Page 44 - Pressure Vessel Design Manual

30 Pressure Vessel Design Manual

PROCEDURE 2-4

STRESSES IN HEADS DUE TO INTERNAL PRESSURE [e, 31

Notation

L =crown radius, in.
r =knuckle radius, in.
h =depth of head, in.
RL =latitudinal radius of curvature, in.
R, = meridional radius of curvature, in.
r~# =latitudinal stress, psi
ox = meridional stress, psi
P =internal pressure, psi

Formulas
Figure 2-2. Direction of stresses in a vessel head.
Lengths of RL and R, for ellipsoidal heads:
At equator:

h2
R, =-
R
RL = R

At center of head:

a At any point X:
:

Figure 2-3. Dimensional data for a vessel head.
Notes

1. Latitudinal (hoop) stresses in the knuckle become com- covered in the previous section. Torisphericz (also
pressive when the R/h ratio exceeds 1.42. These heads known as flanged and dished heads) and ellipsoidal
will fail by either elastic or plastic buckling, depending head formulas for stress are outlined in the following
on the R/t ratio. form.
2. Head types fall into one of three general categories:
hemispherical, torispherical, and ellipsoidal. Hemi-
spherical heads are analyzed as spheres and were