Page 285 - Marine Structural Design
P. 285
Chapter 13 Collapse Analysis ofship Hulls 26 1
(13.27)
Here (SM), is the elastic section modulus. Due to the use of greater slenderness ratios for
stiffeners and plate panels, and high yield steels, the possibility of buckling failure has
increased. The initial yield moment may not always be the lower bound to hull girder strength,
since the buckling of the individual structural elements has not been accounted for.
Due to the simplicity of the initial yield moment equation, it may be kequently used in
practical engineering. Vasta (1958) suggested that the ship hull would reach its ultimate
strength when the compression flange in the upper deck (in the sagging condition) or the
bottom plating (in the hogging condition) collapses, and that the yield stress in the initial yield
moment Eq. (13.24) may be replaced by the ultimate strength ou of the upper deck or bottom
plating.
Mansour and Faulkner (1 973) suggested the Vasta formula may be modified to account for the
shift of the neutral axis location after buckling of the compression flange.
M, = (1 + k) (SM),a, (1 3.28)
where k is a function of the ratio of the areas of one side shell to the compression flange. For a
frigate, they calculated the value of k to be approximately 0.1.
Viner (1986) suggested that hull girder collapses immediately after the longitudinals on the
compression flange reach its ultimate strength, and suggested the following ultimate moment
equation,
M, =a (SM),o, (13.29)
where a is normal in the range of 0.92 - 1.05 (mean 0.985).
The findings of Mansour and Faulkner (1973) and Viner (1986) are very useful because of
their simplicity - ultimate moment capacity is approximately the product of the elastic section
modulus and the ultimate strength of compression flange.
Valsgaard and Steen (1991) pointed out that hull sections have strength reserve beyond the
onset of collapse of hull section strength margin, and suggested that a is 1.127 for the single-
hull VLCC Energy Concentration, which collapsed in 1980.
A further modification was made by Faulkner and Sadden (1979) as:
(1 3.30)
where O" is the ultimate strength of the most critical stiffened panels.
13.3.2 Ultimate Moment Capacity Based on Fully Plastic Moment
Caldwell(l965) assumed that the ultimate collapse condition is reached when the entire cross-
section of the hull including side shell has reached the yield state. The material is assumed to
be elastic-perfectly-plastic, e.g. strain-hardening effect is ignored. Also, the effect of buckling,
and the effects of axial and shear forces are neglected. With these assumptions, the fully
plastic collapse moment, M, can be estimated as:
(1 3.3 1)