Inside Diameter of Hemispherical Head

I assume you are still looking at ASME Div 2 - please see section 4.3.2.2

By using the following nomenclature:

t_s = Shell nominal thickness

t_h = Hemispherical head nominal thickness

R_s = Shell inside radius

R_h = Hemispherical head inside radius

R_m = Mean radius

R_ms = Shell mean radius = R_s + t_s/2

R_mh = Hemispherical head mean radius = R_h + t_h/2

Offset = Offset between two radii of hemispherical head and shell.

There are 3 cases that govern the relation between inside diameters of both shell and hemispherical head.

• Coincident centerlines, R_ms = R_mh = R_m : Offset = 0 and R_m = R_h + t_h/2 = R_s + t_s/2

• Offset where t_s > t_h (for both cases R_ms > R_mh & R_mh > R_ms): Offset per ASME code must be ≤ o.5 (t_s-t_h)

• Offset where t_h > t_s (for both cases R_ms > R_mh & R_mh > R_ms): Offset per ASME code must be ≤ o.5 (t_h-t_s)

Very Important Notes.

• In shell-to-hemispherical head connections, the distance between the tangent line-to-welding line L (to be cut from the hemispherical head before welding to shell and this distance shall be compensated by extension of shell beyond the welding line up to tangent line) is mainly depends on t_s, t_h , R_s and R_h. And can be easily determined by the following equations which are derived by myself using simple mathematics or can easily be attained by using graphics:

a. In case of coincident centerlines (R_ms = R_mh) : L = (1 + t_h/2R_h) * √(R_h² - R_s²)

b. In case of offset centerlines: L = [(R_s + t_s/2 ± x)/R_h] * √(R_h² - R_s²),

where, x with positive sign @ R_mh > R_ms, and x with negative sign @ R_mh < R_ms

and to find x, use the following relation: R_h = R_s + (t_s - t_h)/2 ^± x

• Till this instance, I didn't found any design handbook that demonstrates the prescribed relationships, and I did them more than 25 years ago to help myself in design of pressure vessels furnished with hemispherical heads, and I see that this CR4 Thread is a good chance to help my friends who interesting in design and fabrication of pressure vessels.

Offset = Offset between two radii of hemispherical head and shell.

I mean that offset x is the distance between the two midlines of wall thicknesses for both shell and hemispherical head, and per code x ≤ 0.5 (t_s - t_h) or x ≤ 0.5 (t_h - t_s).