Page 26 - Pressure Vessel Design Manual

Stresses in Pressure Vessels 13

very high magnitude. Discontinuity stresses are “secondary Although considered beyond the scope of this text as well,
stresses” and are self-limiting. That is, once the structure the designer must be aware of conditions that would require
has yielded, the stresses are reduced. In average application a fatigue analysis to be made.
they will not lead to failure. Discontinuity stresses do When a vessel is subject to repeated loading that could
become an important factor in fatigue design where cyclic cause failure by the development of a progressive fracture,
loadlng is a consideration. Design of the juncture of the the vessel is in cyclic service. ASME Code, Section VIII,
two parts is a major consideration in reducing discontinuity Division 2, has established specific criteria for determining
stresses. when a vessel must be designed for fatigue.
In order to find the state of stress in a pressure vessel, it is It is recognized that Code formulas for design of details,
necessary to find both the membrane stresses and the dis- such as heads, can result in yielding in localized regions.
continuity stresses. From superposition of these two states Thus localized stresses exceeding the yield point may be
of stress, the total stresses are obtained. Generally when encountered even though low allowable stresses have been
combined, a higher allowable stress is permitted. Due to used in the design. These vessels, while safe for relatively
the complexity of determining dlscontinuity stress, solutions static conditions of loading, would develop “progressive frac-
will not be covered in detail here. The designer should be ture” after a large number of repeated loadings due to these
aware that for designs of high pressure (>1,500 psi), brittle high localized and secondary bending stresses. It should be
material or cyclic loading, discontinuity stresses may be a noted that vessels in cyclic service require special considera-
major consideration. tion in both design and fabrication.
Since discontinuity stresses are self-limiting, allowable Fatigue failure can also be a result of thermal variations as
stresses can be very high. One example specifically well as other loadings. Fatigue failure has occurred in boiler
addressed by the ASME Code, Section VIII, Division 1, drums due to temperature variations in the shell at the feed
is discontinuity stresses at cone-cylinder intersections water inlet. In cases such as this, design details are of
where the included angle is greater than 60”. Para. 1-5(e) extreme importance.
recommends limiting combined stresses (membrane + dis- Behavior of metal under fatigue conrlltions vanes signifi-
continuity) in the longitudinal direction to 4SE and in the cantly from normal stress-strain relationships. Damage
circumferential direction to 1.5SE. accumulates during each cycle of loading and develops at
ASME Code, Section VIII, Division 2, limits the com- localized regions of high stress until subsequent repetitions
bined stress, primary membrane and discontinuity stresses finally cause visible cracks to grow, join, and spread. Design
to 3S,,, where S, is the lesser of %FFy or ‘/,U.T.S., whichever details play a major role in eliminating regions of stress
is lower. raisers and discontinuities. It is not uncommon to have
There are two major methods for determining dis- the design strength cut in half by poor design details.
continuity stresses:
Progressive fractures develop from these discontinuities
even though the stress is well below the static elastic strength
1. Displacement Method-Conditions of equilibrium are of the material.
expressed in terms of displacement. In fatigue service the localized stresses at abrupt changes
2. Force Method-Conditions of compatibility of dis-
placements are expressed in terms of forces. in section, such as at a head junction or nozzle opening,
See References 2, Article 4-7; 6, Chapter 8; and 7, misalignment, defects in construction, and thermal gradients
Chapter 4 for detailed information regarding calculation of are the significant stresses.
discontinuity stresses. The determination of the need for a fatigue evaluation is
in itself a complex job best left to those experienced in this
type of analysis. For specific requirements for determining if
Fatigue Analysis a fatigue analysis is required see ASME Code, Section VIII,
Division 2, Para. AD-160.
ASME Code, Section VIII, Division 1, does not speci- For additional information regarding designing pressure
fically provide for design of vessels in cyclic service. vessels for fatigue see Reference 7, Chapter 5.