Page 244 - Marine Structural Design

220 Part II Ultimate Strength

and where L, is the ring spacing. The coefficient axL may be expressed as (Capanoglu and
Balint, 2002):
9
a, = (11.30)
[300+DltY
Eq.(l 1.27) will yield to buckling stress for flat plate when the plate curvature is small. This is
an advantage over the critical buckling stress equation for long cylinders used in API Bulletin
2U and MI RP 2A.
Inelastic buckling strength may be estimated using plasticity correction factor presented in
Part IT Chapter 10.

11.3.2 Hydrostatic Pressure
General
Three failure modes may possibly occur for ring stiffened cylinders under external pressure:
Local inter-ring shell failure
General instability
Ring stiffener failure
For ring-framed cylinders subject to external hydrostatic pressure, BS5500 (1976) and
Faulkner et a1 (1 983) combined elastic buckling stress with Johnson-Ostenfeld plasticity
correction factor, that was presented in Part I1 Chapter 10. It is noted that about 700 model
tests, with geometries in the range of 6 I Wt I 250 and 0.04 I L./R S 50, lie above the so-
called 'guaranteed' shell collapse pressure predicted by this formulation. The bias of the mean
strength for this lower bound curve is estimated to be 1.17 and in the usual design range the
COV is estimated to be 5% (Faulkner et al, 1983).
Local Inter-Ring Shell Failure
The best known solution for elastic buckling of the unsupported cylinder is that due to Von
Mises which is given by (see Timoshenko and Gere, 1961)

Et
(11.31)

minimized with respect to n (circumferential mode number).
Windenburg (1934) minimized the expression with respect to n, the number of complete
circumferential waves or lobes. By making further approximations he obtained the following
expression for the minimum buckling pressure:

0.919 E(t / R)Z (11.32)
PE =
L /(Rt)x - 0.636
Eq.(11.32) is invalid for very small or very large values of L/(Rt)x , but in the design range
its accuracy is sufficient. The analysis assumes the cylinder is pinned at non-deflecting