Engineering task and calculation objective
The ABRA module calculates brackets and lugs on cylindrical and spherical shells. The local shell stresses at the attachment are determined per WRC Bulletin 537 — the polynomial approximation of the classical Bijlaard charts that supersedes the older WRC 107. Stress evaluation follows the stress categorization of ASME BPVC Section VIII, Division 2, Part 5 (Table 5.6); the attachment itself is checked per paragraph 4.15.5.
A bracket introduces weight, wind, or piping loads into the shell at a single point. The normal force, transverse and longitudinal shear, and circumferential and longitudinal moments produce local membrane and bending stresses that can significantly exceed the general shell stress. Anyone who wants to calculate local stresses at vessel supports per WRC 537 also gets the classical checks of the bracket plate in bending and of the attachment weld with this module.
Typical applications in pressure vessel design are support brackets of vertical vessels, lifting lugs, platform brackets and pipe supports, and generally all welded attachments whose load introduction is not covered by a nozzle calculation.
Standard and calculation basis: ASME BPVC Section VIII Division 2: 2025, 4.15.5 & Part 5 Table 5.6; WRC Bulletin 537
Calculation scope
- Bracket / lug on cylindrical shell (ASME VIII-2 & WRC 537)
- Bracket / lug on spherical shell (ASME VIII-2 & WRC 537)
Calculation workflow
- Define geometry and attachment area: Shell type (cylinder or sphere), diameter, and wall thickness as well as the dimensions of the bracket's attachment footprint are captured. WRC 537 idealizes the attachment as a rectangular or circular load application area; the dimensionless geometry parameters determine the read-off values of the Bijlaard curves.
- Determine the section loads at the attachment: From the external loads (weight, wind, friction, piping forces), the normal force, two shear forces, and the moments at the shell attachment are determined — including the additional moments resulting from the eccentricity of the load application point relative to the shell surface.
- Calculate local shell stresses per WRC 537: For each load component, the polynomial approximations of the Bijlaard charts deliver membrane and bending stress components in the circumferential and longitudinal directions at the governing points on the attachment perimeter. The components are superimposed with correct signs.
- Stress categorization per Part 5: The superimposed stresses are classified as local membrane stress P_L and membrane-plus-bending stress P_L+P_b+Q and checked against the allowable limits of Table 5.6 (e.g., 1.5·S and S_PS respectively).
- Verify bracket plate and weld: Independently of the shell, the bracket plate is verified using classical beam bending and the attachment weld using the weld stress from force and moment components. If the shell is inadequate, a reinforcing pad is provided and the calculation is repeated with the enlarged attachment area.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Load case (1=operation, 2=test) | – | – |
| Design temperature | – | °C |
| Design pressure | – | MPa |
| Material name | – | – |
| Negative tolerance | – | mm |
| Corrosion allowance | – | mm |
| Safety factor K/S | – | – |
| Shell inside diameter Di | – | mm |
| Shell nominal thickness T | – | mm |
| Shell type | – | – |
| Bracket height h | – | mm |
| Footprint length c1 (axial) | – | mm |
| Footprint length c2 (circumferential) | – | mm |
| Bracket plate thickness tL | – | mm |
| Load eccentricity e | – | mm |
| Number of ribs n | – | – |
| Rib thickness tR | – | mm |
| Vertical load Fv (gravity) | – | N |
| Horizontal load Fh | – | N |
| External moment Mext | – | Nmm |
| Weld throat a | – | mm |
| Comment | – | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Material strength at T | – | MPa |
| Allowable stress S = R10 / (K/S) | – | MPa |
| Mean radius Rm = (Di+T)/2 | – | mm |
| Radial load P | – | N |
| Circumferential moment Mc = Fv·e | – | Nmm |
| Longitudinal moment ML = Fh·h + Mext | – | Nmm |
| Dimensionless β = max(c1,c2)/Rm | – | – |
| Dimensionless γ = Rm/T | – | – |
| Shell membrane stress axial σx,m | – | MPa |
| Shell membrane stress circumferential σφ,m | – | MPa |
| Shell bending stress axial σx,b | – | MPa |
| Shell bending stress circumferential σφ,b | – | MPa |
| Primary membrane Pm (pressure hoop) | – | MPa |
| Local membrane PL | – | MPa |
| PL + Pb (primary + bending) | – | MPa |
| PL + Pb + Q (SPS) | – | MPa |
| Allowable Pm ≤ S | – | MPa |
| Allowable PL ≤ 1.5·S | – | MPa |
| Allowable PL+Pb ≤ 1.5·S | – | MPa |
| Allowable PL+Pb+Q ≤ 3·S (SPS) | – | MPa |
| Bracket plate bending stress σb | – | MPa |
| Bracket equivalent stress σv | – | MPa |
| Section modulus W = c1·tL²/6 | – | mm³ |
| Weld equivalent stress σv,w | – | MPa |
Calculation options
Load case (1=operation, 2=test)
Operation · Test
Shell type
Cylindrical shell · Spherical shell
Frequently asked questions
What is the difference between WRC 107 and WRC 537?
WRC 537 is the substantive continuation of WRC 107: the same Bijlaard fundamentals, but the charts formerly read off manually are stored as polynomials, errors in the old curves have been corrected, and the range of validity has been clarified. For software calculation, WRC 537 is the governing state of the art; results may deviate slightly from manual WRC 107 readings.
Where are the limits of validity of the WRC method?
The Bijlaard solutions apply to attachment areas that are small relative to the shell (typically attachment parameters up to about d/D ≤ 0.3 for cylinders) and to thin-walled shells. For large brackets, thick-walled shells, closely spaced attachments, or load introduction near discontinuities (heads, flanges, nozzles), the parameters leave the range of the curves — then a finite element analysis per Part 5 is required.
Why is the eccentricity of the load introduction so important?
The external load acts at the bearing point of the bracket, often 100–300 mm away from the shell wall. The shear force thereby produces an additional moment (force times lever arm) that can dominate the local bending stresses. A common mistake is to apply only the force without this eccentricity moment — which severely underestimates the shell stress.
When is a reinforcing pad under the bracket useful?
If the verification of the local shell stresses fails, a welded-on reinforcing pad distributes the load over a larger attachment area and reduces the stress peaks. It must be welded all around and project sufficiently beyond the bracket attachment. Under cyclic loading or at high temperatures, it should be checked whether a thicker shell or a through-going construction is the better solution.