(^122) A Textbook of Engineering Mechanics

Now moment of inertia of the whole built-up section about an axis through its centre of

gravity and parallel to X-X axis,

IXX = (6.5 × 10^6 ) + (3.0 × 10^6 ) + (0.6 × 10^6 ) = 10.1 × 10^6 mm^4 Ans.

EXERCISE 7.2

- Find the moment of inertia of a T-section having flange and web both 120 mm × 30 mm

about X-X axis passing through the centre of gravity of the section.

[Ans. 14 715 × 10^3 mm^4 ] - Calculate the moment of inertia of an I-section having equal flanges 30 mm × 10 mm and

web also 30 mm × 10 mm about an axis passing through its centre of gravity and parallel

to X-X and Y-Y axes. [Ans. 267.5 × 10^3 mm^4 ; 47 × 10^3 mm^4 ] - Find the moment of inertia of the lamina with a circular hole of 30 mm diameter about

the axis AB as shown in Fig. 7.24. [Ans. 638.3 × 10^3 mm^4 ]

`Fig. 7.24. Fig. 7.25.`

- A circular hole of diameter R is punched out from a circular plate of radius R shown in

Fig. 7.25. Find the moment of inertia about both the centroidal axes.

`15 4429`

;

XX 64 YY 192

`R R`

II

`⎡⎤ππ`

⎢⎥==

⎣⎦

`Ans.`

- The cross-section of a beam is shown in Fig. 7.26. Find the moment of inertia of the

section about the horizontal centroidal axis. [Ans. 1.354 × 10^6 mm^4 ]

`Fig. 7.26. Fig. 7.27.`

6. A built-up section consists of an I-section and two plates as shown in Fig 7.27. Find

values of IXX and IYY of the section. Take values of IXX as 3.762 × 10^6 mm^4 and IYY as

73.329 × 10^6 mm^6 respectively for the I-section.

[Ans. IXX = 17.095 × 10^6 mm^4 ; IYY = 169.46 × 10^6 mm^4 ]