Page 104 - Pressure Vessel Design Manual

General Design 85
PROCEDURE 2-18

BUCKLING OF THIN-WALLED CYLINDRICAL SHELLS

This procedure is to determine the maximum allowable The other type of buckling is a result of local instability
stress for tubular members that are subject to axial com- that may or may not result in a change in the axis of the
pression loadings. Tubular members may be a pressure cylinder. This type is known as local buckling, and the sta-
vessel, a pipe, a silo, a stack, or any axially loaded cylinder bility against local buckling is dependent on t/R ratios.
of any kind. In addition, axial-loaded cylinders may be sub- For short and intermediate cylinders the critical stress is
jected to other load cases simultaneously. Other load cases independent of length. For long cylinders the length of the
include bending and internal or external pressure. cylinder is a key factor. The range of cylinders whose slen-
Axial loads can also result when a vertical vessel, stack, or derness ratios are less than Euler’s critical value are called
silo is transported and erected from the horizontal position short or intermediate columns.
due to bending of the shell. This procedure defines critical There are three kinds of buckling: elastic, inelastic, and
stress and critical load and differentiates between long, plastic. This procedure is concerned with elastic buckling
short, and intermediate columns. only. AISC assumes that the upper limit of elastic buckling
For ASME Code vessels; the allowable compressive stress is defined by an average stress equal to one-half the yield
is Factor “B.” The ASME Code, factor “B,” considers radius point.
and length but does not consider length unless external pres-
sure is involved. This procedure illustrates other methods of
defining critical stress and the allowable buckling stress for
vessels during transport and erection as well as equipment Critical Length, Critical Load,
not designed to the ASME Code. For example, shell com- Critical Stress
pressive stresses are developed in tall silos and bins due to
the “side wall friction” of the contents on the bin wall. The critical length is the length at which the critical stress
Shell buckling is a subtopic of nonlinear shell theory. In is achieved.
cylinders, buckling is a phenomenon that occurs when the The critical stress is the stress from the critical load.
cylinder fails in compression substantially before the ulti- Any shell longer than its critical length is considered of
mate compressive strength is reached. It is a function of “infinite” length because the additional length does not con-
the geometry of the item and is affected by imperfections tribute to stiffness.
in shape. A short, thick-walled column fails by yield due to
pure compression. A long, thin-walled column fails by buck-
ling. There is an intermediate region between the two. But in Effects of Internal or External Pressure
intermediate and long cylinders the mode of failure is very
different. The longitudinal pressure stresses either add or subtract
The term buckling refers to an unstable state. The force from the axial compressive stresses. Internal pressure
causing the instability is called the critical force. The stress stresses are in the opposite direction of axial compression
that causes buckling failure is always less than that required and therefore are subtracted. External pressure stresses
for a direct compressive failure. add to the axial compression stresses since they are in the
The terms buckling and collapse are often used in- same direction.
terchangeably. Buckling is defined as localized failure In addition, the hoop stresses resulting from external pres-
caused by overstress or instability of the wall under com- sure reduce the ability of the cylinder to resist the overall
pressive loading. Collapse is a general failure of the entire axial load. The uniform circumferential compressive forces
cross section by flattening due to external pressure. from external pressure aid in the buckling process. The crit-
Cylinders can buckle or collapse due to circumferential ical load is higher for a cylinder subjected to an axial load
loadings as well. This procedure does not analyze cylinders alone than for a cylinder subjected to the same overall load
for buckling due to circumferential loadings. There is a crit- but a portion of which is a result of external pressure. This is
ical uniform circumferential loading as well as a longitudinal because of the circumferential component of the external
one, as discussed in this procedure. pressure. By the same token, internal pressure aids in a
There are two kinds of failure due to buckling. The first, cylinder’s ability to resist compressive axial loading, for the
general buckling, involves bending of the axis of the cylinder, same reasons. The longitudinal stress induced by the internal
resulting in instability. This is the type addressed by Euler pressure is in the opposite direction of weight and any axial
and designed for by a “slenderness ratio” method. compressive loads.