Page 15 - Pressure Vessel Design Manual

2 Pressure Vessel Design Manual

effects long or short term? Do they apply to a localized In any pressure vessel subjected to internal or external
portion of the vessel or are they uniform throughout? pressure, stresses are set up in the shell wall. The state of
How these stresses are interpreted and combined, what stress is triaxial and the three principal stresses are:
significance they have to the overall safety of the vessel, and
what allowable stresses are applied will be determined by ox = 1ongitudmaVmeridional stress
three things: 04 = circumferentialAatitudina1 stress
or = radial stress
1. The strengtwfailure theory utilized.
2. The types and categories of loadings. In addition, there may be bending and shear stresses. The
3. The hazard the stress represents to the vessel. radial stress is a direct stress, which is a result of the pressure
acting directly on the wall, and causes a compressive stress
equal to the pressure. In thin-walled vessels this stress is so
small compared to the other “principal” stresses that it is
Membrane Stress Analysis generally ignored. Thus we assume for purposes of analysis
that the state of stress is biaxial. This greatly simplifies the
Pressure vessels commonly have the form of spheres, method of combining stresses in comparison to triaxial stress
cylinders, cones, ellipsoids, tori, or composites of these. states. For thickwalled vessels (RJt < lo), the radial stress
When the thickness is small in comparison with other &men- cannot be ignored and formulas are quite different from
sions (RJt > lo), vessels are referred to as membranes and those used in finding “membrane stresses” in thin shells.
the associated stresses resulting from the contained pressure Since ASME Code, Section VIII, Division 1, is basically for
are called membrane stresses. These membrane stresses are design by rules, a higher factor of safety is used to allow for
average tension or compression stresses. They are assumed the “unknown” stresses in the vessel. This higher safety
to be uniform across the vessel wall and act tangentially to its factor, which allows for these unknown stresses, can impose
surface. The membrane or wall is assumed to offer no resis- a penalty on design but requires much less analysis. The
tance to bending. When the wall offers resistance to bend- design techniques outlined in this text are a compro-
ing, bending stresses occur in addtion to membrane stresses. mise between finding all stresses and utilizing minimum
In a vessel of complicated shape subjected to internal code formulas. This additional knowledge of stresses warrants
pressure, the simple membrane-stress concepts do not suf- the use of higher allowable stresses in some cases, while meet-
fice to give an adequate idea of the true stress situation. The ing the requirements that all loadings be considered.
types of heads closing the vessel, effects of supports, varia- In conclusion, “membrane stress analysis’’ is not completely
tions in thickness and cross section, nozzles, external at- accurate but allows certain simplifymg assumptions to be
tachments, and overall bending due to weight, wind, and made while maintaining a fair degree of accuracy. The main
seismic activity all cause varying stress distributions in the simplifying assumptions are that the stress is biaxial and that
vessel. Deviations from a true membrane shape set up bend- the stresses are uniform across the shell wall. For thin-walled
ing in the vessel wall and cause the direct loading to vary vessels these assumptions have proven themselves to be
from point to point. The direct loading is diverted from the reliable. No vessel meets the criteria of being a true
more flexible to the more rigid portions of the vessel. This membrane, but we can use this tool with a reasonable
effect is called “stress redistribution.” degree of accuracy.

STRESS/FAILURE THEORIES

As stated previously, stresses are meaningless until com- They are the “maximum stress theory” and the “maximum
pared to some stresdfailure theory. The significance of a shear stress theory.”
given stress must be related to its location in the vessel
and its bearing on the ultimate failure of that vessel.
Historically, various ‘‘theories” have been derived to com- Maximum Stress Theory
bine and measure stresses against the potential failure
mode. A number of stress theories, also called “yield cri- This theory is the oldest, most widely used and simplest to
teria,” are available for describing the effects of combined apply. Both ASME Code, Section VIII, Division 1, and
stresses. For purposes of this book, as these failure theories Section I use the maximum stress theory as a basis for
apply to pressure vessels, only two theories will be discussed. design. This theory simply asserts that the breakdown of