MOMENT OF INERTIA

Find moment of inertia about centroidal axis 1. 2.

IXX= 98.18 X 106 mm4 IXX= 65.27 X 106 mm4 IYY= 62.83 X106 mm4 IYY= 43.04 X106 mm4 3. 4. IXX= 3.12 X 106 mm4 IXX = 41.62 X 106 mm4 IYY= 0.526 X 106 mm4 IYY = 11.4 X 106 mm4 5. 6. 7. 8.

40mm

250mm

200mm

50 mm

Y

X = 64.4mm

X

Y = 80.5mm

X

12mm

175mm 175mm Y

20 mm

250mm

X = 0 Y = 184mm

X

50mm

10mm

Y

100mm

50mm

X = 5 mm Y = 55mm

90.6mm

108mm

200mm

12mm

12mm

Y

150mm

12mm X

X = 0 Y = 108.4mm

175mm

12cm

5 cm 5 cm

15cm

Y

Y

X

X

IXX = 2.885 x 107 mm4

IYY = 8.410 x 106 mm4 Ixx = 8796.19 mm4 Iyy = 5987.25 mm4

y

y

x x

22.04 mm R = 20mm

10mm

10mm 10mm

15mm

B

G

F

D

Y

x

O Y 500mm

9. Find Ixx and Iyy 10. Find IXX and IYY IXX = 17.71 x 106mm4 IXX = 316.92 x 104mm4 IYY = 5.09 x 106mm4 IYY = 14.11 x 106mm4 11. Find IAB. 12. Find IAB 13. Find IAB. 14. Find IAB.

A B

10cm

15 cm

IAB =11004.56cm4

100mm

12mm

125mm

25mm

12mm

Y

X

70mm

30mm 30mm

100mm

50mm

B

4 cm

10 cm

4 cm

A

6 cm

IAB = 3078.86 cm4

3.00m

1m

120° 120°

R = 2m

X X

IXX = 28.51 mm4

IYY = 23.757 mm4

100mm 100mm 145mm 145mm 10mm

16mm 14mm

572mm

14mm

15. Find IAB. 16.Find Ixx & Iyy 17. Find Ixx & Iyy 18. Find Ixx & Iyy Find M.I. of plane lamina about axis AB.

4.5 cm

12 cm

24 cm

IAB = 12581.48 cm4

4 cm 4 cm 4 cm

2 cm A

B

IAB = 498.3cm4

10 cm

10 cm

13 cm

4 cm 4 cm

IAB = 3299 cm4

50 mm

φ 25mm

φ 50mm

IXX = 6.55 x 105 mm4

IYY = 3.95 x 105 mm4

250mm

250mm

250mm

250mm

R = 750mm

IXX = IYY = 1.043 x 1011 mm4

R2 = 80mm

R1 = 40mm

X

Y

IXX = 3.0159 x 106 mm4

IYY = 7.037 x 106 mm4

19. 20. Find IAB 21. Find IAB 22. Two equal channels are kept as shown

In figure at a distance 'd' between them, to form the cross section of a column. Find the value of the distance 'd' if the centroidal moments of inertia IX and IY of the cross section are equal.

[ d = 77.41 mm ] 23. Find P.M.I about centroidal axis. 24.Find P.M.I about points 1 & 2.

D = 4 cm

R = 4 cm

A B

IAB = 429.29cm4

R = 8 cm

R= 16 cm

R = 8 cm

IAB = 25736 cm4

A B

35 mm R = 70mm

70mm 80mm 65mm

IAB = 401.4 x 106 mm4

A

B 40mm

45 mm 45 mm

18 mm 18 mm

18 mm

18 mm 18 mm

18 mm

72 mm 72 mm

o

d

X

144 mm

4 cm

4 cm

8 cm

6 cm 6 cm 12 cm

2 cm

Izz = 5308 cm4

2

1

r

Izz 1 = 2.35 r 4 Izz 2 = 1.02 r 4