Page 19 - Pressure Vessel Design Manual

6 Pressure Vessel Design Manual

LOADINGS

Loadings or forces are the “causes” of stresses in pres- primary and secondary stresses. If the material cannot
sure vessels. These forces and moments must be isolated yield to reduce the load, then the definition of secondary
both to determine where they apply to the vessel and stress does not apply! Fortunately current pressure vessel
when they apply to a vessel. Categories of loadings codes require the use of ductile materials.
define where these forces are applied. Loadings may be This should make it obvious that the type and category of
applied over a large portion (general area) of the vessel or loading will determine the type and category of stress. This
over a local area of the vessel. Remember both general will be expanded upon later, but basically each combina-
and local loads can produce membrane and bending tion of stresses (stress categories) will have different allow-
stresses. These stresses are additive and define the overall ables, i.e.:
state of stress in the vessel or component. Stresses from
local loads must be added to stresses from general load- 0 Primary stress: P, < SE
ings. These combined stresses are then compared to an 0 Primary membrane local (PL):
allowable stress. PL = P, + PL < 1.5 SE
Consider a pressurized, vertical vessel bending due to PL = P,, + Q, < 1.5 SE
wind, which has an inward radial force applied locally.
The effects of the pressure loading are longitudinal and 0 Primary membrane + secondary (Q):
circumferential tension. The effects of the wind loading
are longitudinal tension on the windward side and lon- Pm + Q < 3 SE
gitudinal compression on the leeward side. The effects of
the local inward radial load are some local membrane stres- But what if the loading was of relatively short duration? This
ses and local bending stresses. The local stresses would be describes the “type” of loading. Whether a loading is steady,
both circumferential and longitudinal, tension on the inside more or less continuous, or nonsteady, variable, or tempo-
surface of the vessel, and compressive on the outside. Of rary will also have an effect on what level of stress will be
course the steel at any given point only sees a certain level acceptable. If in our hypothetical problem the loading had
of stress or the combined effect. It is the designer’s job to been pressure + seismic + local load, we would have a
combine the stresses from the various loadings to arrive at different case. Due to the relatively short duration of seismic
the worst probable combination of stresses, combine them loading, a higher “temporary” allowable stress would be ac-
using some failure theory, and compare the results to an ceptable. The vessel doesn’t have to operate in an earth-
acceptable stress level to obtain an economical and safe quake all the time. On the other hand, it also shouldn’t fall
design. down in the event of an earthquake! Structural designs allow
This hypothetical problem serves to illustrate how cate- a one-third increase in allowable stress for seismic loadings
gories and types of loadings are related to the stresses they for this reason.
produce. The stresses applied more or less continuously and For steady loads, the vessel must support these loads more
unqomly across an entire section of the vessel are primary or less continuously during its useful life. As a result, the
stresses. stresses produced from these loads must be maintained to
The stresses due to pressure and wind are primary mem- an acceptable level.
brane stresses. These stresses should be limited to the code For nonsteady loads, the vessel may experience some
allowable. These stresses would cause the bursting or or all of these loadings at various times but not all at once
collapse of the vessel if allowed to reach an unacceptably and not more or less continuously. Therefore a temporarily
high level. higher stress is acceptable.
On the other hand, the stresses from the inward radial For general loads that apply more or less uniformly across
load could be either a primary local stress or secondary an entire section, the corresponding stresses must be lower,
stress. It is a primary local stress if it is produced from an since the entire vessel must support that loading.
unrelenting load or a secondary stress if produced by a For local loads, the corresponding stresses are confined to
relenting load. Either stress may cause local deformation a small portion of the vessel and normally fall off rapidly in
but will not in and of itself cause the vessel to fail. If it is distance from the applied load. As discussed previously,
a primary stress, the stress will be redistributed; if it is a pressurizing a vessel causes bending in certain components.
secondary stress, the load will relax once slight deforma- But it doesn’t cause the entire vessel to bend. The results are
tion occurs. not as significant (except in cyclic service) as those caused by
Also be aware that this is only true for ductile materials. In general loadings. Therefore a slightly higher allowable stress
brittle materials, there would be no difference between would be in order.