1. Centroid & Moment of Inertia of
Composite Figures
Composite Figures – Made of more
than one simple figures

2. Composite Figures Type - I
Centroidal Axes of the elements coincide
with each other and also coincide with
the centroid of the resultant figure

3. Composite Figures Type - II
Centroidal axes of elements are different and do
not coincide with centroid of composite figure

4. Composite Figures Type - I
Y
External Dia = D1;
Internal Dia = D2
IOX = IGX = IOY = IGY
X =
(
π D −D 4
1
4
2 )
64
IOz = IGz =
(
π D −D4
1
4
2 )
32

5. Composite Figures Type - I
Y
BH3 πD 4
IGX = −
12 64
H HB3 πD 4
D IGY = −
X 12 64
BH(H + B ) πD
2 2 4
B IGz = −
12 32

6. Un Symmetric I Section –
Composite Figure – Type - II
3 Y
20 cm
2 cm
2 cm
30 cm
2
4 cm
10 cm X
1

7. Un Symmetric I Section –
Composite Figure – Type - II
Sl. Ai Yi Aiyi Aiyi2 I Self, OX
No (cm2) (cm) (cm3) (cm3) (cm4)
1 40 2 80 160 53.33
2 48 16 768 12288 2304
3 40 29 1160 33640 13.33
∑
128 2008 46088 2370.66

8. Un Symmetric I Section –
Composite Figure – Type - II
Yb =
∑ A y = 2008 = 15.6875cm
i i
∑ A 128 i
IOX = ∑ I + ∑ A y = 48.459 × 10 cm
self i
2
i
3 4
IGX = IOX − AY = 16.958 × 10 cm
2
b
3 4
3 3 3
4(10 ) 24( 2 ) 2( 20 )
IGY = + + = 1682.667cm 4
12 12 12

9. Un Symmetric I Section –
Composite Figure – Type - II
3 Y
20 cm Yb = 15.6875 cm
2 cm
2
2 cm
IGX = 16.958 × 10 cm
3 4
30 cm
IGY = 1.682 × 10 cm
3 4
4 cm
10 cm X
1

10. Angle Section - Composite Figure – Type - II
Y
4 mm Y
Un Symmetric w.r.t both
2 the axes, hence Xb & Yb
is to be found
40 mm G X
6 mm
1
O 20 mm X

11. Angle Section - Composite Figure – Type – II
Calculating Yb, IOX, IGX
Sl. Ai Yi Aiyi Aiyi2 I Self, OX
No (cm2) (cm) (cm3) (cm3) (cm4)
1 120 3 360 1080 360
2 160 26 4160 108160 21333.33
∑ 280 4520 109240 21693.33

12. Angle Section - Composite Figure – Type – II
Calculating Yb, IOX, IGX
Y =
∑ A y = 4520 = 16.143 mm
i i
∑ A 280
b
i
IOX = ∑I + ∑ A y = 130.933 × 10 mm
self ,OX i
2
i
3 4
IGX = IOX − AY = 57.966 × 10 mm
2
b
3 4

13. Angle Section - Composite Figure – Type – II
Calculating Xb, IOY, IGY
Sl. Ai Xi Aixi Aixi2 I Self, OY
No (cm2) (cm) (cm3) (cm3) (cm4)
1 120 10 1200 12000 4000
2 160 2 320 640 213.33
∑ 280 1520 12640 4213.33

14. Angle Section - Composite Figure – Type – II
Calculating Xb, IOY, IGY
X =
∑ A x = 1520 = 5.43 mm
i i
∑ A 280
b
i
IOY = ∑I + ∑ A x = 16.853 × 10 mm
self ,OY i
2
i
3 4
IGY = IOY − AX = 8.597 × 10 mm 2
b
3 4

15. Angle Section - Composite Figure – Type - II
Y
4 mm Y Y = 16.143 mm
b
2 Xb = 5.43 mm
40 mm G X
IGX = 57.966 × 10 mm
3 4
6 mm
1
O 20 mm X IGY = 8.597 × 10 mm
3 4

16. Composite Figure – Type - II
2
10 cm Diameter of the circular
opening = 6 cm
3
20 cm
12 cm
1
10 cm

17. Composite Figure – Type - II
Sl. Ai Yi Aiyi Aiyi2 I Self, OX
No (cm2) (cm) (cm3) (cm3) (cm4)
1 200 10 2000 20000 6666.67
2 50 23.33 1166.67 27218.33 277.78
3 -28.27 12 -339.29 -4071.5 -63.62
221.73 2827.38 43146.83 6880.83

18. Composite Figure – Type – II
Calculating Yb, IOX, IGX
Y =
∑ A y = 2827.38 = 12.75 cm
i i
∑ A 221.73
b
i
I = ∑I
OX + ∑ A y = 50.028 × 10 cm
self ,OX i
2
i
3 4
IGX = IOX − AY = 13.98 × 10 cm
2
b
3 4
20(103 ) 10(53 ) π(6 4 )
IGY = + ×2− = 1.81 × 103 cm 4
12 12 64