Page 22 - Pressure Vessel Design Manual

Stresses in Pressure Vessels 9

stresses have some self-limiting characteristics like secondary Discontinuity stresses are only considered as secondary
stresses. Since they are localized, once the yield strength of stresses if their extent along the length of the shell is limited.
the material is reached, the load is redistributed to stiffer Division 2 imposes the restriction that the length over which
portions of the vessel. However, since any deformation the stress is secondary is m. Beyond this distance, the
associated with yielding would be unacceptable, an allowable stresses are considered as primary mean stresses. In a cylin-
stress lower than secondary stresses is assigned. The basic drical vessel, the length a represents the length over
difference between a primary local stress and a secondary which the shell behaves as a ring.
stress is that a primary local stress is produced by a load that A further restriction on secondary stresses is that they may
is unrelenting; the stress is just redistributed. In a secondary not be closer to another gross structural Qscontinuity than
stress, yielding relaxes the load and is truly self-limiting. The a distance of 2.5m. This restriction is to eliminate the
ability of primary local stresses to redistribute themselves additive effects of edge moments and forces.
after the yield strength is attained locally provides a safety- Secondary stresses are divided into two additional groups,
valve effect. Thus, the higher allowable stress applies only to membrane and bending. Examples of each are as follows:
a local area.
Primary local membrane stresses are a combination of Seconda y membrane stress, Q,,,.
membrane stresses only. Thus only the “membrane” stresses a. Axial stress at the juncture of a flange and the hub of
from a local load are combined with primary general the flange.
membrane stresses, not the bending stresses. The bending b. Thermal stresses.
stresses associated with a local loading are secondary c. Membrane stress in the knuckle area of the head.
stresses. Therefore, the membrane stresses from a WRC- d. Membrane stress due to local relenting loads.
107-type analysis must be broken out separately and com-
bined with primary general stresses. The same is true for Secondary bending stress, QL.
discontinuity membrane stresses at head-shell junctures, a. Bending stress at a gross structural discontinuity:
cone-cylinder junctures, and nozzle-shell junctures. The nozzles, lugs, etc. (relenting loadings only).
bending stresses would be secondary stresses. b. The nonuniform portion of the stress distribution in a
Therefore, PL = P, + Qlllr where Q,, is a local stress from thick-walled vessel due to internal pressure.
a sustained or unrelenting load. Examples of primary local c. The stress variation of the radial stress due to internal
membrane stresses are: pressure in thick-walled vessels.
d. Discontinuity stresses at stiffening or support rings.
a. PI,, + membrane stresses at local discontinuities:
1. Head-shell juncture Note: For b and c it is necessary to subtract out the average
2. Cone-cylinder juncture stress which is the primary stress. Only the varymg part of
3. Nozzle-shell juncture the stress distribution is a secondary stress.
4. Shell-flange juncture
5. Head-slurt juncture Peak stress, E Peak stresses are the additional stresses due
6. Shell-stiffening ring juncture to stress intensification in highly localized areas. They apply
b. P,, + membrane stresses from local sustained loads: to both sustained loads and self-limiting loads. There are no
1. support lugs significant distortions associated with peak stresses. Peak
2. Nozzle loads stresses are additive to primary and secondary stresses pre-
3. Beam supports sent at the point of the stress concentration. Peak stresses are
4. Major attachments only significant in fatigue conditions or brittle materials.
Peak stresses are sources of fatigue cracks and apply to
Secondary stress. The basic characteristic of a second- membrane, bending, and shear stresses. Examples are:
ary stress is that it is self-limiting. As defined earlier, this
means that local yielding and minor distortions can satisfy a. Stress at the corner of a discontinuity.
the conditions which caused the stress to occur. Application b. Thermal stresses in a wall caused by a sudden change
of a secondary stress cannot cause structural failure due in the surface temperature.
to the restraints offered by the body to which the part is c. Thermal stresses in cladding or weld overlay.
attached. Secondary mean stresses are developed at the junc- d. Stress due to notch effect (stress concentration).
tions of major components of a pressure vessel. Secondary
mean stresses are also produced by sustained loads other Categories of Stress
than internal or external pressure. Radial loads on nozzles
produce secondary mean stresses in the shell at the junction Once the various stresses of a component are calculated,
of the nozzle. Secondary stresses are strain-induced stresses. they must be combined and this final result compared to an