Page 286 - Marine Structural Design

262 Part II Ultimate Strength

where M, is the fully-plastic moment, cry is the yield strength of the material and (SM), is
the plastic section modulus.
Frieze and Lin (1991) derived ultimate moment capacity as a function of normalized ultimate
strength of the compression flange using quadratic equation,
/ \2
M,/M,=d,+d,L+d, - (13.32)
CT
OY
where
d,=-0.172, d,= 1.548, d,=-0.368, for sagging

d,=0.003, d, = 1.459, d,=0.461, for sagging
Mansour (1 997) reviewed the above mentioned empirical moment capacity equations and
compared them with test results.
Based on fully plastic moment interaction, Mansour and Thayamballi (1980) derived the
following ultimate strength relation between vertical and horizontal moments,
m,+km;=1 if lmyl<\m,\ (1 3.33)

=I
my +b: if Imyl 2lm,l (13.34)
where

(1 3.35)

(A+2A,)Z
k= (13.36)
16A,(A-A,)-4(AD -AB)2
A= A, +AB +2A, (1 3.37)
and where
M, = bending moment in vertical direction

My =bending moment in horizontal direction
M, = vertical ultimate collapse bending moment

M, = horizontal ultimate collapse bending moment
= cross-sectional area of the deck including stiffeners
AD
= cross-sectional area of the bottom including stiffeners
AB
As = cross-sectional area of one side including stiffeners
Mansour (1997) demonstrated the above equations fit well with finite element analysis results
for ultimate strength of hull girders under combined vertical and horizontal moments.