Page 173 - Marine Structural Design

Chapter 8 Buckling/ColIapse of Columns and Beam-columns 149

A
A
A
M, =yu-ay +y,--a, =-a,bu +YA (8.44)
2 2 2
where A is sectional area and a,denotes yield strength of the material. If we define plastic
modulus Z as
Z = M, la, (8.45)

Substituting Eq.(8.44) into Eq.(8.45), we may get,
A
=,h +Yo) (8.46)
The initial yielding moment My, may be defined using elastic sectional modulus W as.
My =o,w (8.47)

It is then easy to get the ratio of fully plastic moment and initial yielding moment as
f=’;/M, = z/w (8.48)

Some of the sectional modules for typical cross-sections are given in the following.

Rectangular Cross-Section
A
z =-br +y&, bh2 (8.49)
2
bh2
W=- (8.50)
6
Z
=i7=1.5 (8.51)

Tubular Cross-Section (t<<d)
z
I = -d’t (8.52)
8
7t
W = -d2t (8.53)
4
z
f =-=1.27 (8.54)
W
I-Profile (t<<h)
sh2
Z=bth+- (8.55)
4
W = bth +- bh2 (8.56)
6
For some standard types of hot rolled I-profiles, the ratio of hlly plastic moment and initial
yielding moment lies in the range of 1.1-1.18.