Page 224 - Marine Structural Design

200 Part II Ultimate Strength

Factors affecting the behavior of stiffened plates are e.g. stiffener slenderness and spacing,
plate geometry and material yield stress. In addition, residual stresses, initial deformation,
boundary conditions and types of loading will also affect the behavior of stiffened plates.
The potential failure modes for plates (or stiffened plates) under combined loads may be
classified as:
Buckling and collapse of plates - Lateral deflection develops in post-buckling region and
ultimate strength is reached due to yielding, see Sections 10.3 and 10.4.
Collapse of stiffeners with associated plates - Beam-column mode buckling in which
attaching plates are accounted for as effective plates, see Section 10.5.1.
Tripping of stiffeners - Tripping due to buckling of stiffeners and loss of the rotational
restraint provided by the plating, see Section 10.5.2.
Grillage buckling - Involves bending of transverse girders and longitudinal stiffeners, see
Section 10.6.
As a book for graduate courses, the objective of this Chapter is to give an introduction to
buckling strength analysis, while more details for mathematical theory may be found from the
books listed in the references. Some equations from design codes are used for illustration and
educational purpose only and engineering projects should directly use the relevant codes
without any deviations from them.
10.1.2 Solution of Differential Equation

The procedure for calculating the elastic buckling load is illustrated for an initially plane plate
subjected to an in-plane uniform compression. The equilibrium equation for a plate is given
by:

(10.1)

where the plate stiffness is given by:
Et3 (1 0.2)
=.-
and,

(10.3)

The quantities,

N, = o,t
N, = o,t (1 0.4)
Nx, = 0,t
are the membrane stress resultants.
For simply supported plates under pure compression (see Figure 10.2), Eq. (10.1) takes the
form: