Page 107 - Marine Structural Design

Chapter 4 Scantling of Ship$ Hulls by Rules 83

4.5.3 Structure Design of Bulkheads, Decks, and Bottom
For each individual longitudinal or verticalhorizontal stiffener on longitudinal and transverse
bulkheads, along with the effective plating to which it is attached, the net section modulus is
not to be less than that obtained from the following equations:
M
SM=- (cm3) (4.23)
ab
where
M=- 1000 c, c2 psP (Ncm) (4.24)
12
c, , is different for longitudinal, horizontal, and vertical stiffeners, c2 depends on the design
and loading of the tank. I, is the span of longitudinals or stiffeners between effective supports,
p, is defined above, and cb , is the permissible bending stress, which depends on the type and
position of the stiffener.

4.5.4 Buckling of Platings
General
Buckling is one of the main concerns in structural design. Structural elements, which are
exposed to high compressive stress, may experience instability before reaching the yield stress.
Platings should be evaluated to avoid local buckling of plates between stiffeners. This section
discusses the scantling of longitudinal members with respect to buckling control by
considering the total compressive stresses
Elastic Compressive Buckling Stress
The elastic buckling stress is the highest value of the compressive stress in the plane of the
initially flat plate for which a nonzero out-of-plane deflection of the middle portion of the
plate can exist. The Bryan Formula gives the theoretical solution for the compressive buckling
stress in the elastic range. For a rectangular plate subject to a compressive in-plane stress in
one direction, it may be expressed as:

(4.25)
The plate nomenclature may be obtained from Figure 4.1 1 , and t, is the net thickness, reduced
by corrosion addition. The buckling coefficient k, is a function of the plate aspect ratio PUS,
boundary conditions and loading conditions. If the plate is assumed to have the load applied
uniformly to a pair of opposite edges only and if all four edges are simply supported, then k,
is given by the following equation:

(4.26)

Here, n is the number of half-waves of the deflected plate in the longitudinal direction.