Torispherical or Korbbogen Head? Dished End Geometry per DIN 28011 and DIN 28013
Dished ends close almost every cylindrical pressure vessel. In German-speaking markets two shapes are standard: the torispherical (Klöpper) head per DIN 28011 and the korbbogen head per DIN 28013. They look alike at first glance but differ clearly in height, material and load-carrying behaviour. This post explains the geometry, works through an example, and shows where geometry ends and the strength calculation begins.
A German version of this article is available — switch the language to Deutsch.
:::info Tool Every value in this post can be reproduced with the Dished End Calculator, which runs entirely in the browser. :::
Anatomy of a dished end
A head per DIN 28011 or DIN 28013 has three regions:
- Crown – the central spherical cap with the crown radius R.
- Knuckle – the toroidal transition with the knuckle radius r.
- Straight flange – the cylindrical portion of height h₁ that is welded to the shell.
All dimensions refer to the outside diameter Dₐ. Calculating from the inside diameter by mistake produces a head that does not fit the shell.
The formulas
| Quantity | Torispherical (DIN 28011) | Korbbogen (DIN 28013) |
|---|---|---|
| Crown radius R | R = Dₐ | R = 0.8 · Dₐ |
| Knuckle radius r | r = 0.1 · Dₐ | r = 0.154 · Dₐ |
| Inside dish depth h₂ | h₂ = 0.1935 · Dₐ − 0.455 · s | h₂ = 0.255 · Dₐ − 0.635 · s |
| Usual straight flange h₁ | h₁ ≥ 3.5 · s | h₁ ≥ 3 · s |
The overall height is straight flange plus inside dish depth plus wall thickness:
H = h₁ + h₂ + s
The korbbogen head has a smaller crown radius and a much larger knuckle. It is therefore taller and needs more plate – but it distributes the stresses in the knuckle more favourably. That is why it is preferred for higher pressures or wall thicknesses. The flatter torispherical head is the economical choice for lower pressures and where headroom is limited.
Worked example: Dₐ = 1000 mm, s = 10 mm
Torispherical head per DIN 28011
R = 1000 mm
r = 0.1 · 1000 = 100 mm
h₂ = 0.1935 · 1000 − 0.455 · 10 = 188.95 mm
h₁ = 3.5 · 10 = 35 mm
H = 35 + 188.95 + 10 = 233.95 mm
Korbbogen head per DIN 28013
R = 0.8 · 1000 = 800 mm
r = 0.154 · 1000 = 154 mm
h₂ = 0.255 · 1000 − 0.635 · 10 = 248.65 mm
h₁ = 3 · 10 = 30 mm
H = 30 + 248.65 + 10 = 288.65 mm
At the same diameter and wall thickness the korbbogen head is about 55 mm taller.
Blank size and weight
The head is spun or pressed from a circular blank. For a first estimate of the blank diameter the calculator uses the approximations common in practice:
Torispherical: D_blank ≈ 1.09 · Dₐ + 2 · h₁
Korbbogen: D_blank ≈ 1.14 · Dₐ + 2 · h₁
For the example in steel (7.85 kg/dm³):
| Torispherical | Korbbogen | |
|---|---|---|
| Blank diameter | 1.09 · 1000 + 70 = 1160 mm | 1.14 · 1000 + 60 = 1200 mm |
| Blank weight | ≈ 83.0 kg | ≈ 88.8 kg |
This is an estimate for quoting and material planning, not the final cutting size. Forming method, trim allowance and thinning in the knuckle are set by the head manufacturer. The calculator therefore also reports an estimated minimum wall thickness after forming – an indication, not proof.
Where geometry ends
DIN 28011 and DIN 28013 define the shape. Whether a head withstands the pressure is a separate question:
- In Europe, dished ends under internal pressure are verified per EN 13445-3, Clause 7.
- In Germany, AD 2000-Merkblatt B3 (dished ends under internal and external pressure) is also widely used.
Both account for the highest stresses occurring in the knuckle – exactly where the material flows most during forming. The nominal thickness from the geometry must therefore always be checked against the minimum thickness after forming and the corrosion allowance.
Common mistakes
- Inside instead of outside diameter. All formulas use Dₐ.
- Forgetting the straight flange. Without enough straight flange the weld ends up in the knuckle – exactly where it does not belong.
- Taking the blank weight as the finished weight. Trim is lost; the finished head is lighter.
- Thickening a torispherical head instead of choosing a korbbogen head. More wall helps less in the knuckle than a more favourable shape.
:::caution Note Results support preliminary design. The current editions of DIN 28011, DIN 28013, EN 13445 or AD 2000 and the head manufacturer's data govern. Release requires a qualified engineer. :::
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