Page 24 - Pressure Vessel Design Manual

Stresses in Pressure Vessels 11

and then the core is expanded hydraulically. The
core is stressed into plastic range but below ultimate
strength. The outer rings are maintained at a margin
below yield strength. The elastic deformation resi-
dual in the outer bands induces compressive stress
in the core, which is relaxed during pressurization.
5. Wire wrapped z)essels--Begin with inner core of thick-
ness less than required for pressure. Core is wrapped
with steel cables in tension until the desired auto-
frettage is achieved.
6. Coil wrapped cessels-Begin with a core that is subse- A
quently wrapped or coiled with a thin steel sheet until
the desired thickness is obtained. Only two longitudinal
welds are used, one attaching the sheet to the core and
the final closure weld. Vessels 5 to 6ft in diameter for
pressures up to 5,OOOpsi have been made in this
manner.

Other techniques and variations of the foregoing have been
used but these represent the major methods. Obviously
these vessels are made for very high pressures and are very
expensive.
For materials such as mild steel, which fail in shear rather
than direct tension, the maximum shear theory of failure
should be used. For internal pressure only, the maximum
shear stress occurs on the inner surface of the cylinder. At B
this surface both tensile and compressive stresses are max-
imum. In a cylinder, the maximum tensile stress is the cir- Figure 1-3. Comparision of stress distribution between thin-walled (A)
cumferential stress, 06. The maximum compressive stress is and thick-walled (B) vessels.
the radial stress, or. These stresses would be computed as
follows:

0 Spherical shells (Para. 1-3) where t > ,356 Ri or P >.665 SE:

2(SE + P)
Y=
2SE - P

Therefore the maximum shear stress, 5, is [9]:
The stress distribution in the vessel wall of a thick-walled
vessel varies across the section. This is also true for thin-
walled vessels, but for purposes of analysis the stress is
considered uniform since the difference between the inner
ASME Code, Section VIII, Division 1, has developed and outer surface is slight. A visual comparison is offered
alternate equations for thick-walled monobloc vessels. The in Figure 1-3.
equations for thickness of cylindrical shells and spherical
shells are as follows:
Thermal Stresses
0 Cylindrical shells (Para. 1-2 (a) (1)) where t > .5 Ri or
P > ,385 SE: Whenever the expansion or contraction that would occur
normally as a result of heating or cooling an object is
SE+P
Z=- prevented, thermal stresses are developed. The stress is
SE - P always caused by some form of mechanical restraint.