|The illustration above is a finite element, asisymetric model of a
dished head subject to internal pressure. It clearly shows the knuckle
region acting as a hinge for the spherical portion.
The illustration below is an extract from the German pressure vessel
code, ADM. It plots the inside and outside stress in both the hoop
and longitudinal direction; starting from the centre of the spherical portion,
travelling left across the head, around the knuckle and down the cylindrical
The peak stress levels in the knuckle region can be up to three times
the design stress of the material; this is permitted as these stresses
only cover a small area and support is provided from neighbouring material
subject to much lower stress levels. However, these peak stresses
can give rise to catastrophic failure if attachments or nozzles are welded
into, or onto the knuckle region, without careful consideration.
It should also be noted that these peak stresses extend beyond the knuckle
into the spherical and cylindrical sections of the vessel.