(^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