Page 234 - Marine Structural Design

210 Part II Ultimate Strength

1s =stiffener length

A, =Cross sectional area of the stiffened plate
While Johnson-Ostenfeld formula for column buckling is very simple, it does not account for
the effect of initial imperfection. An alternative equation is Perry-Robertson formula, see Part
I1 Chapter 8 of this book. The coefficient C, is a hction of the ratio of the bending moment
acting at the two ends of the beam MA M, :
I
c, = 0.6 + 0.4MA I M, (10.31)
1-olo,
The ultimate bending stress for the stiffened plates under pure bending may be taken as filly
plastic bending moment.
10.52 Tripping of Stiffeners
When the web height to thickness ratio is large combined with a flange that is inadequate to
remain straight under the combined uniaxial compressive load and lateral pressure, the
stiffener may twist sideways in the tripping failure mode. The tripping strength may be
predicted Johnson-Ostenfeld formula and elastic buckling stress equation (see Eq.(4.30) in
Part I Chapter 4 and e.g. Ma (1994)).

10.6 Gross Buckling of Stiffened Panels (Overall Grillage Buckling)
Using orthotropic plate theory, Mansour (1977) derived the following buckling equation that
may be used in the number of stiffeners in each direction exceeds 3,

(10.32)

where B is gross panel width, h, is effective thickness. For simply supported gross panel, k
may be taken as
m2
k = 7+2pu+--;- P2 (10.33)
P m
where m is number of half-waves of buckled plate, p and p are torsion coefficient and virtual
aspect ration respectively.

10.7 References
1. ABS (2001), “Rules for Building and Classing Steel Vessels”, American Bureau of
Shipping.
2. MI 2V (1987), “Bulletin on Design of Flat Plate Structures”, 1st Edition, 1987
(ANSVAPI Bull 2V-1992).
3. Amdhal, J. (1997), “Buckling and Collapse of Structures”, Lecture Notes, NTNU.
4. Bai, Y. (2001), “Pipelines and Risers”, Elsevier Ocean Engineering Book Series, Vol.
3.