Engineering Mechanics

(^118) „„„„„ A Textbook of Engineering Mechanics
Moment of inertia of the section about X-X axis.
We also know that moment of inertia of the triangular section through its centre of gravity and
parallel to X-X axis,
33
34
1
100 (90)
2025 10 mm
36 36
G
bd
I
×
== = ×
and distance between the centre of gravity of the section and X-X axis,
h 1 = 30 – 27.7 = 2.3 mm
∴ Moment of inertia of the triangular section about X-X axis
=+ = ×+IahG 121232025 10 [4500×(2.3) ]^2 = 2048.8 × 10^3 mm^4
Similarly moment of inertia of the rectangular hole through its centre of gravity and parallel
to the X-X axis
33
34
2
20 (30)
45 10 mm
G 12 12
bd
I
×
== =×
and distance between the centre of gravity of the section and X-X axis
h 2 = 45 – 27.7 = 17.3 mm
∴ Moment of inertia of rectangular section about X-X axis
(^) =+ =× + ×IahG 22223 (45 10 ) [600 (17.3) ]^2 = 224.6 × 10^3 mm^4
Now moment of inertia of the whole section about X-X axis.
Ixx = (2048.8 × 10^3 ) – (224.6 × 10^3 ) = 1824.2 × 10^3 mm^4 Ans.
Moment of inertia of the section about the base BC
We know that moment of inertia of the triangular section about the base BC
33
34
1
100 (90)
6075 10 mm
12 12
G
bd
I
×
== =×
Similarly moment of inertia of the rectangular hole through its centre of gravity and parallel
to X-X axis,
33
34
2
20 (30)
45 10 mm
G 12 12
bd
I
×
== =×
and distance between the centre of gravity of the section about the base BC,
2
30
30 45 mm
2
h =+ =
∴ Moment of inertia of rectangular section about the base BC,
23 2 34
=+ =× + × = ×IahG 222 (45 10 ) [600 (45) ] 1260 10 mm
Now moment of inertia of the whole section about the base BC,
IBC = (6075 × 10^3 ) – (1260 × 10^3 ) = 4815 × 10^3 mm^4 Ans.
7.16. MOMENT OF INERTIA OF A BUILT-UP SECTION
A built-up section consists of a number of sections such as rectangular sections, channel
sections, I-sections etc., A built-up section is generally made by symmetrically placing and then
fixing these section by welding or riveting. It will be interesting to know that a built-up section