(^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

**joyce**(Joyce) #1