Pressure vessels 1

Cylindrical or spherical vessels are commonly used in industry to serve as
boilers or tanks. When under pressure, the material of which they are
made is subjected to a loading from all directions. Although this is the
case, the vessel can be analyzed in a simple manner provided it has a thin
wall. In general, “ thin wall ” refers to a vessel having an inner-radius-towall-
thickness ratio of 10 or more (r>t ? 10). Specifically, when r>t = 10
the results of a thin-wall analysis will predict a stress that is approximately
4% less than the actual maximum stress in the vessel. For larger r>t ratios
this error will be even smaller.
Provided the vessel wall is “thin,” the stress distribution throughout its
thickness will not vary significantly, and so we will assume that it is
uniform or constant. Using this assumption, we will now analyze the state
of stress in thin-walled cylindrical and spherical pressure vessels. In both
cases, the pressure in the vessel is understood to be the gauge pressure,
that is, it measures the pressure above atmospheric pressure, since
atmospheric pressure is assumed to exist both inside and outside the
vessel’s wall before the vessel is pressurized.