Engineering task and calculation objective
Module B5A1 calculates pressure vessels of rectangular cross-section to AD 2000-Merkblatt B5/1, a sheet of the German AD 2000 pressure vessel code — plain rectangular tubes, sectional headers and box-shaped components such as the headers and distribution chambers of heat exchangers, air cooler headers, or rectangular housings in compressed air and hydraulic systems. Only loading due to internal pressure is considered.
Unlike a cylinder, which carries the pressure predominantly through membrane stresses, the flat walls of a rectangular cross-section are loaded in bending. The governing quantities are therefore the bending stresses at mid-side and in the corners, determined via design coefficients from the side-length ratios. Rows of holes — single openings, central, offset, axially or diagonally adjacent holes — additionally weaken the walls; the code sheet covers this through ligament efficiency factors for the webs between the openings.
After entering the geometry (cross-section dimensions, inner corner radius, opening diameters and pitches), the material and the allowances, the program calculates the required wall thicknesses for the side wall and the corners as well as the stress checks for the operating and test conditions — everything needed to calculate a rectangular tube or sectional header to AD 2000 B5/1.
Standard and calculation basis: AD2000 B5/1: 2006-05
Calculation workflow
- Capture the geometry of the rectangular cross-section: The clear dimensions along and perpendicular to the considered calculation wall, the inner corner radius and the as-built wall thicknesses of the side wall and corner are entered. From the manufacturing and corrosion allowances (c1, c2), the corroded, effective wall thicknesses used in the calculation follow.
- Define the opening configuration: For perforated walls, the type and position of the openings are defined: single opening, central or offset hole, axially adjacent rows or diagonal ligaments — described by hole diameter, distance from the wall centerline, center-to-center distances and the angle of the connecting line to the axis. From these follow the ligament efficiency factors of the webs.
- Assign material properties and safety factors: From the material and the design temperature, the strength values for the operating and the test condition are determined and combined with the safety factors of the AD 2000 code. Operating pressure and test pressure form the two load cases to be verified.
- Calculate the stresses at the governing locations: Using the design coefficients of the code sheet, the stresses from membrane and bending components are determined at the critical locations: in the corners, at mid-side, and in central, offset and diagonal ligaments between the openings — in each case for operation and test.
- Verify the wall thicknesses: The existing corroded wall thicknesses are compared with the required values with and without openings. If a location is overstressed, a larger wall thickness, wider ligaments (pitch), a larger corner radius or stiffeners must be provided.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Strength condition for type | : | - |
| along the considered wall | b | mm |
| Calculation coefficient | BK | - |
| Calculation coefficient | BW | - |
| Calculation coefficient | BZ | - |
| Mill tolerance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Diameter of openings or inside diameter of nozzles | dAi | mm |
| Center distance between opening and wall (0=central) | e | mm |
| Angle between the line of openings and wall axis | φ | ° |
| perpendicular to the considered wall | l | mm |
| Material strength for operation | K | N/mm² |
| Material strength for testing | K20C | N/mm² |
| Operating pressure | P | bar |
| Inside corner radius | ri | mm |
| Safety factor for operation | SS | - |
| Safety factor for testing | S20C | - |
| Final side wall thickness with allowances | se | mm |
| Corroded side wall thickness se-c1-c2 | sec | mm |
| Final corner wall thickness with allowances | s0 | mm |
| Corroded corner wall thickness s0-c1-c2 | s0c | mm |
| in the corners | (4) s0 s'0 | mm |
| in the side wall center | (5) sv2 s'2 | mm |
| in central ligaments | (6) sv3a s'3a | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Corroded side wall thickness se-c1-c2 | sec | mm |
| Corroded corner wall thickness s0-c1-c2 | s0c | mm |
Frequently asked questions
Why do rectangular cross-sections need so much thicker walls than cylindrical ones?
A cylinder carries internal pressure almost exclusively through membrane tensile stresses — the statically most favorable load path. The flat walls of a rectangular box, by contrast, bend under the pressure; the loading grows with the square of the free wall span. Rectangular chambers are therefore economical only for smaller dimensions or moderate pressures, and at higher pressures they are replaced by stays, webs or cylindrical shapes.
Which location governs — the corner or mid-side?
That depends on the side-length ratio, the corner radius and the position of the openings. At mid-side, the largest span moment acts; in the corners, the support moment with superimposed membrane tensile force; with perforated walls, the weakened ligaments may govern. The module therefore reports all locations separately — checking only mid-side is not sufficient.
How do rows of holes affect the required wall thickness?
Openings reduce the load-bearing cross-section to the ligaments between the holes. The ligament efficiency follows from the ratio of ligament width to pitch; for diagonally adjacent holes, the effective pitch is corrected via the angle of the connecting line. Offset openings are less favorable when they lie in zones of high bending stress — the distance from the wall centerline therefore enters the assessment directly.
Does B5/1 also cover external pressure or additional loads?
No. The design rules of this code sheet cover internal pressure only. External pressure (buckling risk of the flat walls), piping loads, thermal stresses or cyclic loading must be assessed separately — for example via the general AD 2000 code sheets or a finite element analysis. Welded-on stays and support webs that stiffen the walls also require their own analysis.