Page 290 - Marine Structural Design

266 Part N Ultimate Strength

om = min(ouf ,cup) (13.41)
where o~ and cup are the ultimate beam-column failure values of the panel when lateral
pressure causes compression of stiffener flange and plating respectively. According to Hughes
(1983), a solution may be obtained by solving the following equations for stiffener failure,

(13.42)

and for plate failure,

where A is the initial eccentricity, So and Mo are the maximum deflection and bending
moment due to lateral load alone; A,, is the eccentricity caused by reduced stiffness of
compressed plating; I and A are respectively the second moment and the sectional area of the
panel, considering bp (panel width) is fully effective where as I, and A, are the similar
properties but for transformed section replacing b, by b, (effective width); y is the distance
from the panel neural axis to the stiffener flange and yp to the plating of the transformed
section; @ is the magnification factor for combined loading.
13.4.3 Crack Propagation Prediction
To predict the crack propagation and fatigue life, the Paris-Erdogan equation is used
da
-= CAK" (13.44)
dN
where a is the crack size, N is the number of cycles, AK is the stress range intensity factor and
C and m are material parameters. The stress intensity factor is given by:
AK = AoY(a)& (13.45)

where Aois the stress range and Y(a) is the geometry function.
If Y(a)=Y is a constant and tn&, then integration of Eq(13.44) gives
-
I
a(t) = [ai'*' +(1 -~)C(ACTY&)"'~,~]'-~ (1 3.46)
2
where a,, is the initial crack size, and the complete fatigue life T, is equaI to the sum of the
time to crack propagation Tp and the time to crack initiation
= kTp (1 3.47)
where k can vary from 0.1 to 0.15. The crack size is assumed to have a normal distribution
with the mean and variance, see Guedes Soares and Garbatov (1996,1999).
Two types of cracks are considered in the stiffened panel, one propagating away from the
stiffener in a transverse direction decreasing the width of attached plating, and the other across
the web of stiffener decreasing the web height.