Page 245 - Marine Structural Design

Chapter I I Ultimate Strength of Cylindrical Shells 22 1

cylindrical supports. More refined analyses are now available which, for example, consider
the influence of the ring frames on the deformations before and during buckling. These
analyses show that pE becomes inaccurate for closely spaced frames. Nevertheless, the Von
Mises expression is still widely used because it can be represented in a relatively simple form
and it is in most cases only slightly conservative.
General Instability
Due to the catastrophic post-collapse characteristics associated with this failure mode, design
codes require the effective moment of inertia for the ring stiffeners with associated shell
plating to be sufficiently high so that the ratio of general and local elastic buckling stresses is
1.2 (e.g. ASME (1980) Boiler and Pressure Vessel Code).
Ring Stiffener Failure
Ring stiffener failure may occur as torsional buckling or tripping of the stiffeners, seriously
weakening the resistance of the shell to general instability. Therefore, design codes specify
requirements on the ring stiffener geometry to prevent this type of failure from occurring.
Imperfections in the form of lateral deformations of the ring stiffeners may have a strong
detrimental effect in reducing the stiffener’s resistance to torsional buckling. Similar to
tripping of stiffened plates, fabrication tolerance has been established on such imperfections.
11.3.3 Combined Axial Compression and Pressure

The strength of ringer stiffened cylinders under combined axial compression and external
pressure may be expressed as:

(1 1.33)

Recommendations by various codes are found differing widely, ranging from the linear
interaction (m = n = 1) recommended by ECCS (1976) to a circular one (m = n = 2) required
by DNV (2000). The ASME Code Case N-284 suggests a combination of straight lines and
parabolas that appears to agree quite well with test data. Das et a1 (2001) suggested that the
parabola (m = 1, n = 2) offers the best fit to available data and is very close to the ASME
recommendations.

11.4 Buckling of Stringer and Ring Stiffened Shells

11.4.1 Axial Compression
General
This section is based on simplifications to Faulkner et a1 (1983), Ellinas (1984), Das et a1
(1992) and Das et a1 (2001). Stinger-stiffened cylinder buckling is usually the governing
failure mode. Other failure modes such as local panel buckling, local stiffener tripping and
general instability may also occur, see Ellinas (1984). In many practical design situations,
buckling of stringer and ring stiffened shells is assessed as buckling of stiffened plates using
formulation presented in Part II Chapterlo.