AREA MOMENT OF INERTIA

Area Moment of Inertia

) The moment of nertia of any plane area about any
about any axis
axiS ts
is
the
Second moment of area about that axis


The 1st moment of area
The Area X distan ce


nd
Hnd the
the 2nd moment of area = Areo X dis tance) dA(d)

d.dA
I Ad* dA
where
d centrozdal distance rom axts

The unit of moment of inertta is mm, Cm

f moment of area ig taken about X-axis, -axis or z-axis
res. the M1. is denoted by Ix , Iyy and Izz.

2) Perbendicular Axis Theorem

1f Ixx and Iyy be the M:1 of any plane area. about two lar
axis xx and yy Passing through centrozd, the M1 about
0xís
zz perpendicular to area and passing through intersection o
-X and ts
y-y given by
Izz =
Ixx + lyy
where Izz is colled as polar moment of inertra




ran1n

, Proof
Consider the area. A in -y Plane

The moments of inertta of the
element
dA about the Xand y axes are


dIx *d A, dly : x*dA dlz rdA dA

dlz dA ----7x

=SrdA (x*+y*)dA

xdA+ Jy*dA


8) Parallel Axis Theorem
If I be the MI. of any plane area about an axiS passing

the MI about any other axis AB
through centro2d ot area ,


and at distance h o r d' ftom it is given by-
parallel to irst
a




I Ah2
IAB 1l + Ad* or t




Proof
dy

9 axis Passing through.
Centrod of the area


M'i of the eleme-7 dx
By definttion, the
nt dA about the x-axis is -x
d Y. +da) dA