(^114) A Textbook of Engineering Mechanics
We know that distance between the centre of gravity of the section and bottom face,
11 2 2
12
(2000 50) (1200 10)
35 mm
2000 1200
ay a y
y
aa
- ×+ ×
== =
++
We know that moment of inertia of rectangle (1) about an axis through its centre of gravity
and parallel to X-X axis,
3
64
1
20 (100)
1.667 10 mm
G 12
I
×
==×
and distance of centre of gravity of rectangle (1) from X-X axis,
h 1 = 50 – 35 = 15 mm
∴ Moment of inertia of rectangle (1) about X-X axis
(^) =+ =IahG 1126 (1. 6 6 7× + ×10 ) [ 20 0 0 (1 5) ]^2 = 2.117 × 10^6 mm^4
Similarly, moment of inertia of rectangle (2) about an axis through its centre of gravity and
parallel to X-X axis,
3
64
2
60 (20)
0.04 10 mm
12
IG
×
=×
and distance of centre of gravity of rectangle (2) from X-X axis,
h 2 = 35 – 10 = 25 mm
∴ Moment of inertia of rectangle (2) about X-X axis
(^) =+= × + ×IahG 2226 (0.04 10 ) [1200 (25) ]^2 = 0.79 × 10^6 mm^4
Now moment of inertia of the whole section about X-X axis,
IXX = (2.117 × 10^6 ) + (0.79 × 10^6 ) = 2.907 × 10^6 mm^4 Ans.
Moment of inertia about centroidal Y-Y axis
Let left face of the angle section be the axis of reference.
Rectangle (1)
a 1 = 2000 mm^2 ...(As before)
and 1
20
10 mm
2
x ==
Rectangle (2)
a 2 = 1200 mm^2 ...(As before)
and 2
60
20 50 mm
2
x =+ =
We know that distance between the centre of gravity of the section and left face,
11 2 2
12
(2000 10) (1200 50)
25 mm
2000 1200
ax a x
x
aa - ×+ ×
== =
++
We know that moment of inertia of rectangle (1) about an axis through its centre of gravity
and parallel to Y-Y axis,
3
64
1
100 (20)
0.067 10 mm
12
IG
×
==×
and distance of centre of gravity of rectangle (1) from Y-Y axis,
h 1 = 25 – 10 = 15 mm
∴ Moment of inertia of rectangle (1) about Y-Y axis
(^) =+ =IahG 11126 (0.067× +10 ) [2000×(15) ]^2 = 0.517 × 10^6 mm^4