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Cgmi3

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Cgmi3

  1. 1. Centroid & Moment of Inertia of Composite Figures Composite Figures – Made of more than one simple figures
  2. 2. Composite Figures Type - ICentroidal Axes of the elements coincide with each other and also coincide with the centroid of the resultant figure
  3. 3. Composite Figures Type - IICentroidal axes of elements are different and donot coincide with centroid of composite figure
  4. 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. 5. Composite Figures Type - I Y BH3 πD 4 IGX = − 12 64H HB3 πD 4 D IGY = − X 12 64 BH(H + B ) πD 2 2 4 B IGz = − 12 32
  6. 6. Un Symmetric I Section – Composite Figure – Type - II 3 Y 20 cm 2 cm 2 cm30 cm 2 4 cm 10 cm X 1
  7. 7. Un Symmetric I Section – Composite Figure – Type - IISl. Ai Yi Aiyi Aiyi2 I Self, OXNo (cm2) (cm) (cm3) (cm3) (cm4)1 40 2 80 160 53.332 48 16 768 12288 23043 40 29 1160 33640 13.33∑ 128 2008 46088 2370.66
  8. 8. Un Symmetric I Section – Composite Figure – Type - IIYb = ∑ A y = 2008 = 15.6875cm i i ∑ A 128 iIOX = ∑ 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. 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 3 430 cm IGY = 1.682 × 10 cm 3 4 4 cm 10 cm X 1
  10. 10. Angle Section - Composite Figure – Type - II Y4 mm Y Un Symmetric w.r.t both 2 the axes, hence Xb & Yb is to be found40 mm G X 6 mm 1 O 20 mm X
  11. 11. Angle Section - Composite Figure – Type – II Calculating Yb, IOX, IGXSl. Ai Yi Aiyi Aiyi2 I Self, OXNo (cm2) (cm) (cm3) (cm3) (cm4)1 120 3 360 1080 3602 160 26 4160 108160 21333.33∑ 280 4520 109240 21693.33
  12. 12. Angle Section - Composite Figure – Type – II Calculating Yb, IOX, IGX Y = ∑ A y = 4520 = 16.143 mm i i ∑ A 280 b iIOX = ∑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. 13. Angle Section - Composite Figure – Type – II Calculating Xb, IOY, IGYSl. Ai Xi Aixi Aixi2 I Self, OYNo (cm2) (cm) (cm3) (cm3) (cm4)1 120 10 1200 12000 40002 160 2 320 640 213.33∑ 280 1520 12640 4213.33
  14. 14. Angle Section - Composite Figure – Type – II Calculating Xb, IOY, IGY X = ∑ A x = 1520 = 5.43 mm i i ∑ A 280 b iIOY = ∑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. 15. Angle Section - Composite Figure – Type - II Y4 mm Y Y = 16.143 mm b 2 Xb = 5.43 mm40 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. 16. Composite Figure – Type - II 210 cm Diameter of the circular opening = 6 cm 3 20 cm 12 cm 1 10 cm
  17. 17. Composite Figure – Type - IISl. Ai Yi Aiyi Aiyi2 I Self, OXNo (cm2) (cm) (cm3) (cm3) (cm4)1 200 10 2000 20000 6666.672 50 23.33 1166.67 27218.33 277.783 -28.27 12 -339.29 -4071.5 -63.62 221.73 2827.38 43146.83 6880.83
  18. 18. Composite Figure – Type – II Calculating Yb, IOX, IGX Y = ∑ A y = 2827.38 = 12.75 cm i i ∑ A 221.73 b iI = ∑IOX + ∑ 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

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