Engineering guide
Pipe ends, header ends and manifold closures must be designed just as safely as the pipes themselves. This module calculates heads (ends) for metallic industrial piping to DIN EN 13480-3, clause 7: hemispherical heads, torispherical heads (Klöpper and Korbbogen types), ellipsoidal heads, and flat circular ends — welded or bolted — each under internal pressure. The reinforcement of openings in unstayed flat ends is also covered.
In practice, this calculation is needed whenever a piping system, a header or a manifold is closed off with an end and the required wall thickness or the allowable pressure must be verified to the European piping code. The design type is selected via a type switch; the module then applies the governing equations of clause 7 — for dished heads separately for crown and knuckle, for flat ends with the design-dependent calculation coefficients.
If you want to calculate a torispherical head — a Klöpper head or Korbbogen head — this worked approach gives you the minimum wall thickness of all head regions, so you can directly check the selected nominal wall thickness, including allowances, against the requirements of DIN EN 13480-3.
Scope
- Elliptical heads under internal pressure
- Unstayed flat circular ends welded to cylindrical shells/pipes under internal pressure
- Unstayed flat circular bolted ends under internal pressure
- Reinforcement of openings in unstayed flat ends under internal pressure
- Hemispherical ends under internal pressure
- Torispherical ends (korbbogen type / kloepper type) under internal pressure
Typical workflow
Select the head type
The head type is selected via the design-type variable: hemispherical head, Klöpper head, Korbbogen head, ellipsoidal head or flat circular end (welded or bolted, with or without an opening). The design type determines which equations of clause 7 of DIN EN 13480-3 are applied.
Enter design data and material properties
The inputs are design pressure and design temperature, the head geometry (diameter, and for dished heads the crown and knuckle radii) and the material. From these, the module determines the nominal design stress f from yield strength and tensile strength using the safety factors of the code; the joint efficiency z enters for welded heads.
Calculate the minimum wall thickness of the governing regions
For dished heads, the required wall thicknesses are determined separately: for the crown from the membrane stress, and for the knuckle, where increased bending stresses occur due to the change in curvature and where the largest wall thickness is frequently required. For flat ends, the thickness is calculated from plate bending using the coefficient C, which depends on design type and edge restraint.
Evaluate openings
If a flat end contains an opening, the module checks its reinforcement via a magnification factor on the end thickness or via the opening rules of clause 7. For dished heads, the code refers to the opening reinforcement rules of clause 8 for nozzles and openings.
Check the nominal wall thickness with allowances
The calculated minimum wall thickness is supplemented by the corrosion allowance and manufacturing tolerances (for dished heads additionally the thinning during forming) and compared with the selected nominal wall thickness. The result states whether the strength condition is satisfied for all head regions.
Frequently asked questions
What is the difference between a Klöpper head and a Korbbogen head?
Both are torispherical heads composed of a spherical crown and a toroidal knuckle. For the Klöpper head (DIN 28011) the crown radius is R = Da and the knuckle radius r = 0.1·Da; for the Korbbogen head (DIN 28013) R = 0.8·Da and r = 0.154·Da. The Korbbogen head is more deeply dished, therefore has lower knuckle stresses and often manages with a smaller wall thickness at the same pressure — but it is more expensive to form and has a greater overall height.
Why does the knuckle, rather than the crown, usually govern for dished heads?
In the knuckle, the curvature changes from the small knuckle radius to the large crown radius. Significant bending stresses arise there in addition to the membrane stresses, and for thin-walled heads there is the additional risk of elastic-plastic buckling of the knuckle under internal pressure. The code therefore requires separate verifications, and for common geometries the knuckle condition yields the largest required wall thickness.
When does a flat end make sense compared with a dished head?
Flat ends carry the pressure by plate bending instead of membrane action and therefore need considerably larger wall thicknesses — as a rule of thumb, several times that of a dished head of the same diameter. They are worthwhile for small diameters, low pressures, as bolted, removable closures, or where the overall height is limited. For larger diameters and higher pressures the dished head is almost always more economical.
Does clause 7 of DIN EN 13480-3 also apply to heads under external pressure?
No. Clause 7 covers heads under internal pressure. For dished heads under external pressure — for instance in vacuum operation or in jacketed lines — the stability verification to clause 9 of DIN EN 13480-3 must be carried out, which is implemented in module ER09.
Worked example
A hemispherical head for a DN 1000 header is to be designed to DIN EN 13480-3, clause 7. Design pressure 16 bar (1.6 MPa) at 200 °C, material P265GH, seamlessly formed head with joint efficiency z = 1.0. Find the required minimum wall thickness — a typical worked example for calculating wall thickness to EN 13480.
Given
| Inside diameter Di | 1,000 mm |
|---|---|
| Design pressure p | 1.6 MPa (16 bar) |
| Design temperature | 200 °C |
| Material | P265GH |
| Joint efficiency z | 1.0 |
Solution
Determine the nominal design stress
For P265GH at 200 °C the minimum yield strength is Rp0.2/200 °C = 192 MPa; the tensile strength at room temperature is Rm = 410 MPa. The nominal design stress is the smaller of Rp0.2/T/1.5 and Rm/2.4:
f = min(192/1.5; 410/2.4) = min(128.0; 170.8) = 128 MPa
Calculate the minimum wall thickness of the hemisphere
For spherical shells and hemispherical heads, using the inside diameter:
e = p · Di / (4 · f · z − p)
e = 1.6 · 1,000 / (4 · 128 · 1.0 − 1.6) = 1,600 / 510.4 = 3.13 mm
Select the nominal wall thickness
The corrosion allowance (e.g. c = 1 mm) and the manufacturing minus tolerance are added to the minimum wall thickness. With a selected nominal wall thickness of 5 mm and a 12.5% minus tolerance, the remaining thickness is 5 · 0.875 − 1.0 = 3.38 mm ≥ 3.13 mm — the strength condition is satisfied. For comparison: a cylindrical shell of the same diameter requires roughly twice the wall thickness.
Result
| Nominal design stress f | 128 MPa |
|---|---|
| Required minimum wall thickness e | 3.13 mm |
| Selected nominal wall thickness | 5 mm |
Technical content source: LV-Solved-Problems-Content 628d313247e7