Engineering Mechanics

(^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

1. 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 ]


2. 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 ]


3. 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.

4. 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.

5. 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 ]