Page 228 - Marine Structural Design

204 Part II Ultimate Strength

be taken as 5 to 10 percent of the plate's yield stress. For high strength steels, a higher value
for the compressive residual stresses should be considered.
For the stiffener web, the residual compressive stresses may be taken as 3 to 5 percent of the
stiffener yield stress for mild steels and a little higher for high strength steels.
Initial structural imperfections may be induced by welding, manufacturing, heat treatment,
transportation, and storage. The effect of imperfections on the ultimate strength of plates
depends strongly on their shape. In most theoretical studies, initial deflections have been
assumed to have the same shape as the buckling mode, because initial deflection has the most
significant influence on the ultimate strength when its shape coincides with the buckling mode.
Statistical analysis of measured plate distortions shows that the amplitude of the buckling
component is about half of the maximum distortions.

Various formulas are available for predicting the maximum distortion. However, the following
relation has been frequently used:

b
5%~ = cz--c,,- b > 40 ( 10.10)
t t t
where, typically, C, = 0.016 and C, = 0.36.
The fabrication tolerance criteria are usually defined in design codes for the strength criteria
defined. If the fabrication tolerance criteria are violated, the imperfections will have to be
repaired. Alternatively the effects of imperfections are to be explicitly accounted for using
advanced formulae or numerical/mechanical tests.
10.1.5 Correction for Plasticity

For plates with a low width to thickness ratio, Eq. (10.7) may theoretically predict a critical
stress if an excess of the yield stress occurs, but physically it cannot. Various methods exist to
account for plasticity effects. A convenient technique for modifying the elastic critical stress
caused by plasticity is the +method, where the elastic-plastic buckling stress is given by:
- (10.11)
ccr = I CTY
where 4 is an empirical function of the structural slenderness, as defined below:

(1 0.12)

Various expressions for + exist. One method for plasticity correction is to use an elliptical
interaction equation (Odland, 1988):

It is seen that:

o,, -+ aywhenaE + a,
-+
c,, crE whenc, << cy
Hence, the formula converges to the correct solution for both of stocky members and slender
members. Solving for CT~, we obtain: