bending moment distribution over the member length in the interaction check for compression plus bending; for a constant moment distribution it is set to 1, more favorable distributions allow smaller values.