
17Structural Distress
is integral is recognized as the rst moment of the section about the x-axis and is equal
to yA and to zero about the centroid located on the x-axis. ese forces are thus repre-
sented as a couple with a bending moment M so that if we integrate over the entire section
we obtain
MAA==
ky dkyd
(2.25)
is integral is the second moment or moment of inertia with respect to the x-axis and is
denoted as I
x
. So with respect to both axes we dene the moments of inertia as
IA
yd ;
xd
(2.26)
We may also dene the polar moment of inertia as
o
= rd
2
(2.27)
It can easily be shown that
oxy
(2.28)
ese concepts are summa