Heads are formed steel plates for pressure vessels and heat exchangers. The heads are usually found at the ends of an equipment, top or bottom for vertical vessels and left right for horizontal vessels. There are only a few shapes used for the heads that have proven to be useful. If the head is cut in half over the diameter of the head, the shapes follow more or less an ellipse, see also the figure below.

The strength calculation of heads are one of the frequently performed calculations since most equipment consist of one or two of them. The Head Thickness page is an example page to calculate the wall thickness of heads, ellipsoidal, torispherical, kloepper and korbbogen heads. Calculation codes are ASME, Dutch Rules and the EN Euronorm.

Below figure gives the an indication of the dimensions used in the calculations. The calculation also require the user to enter a stress value depending the material. The calculation page has a link to a material property page, but the values on the material pages are for reference only and are not to be used in actual calculations. Input: Type of shell Ellipsoidal Torispherical Kloepper Korbbogen Design pressure Pd N/mm2 ( = 1 MPa = 10 Bar ) Design temperature Td 0C Material description - Select yield stress and specific gravity from the material database Yield stress, design temperature Re(Td) N/mm2 Specific gravity kg/m3 Outside diameter De mm Nominal wall thickness dn mm Inside radius knuckle nominal ri1n mm, only for torisph. Inside radius dish nominal ri2n mm, only for torisph. Corrosion allowance Ca mm Tolerance tol mm Strength reduction coëfficient z - Design Code - ASME Dutch Rules EN13445 (PED) (ASME, Dutch R., PED)

Note: Without warranty and for estimating purposes only. Results should be checked and approved by qualified engineer.

Wall thickness calculation of Ellipsoidal head
according Dutch Rules

Calculation thickness d = dn - Ca - tol = 8.2 - 1 - 0 = 7.20 mm
(ellipsoidal only) k1 = 2*(he-dn) / (De-2*dn) = (with he = De/4) 0.4595
Inside radius knuckle nom. ri1n = 0.25 * (De-2*dn) * (1+k12 - (1-k1) * (1+k12) =
==> 0.25 * ( 219.10) * (1+ 0.45952 - (1- 0.4595) * (1+ 0.45952) = 31.24 mm
Inside radius dish nominal ri2n = 1/(4*k1) * (De-2*dn) * (1+k12 + (1-k1) * (1+k12) =
==> 1/(4* 0.4595)*( 219.10)*(1+ 0.45952+(1- 0.4595)* (1+ 0.45952)= 199.15 mm
Inside radius knuckle ri1 = ri1n + Ca + tol = 31.24 + 1.00 + 0.00 = 32.24 mm
Inside radius dish ri2 = ri2n + Ca + tol = 199.15 + 1.00 + 0.00 = 200.15 mm

(Constant 1) C1 = 101.125*(1.6-log(100*(ri1/ri2)))*(1-(d/(1.1*ri1))) =
==> 101.125*(1.6-log(100*( 32.24/ 200.15)))*(1-( 7.20/(1.1* 32.24))) = 2.25
(Constant 2) C2 = 1 + 0.306*ln(1+(d/ri1)) + 0.1574*ln2(1+(d/ri1)) =
==> 1 + 0.306*ln(1+( 7.20/ 32.24)) + 0.1574*ln2(1+( 7.20/ 32.24))= 1.07
(Constant 3) C3 = min ( C1, 2) = min ( 2.25, 2) = 1.50

Allowable stress knuckle fe = C3 * Re(Td) = 1.50 * 175.20 = 262.85 N/mm2
Allowable stress dish f2 = 0.67 * Re(Td) = 0.67 * 175.20 = 117.38 N/mm2

Required wall thickn. knuckle
drk =
 Pd*De*C1*C2 (2*z*fe)
=
 0.50* 219.10* 2.25* 1.07 (2* 1.00* 262.85)
=
0.50 mm
Nominal required thickness k. drkn = drk + Ca + tol = 0.50 + 1 + 0 = 1.50 mm
Required strength reduction kn.
zmin,k =
 Pd*De*C1*C2 (2*drk*fe)
=
 0.50* 219.10* 2.25* 1.07 (2* 7.20* 262.85)
=
0.070
Required wall thickn. dish
drd =
 2*Pd*ri2 (4*z*f2 - Pd)
=
 2* 0.50* 200.15 (4* 1.00* 117.38 - 0.50)
=
0.43 mm
Nominal required thickness d. drdn = drd + Ca + tol = 0.43 + 1 + 0 = 1.43 mm
Required strength reduct. dish
zmin,d =
 Pd*(2*ri2 + d) (4*d*f2)
=
 0.50*(2* 200.15 + 7.20) (4* 7.20* 117.38)
=
0.060
Analysis, z > zmin,k and zmin,d ? dn = 8.2 mm is OK
Stability analysis required ? No

Weight     2.94 kg
Enclosed volume     0.001 m3