Page 243 - Marine Structural Design

Chapter I1 Ultimate Strength of Cylindrical Shells 219

(1 1.26)

Long cylinders fail by ovalization for which n = 2 and the above equation yield to elastic
buckling stress for pipelines and risers under external pressure.

11.3 Buckling of Ring Stiffened Shells
This section discusses the ultimate strength of cylindrical shells strengthened by ring frames,
which are subjected to axial compression, external pressure and their combinations. The
formulation deals with shell failure. For the stiffener design, separate consideration should be
given against general stability and torsional instability, see Ellinas (1984).
11.3.1 Axial Compression
The potential failure modes for ring stiffened shell under compression are:
Un-stiffened cylinder or inter-ring shell failure (axi-symmetric collapse & diamond shape
collapse)
General instability
Ring stiffener failure
Combination of the above
Due to the catastrophic consequence, the failure mode of general instability failure is avoided
by placing requirements on stiffener geometry (such as moment of inertia) in design codes.
Design codes require that the buckling stress for general instability be 2.5 times of that for
local panel buckling.
Once general instability failure is suppressed, ring stiffener failure is unlikely to occur in ring-
stiffened cylinders. However, tripping of the ring stiffeners may possibly occur in conjunction
with general instability, weakening the strength against general instability. Therefore,
geometric requirements are applied to ring stiffeners to avoid the interaction of tripping and
general instability.
In the following, formulation is given for the lst failure mode listed in the above: un-stiffend
cylinder failure. Baht et a1 (2002) proposed to use the format of Batdorf for elastic buckling
of perfect cylinders:

(1 1.27)

where the buckling coefficient kxL is a function of geometric parameter M, (Capanoglu and
Baht, 2002):

(1 1.28)

and where
L,
M, = - (1 1.29)
JRt