Centroid s

Few tips to use the software

1 Always enter the Area as per the formula

Ex Rectangle = Length x Breadth

Triangle = ½ x Length x Breadth

Circle =

Semi Circle =

Quadrant =

2 Always enter the Centroidal Value as per the formula

Ex x y

Rectangle

Triangle

Circle = Centre of Circle and Hence Zero

Semi-Circle =

Quadrant =

If the Centroid of the Sub-divided Figure is lying on the Symetrical axis, then the cetroidal value is zero

2Diameter

4

2Diameter

8

2Diameter

16

LengthFrom Side

3

Breadth

2y

Length

2x

2From Vertex Length

3

4From Diameter

3

R

From the Edge of Circle R

4From Diameter

3

R

If the Centroid of the Sub-divided Figure is lying on the Symetrical axis, then the cetroidal value is zero

S.No Component x (mm) y (mm) ax

1 Rectangle-1 1,200.00 65.00

2 Rectangle-2 600.00 30.00

Sum 1,800.00 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

78,000.00

18,000.00

96,000.00

53.33 mm


1 Rectangle-1 800.00 69.00

2 Rectangle-2 400.00 44.00

3 Rectangle-3 600.00 12.00

Sum 1,800.00 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

55,200.00

17,600.00

7,200.00

80,000.00

44.44 mm


1 Rectangle-1 2,000.00 130.00

2 Rectangle-2 2,000.00 70.00

3 Rectangle-3 3,000.00 10.00

Sum 7,000.00 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

260,000.00

140,000.00

30,000.00

430,000.00

61.43 mm


1 Rectangle-1 720.00 30.00 144.00 21,600.00

2 Rectangle-2 1,280.00 5.00 74.00 6,400.00

3 Rectangle-3 750.00 37.50 5.00 28,125.00

Sum 2,750.00 56,125.00

20.41 mm

Area (mm2)

axx

a

ay

ya

ay

103,680.00

94,720.00

3,750.00

202,150.00

73.51 mm


1 Rectangle-1 15,000.00 25.00 150.00 375,000.00

2 Rectangle-2 22,500.00 125.00 75.00 2,812,500.00

3 Rectangle-3 20,000.00 250.00 100.00 5,000,000.00

Sum 57,500.00 8,187,500.00

142.39 mm

Area (mm2)

axx

a

ay

ya

ay

2,250,000.00

1,687,500.00

2,000,000.00

5,937,500.00

103.26 mm

1

2 3

x

y

10015050All dimensions in mm

300200

150


1 Triangle-1 3,200.00 53.33 26.67 170,666.67

2 Quadrant-2 5,026.55 113.95 33.95 572,790.53

Sum 8,226.55 743,457.19

90.37 mm

Area (mm2)

axx

a

ay

ya

ay

85,333.33

170,666.67

256,000.00

31.12 mm


1 Rectangle-1 27.00 3.00 2.25 81.00

2 Triangle-2 6.75 7.00 1.50 47.25

3 Semicircle-3 7.95 -0.95 2.25 -7.59

Sum 41.70 120.66

2.89 mm

Area (mm2)

axx

a

ay

ya

ay

60.75

10.13

17.89

88.77

2.13 mm


1 Rectangle-1 40,000.00 100.00 100.00 4,000,000.00

2 Triangle-2 -3,750.00 150.00 183.33 -562,500.00

3 Quadrant-3 -17,671.46 63.66 2.25 -1,125,000.00

Sum 18,578.54 2,312,500.00

124.47 mm

Area (mm2)

axx

a

ay

ya

ay

4,000,000.00

-687,500.00

-39,760.78

3,272,739.22

176.16 mm


1 Triangle-1 900.00 20.00 40.00 18,000.00

2 Quadrant-2 2,827.43 55.46 34.54 156,823.00

Sum 3,727.43 174,823.00

46.90 mm

Area (mm2)

axx

a

ay

ya

ay

36,000.00

97,646.00

133,646.00

35.85 mm


1 Rectangle-1 1,200,000.00 600.00 500.00 720,000,000.00

2 Triangle-2 -200,000.00 1,066.67 333.33 -213,333,333.33

3 Semicircle-3 -251,327.41 400.00 169.77 -100,530,964.91

Sum 748,672.59 406,135,701.75

542.47 mm

Area (mm2)

axx

a

ay

ya

ay

600,000,000.00

-66,666,666.67

-42,666,666.67

490,666,666.67

655.38 mm


1 Triangle-1 6.00 1.33 2.00 8.00

2 Rectangle-2 15.00 3.00 3.75 45.00

3 Triangle-3 10.00 5.33 2.67 53.33

4 Rectangle-4 5.00 6.50 0.50 32.50

Sum 36.00 138.83

3.86 mm

Area (mm2)

axx

a

ay

ya

ay

12.00

56.25

26.67

2.50

97.42

2.71 mm

1

2

3

4

y

x1m

1m

4m2m2m

5m

1.5m


1 Rectangle-1 200,000.00 200.00 250.00 40,000,000.00

2 Semicircle-2 62,831.85 200.00 584.88 12,566,370.61

3 Circle-3 -1,963.50 175.00 200.00 -343,611.70

Sum 260,868.36 52,222,758.92

200.19 mm

Area (mm2)

axx

a

ay

ya

ay

50,000,000.00

36,749,259.87

-392,699.08

86,356,560.79

331.04 mm

500

400

200

150

200

50

All dimensions in mm


1 Rectangle-1 12,800.00 40.00

2 Semicircle-2 -1,413.72 67.27

3 Triangle-3 -400.00 16.67

Sum 10,986.28 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

512,000.00

-95,097.34

-6,666.67

410,236.00

37.34 mm


1 Rectangle-1 90.00 5.00 4.50 450.00

2 Triangle-2 9.00 11.00 7.00 99.00

3 Semicircle-3 -6.28 2.00 8.15 -12.57

4 Quadrant-4 -7.07 8.73 1.27 -61.69

Sum 85.65 474.75

5.54 mm

Area (mm2)

axx

a

ay

ya

ay

405.00

63.00

-51.22

-9.00

407.78

4.76 mm


1 Rectangle-1 9,600.00 80.00 30.00 768,000.00

2 Semicircle-2 -628.32 20.00 51.51 -12,566.37

3 Triangle-3 -400.00 146.67 53.33 -58,666.67

4 Rectangle-4 -1,600.00 80.00 20.00 -128,000.00

Sum 6,971.68 568,766.96

81.58 mm

Area (mm2)

axx

a

ay

ya

ay

288,000.00

-32,365.78

-21,333.33

-32,000.00

202,300.89

29.02 mm


1 Rectangle-1 12,000.00 60.00 50.00 720,000.00

2 Triangle-2 3,600.00 40.00 120.00 144,000.00

3 Semicircle-3 3,926.99 141.22 50.00 554,572.23

4 Circle-4 -1,256.64 60.00 50.00 -75,398.22

Sum 18,270.35 1,343,174.01

73.52 mm

Area (mm2)

axx

a

ay

ya

ay

600,000.00

432,000.00

196,349.54

-62,831.85

1,165,517.69

63.79 mm


1 Rectangle-1 900.00 -15.00 15.00 -13,500.00

2 Quadrant-2 706.86 12.73 12.73 9,000.00

3 Quadrant-3 -706.86 -17.27 17.27 12,205.75

Sum 900.00 7,705.75

8.56 mm

Area (mm2)

axx

a

ay

ya

ay

13,500.00

9,000.00

-12,205.75

10,294.25

11.44 mm


1 Rectangle-1 30,000.00 100.00 75.00 3,000,000.00

2 Triangle-2 -3,750.00 166.67 125.00 -625,000.00

3 Circle-3 -7,853.98 90.48 67.86 -710,598.34

Sum 18,396.02 1,664,401.66

90.48 mm

Area (mm2)

SOLVE-X

axx

a

ay

ya

ay

2,250,000.00

-468,750.00

-532,948.75

1,248,301.25

67.86 mm

SOLVE-Y


1 Rectangle-1 1,000.00 315.00

2 Rectangle-2 3,000.00 160.00

3 Rectangle-3 2,000.00 5.00

4 Rectangle-4 2,000.00 315.00

Sum 8,000.00 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

315,000.00

480,000.00

10,000.00

630,000.00

1,435,000.00

179.38 mm


1 Triangle-1 19,200.00 160.00

2 Semicircle-2 -2,513.27 223.02

3 Rectangle-3 -2,400.00 140.00

4 Circle-4 -1,256.64 60.00

Sum 13,030.09 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

3,072,000.00

-560,519.12

-336,000.00

-75,398.22

2,100,082.65

161.17 mm


1 Triangle-1 1,500.00 33.33 20.00 50,000.00

2 Rectangle-2 12,000.00 150.00 30.00 1,800,000.00

3 Triangle-3 8,000.00 150.00 86.67 1,200,000.00

4 Semicircle-2 -3,926.99 150.00 21.22 -589,048.62

5 Quadrant-5 2,827.43 275.46 25.46 778,858.35

Sum 20,400.44 3,239,809.72

158.81 mm

Area (mm2)

axx

a

ay

ya

ay

30,000.00

360,000.00

693,333.33

-83,333.33

72,000.00

1,072,000.00

52.55 mm


1 Rectangle-1 80.00 -4.00 5.00 -320.00

2 Semicircle-2 39.27 -10.12 5.00 -397.49

3 Triangle-3 9.00 -4.00 -1.00 -36.00

4 Quadrant-5 -3.14 -0.85 0.85 2.67

5 Circle -3.14 -8.00 5.00 25.13

Sum 121.99 -725.69

-5.95 mm

Area (mm2)

axx

a

ay

ya

ay

400.00

196.35

-9.00

-2.67

-15.71

568.97

4.66 mm


1 Rectangle-1 2,500.00 82.50

2 Rectangle-2 1,400.00 35.00

Sum 3,900.00 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

206,250.00

49,000.00

255,250.00

65.45 mm


1 Rectangle-1 160,000.00 200.00 200.00 32,000,000.00

2 Triangle-2 -45,000.00 300.00 300.00 -13,500,000.00

3 Quadrant-3 -70,685.83 127.32 127.32 -9,000,000.00

Sum 44,314.17 9,500,000.00

214.38 mm

Area (mm2)

axx

a

ay

ya

ay

32,000,000.00

-13,500,000.00

-9,000,000.00

9,500,000.00

214.38 mm


1 Quadrant-1 31,415.93 84.88 84.88 2,666,666.67

2 Semicircle-2 -15,707.96 100.00 42.44 -1,570,796.33

Sum 15,707.96 1,095,870.34

69.77 mm

Area (mm2)

axx

a

ay

ya

ay

2,666,666.67

-666,666.67

2,000,000.00

127.32 mm


1 Rectangle-1 432.00 12.00 9.00 5,184.00

2 Triangle-2 -54.00 20.00 15.00 -1,080.00

3 Circle-3 -113.10 10.86 8.14 -1,227.91

Sum 264.90 2,876.09

10.86 mm0.00

Area (mm2)

SOLVE-X

axx

a

ay

ya

ay

3,888.00

-810.00

-920.94

2,157.06

8.14 mm0.00

SOLVE-Y

Solve-x

Page 60

103.5714293

Solve-y

Page 61

15.32394351


1 Semicircle-1 62,831.85 200.00 84.88 12,566,370.61

2 Semicircle-2 251,327.41 400.00 -169.77 100,530,964.91

3 Semicircle-3 -62,831.85 600.00 -84.88 -37,699,111.84

Sum 251,327.41 75,398,223.69

300.00 mm

Area (mm2)

axx

a

ay

ya

ay

5,333,333.33

-42,666,666.67

5,333,333.33

-32,000,000.00

-127.32 mm

a= 10 mm


1 Rectangle-1 3,200.00 40.00 20.00 128,000.00

2 Triangle-2 450.00 20.00 50.00 9,000.00

3 Triangle-3 750.00 46.67 50.00 35,000.00

4 Semicircle-4 -628.32 40.00 8.49 -25,132.74

Sum 3,771.68 146,867.26

38.94 mm

Area (mm2)

axx

a

ay

ya

ay

64,000.00

22,500.00

37,500.00

-5,333.33

118,666.67

31.46 mm


1 Rectangle-1 3,280.00 41.00 20.00 134,480.00

2 Semicircle-2 -628.32 27.00 31.51 -16,964.60

3 Rectangle-3 -455.00 64.50 6.50 -29,347.50

Sum 2,196.68 88,167.90

40.14 mm

Area (mm2)

axx

a

ay

ya

ay

65,600.00

-19,799.41

-2,957.50

42,843.09

19.50 mm


1 Triangle-1 3,600.00 40.00 120.00 144,000.00

2 Semicircle-2 3,926.99 141.22 50.00 554,572.23

3 Rectangle-3 12,000.00 60.00 50.00 720,000.00

4 Circle-4 -1,256.64 60.00 50.00 -75,398.22

Sum 18,270.35 1,343,174.01

73.52 mm

Area (mm2)

axx

a

ay

ya

ay

432,000.00

196,349.54

600,000.00

-62,831.85

1,165,517.69

63.79 mm


1 Rectangle-1 16.00 2.00 2.00 32.00

2 Triangle-2 8.00 5.33 1.33 42.67

3 Semi Circle-3 12.57 6.85 2.85 86.06

Sum 36.57 160.73

4.40 mm

Area (mm2)

axx

a

ay

ya

ay

32.00

10.67

35.80

78.47

2.15 mm

4m

4m

8mx

y

C1

C2

C3


1 Rect-1 12,000.00 60.00 50.00 720,000.00

2 Tria-2 3,000.00 140.00 33.33 420,000.00

3 Rect-3 -800.00 120.00 40.00 -96,000.00

4 Semicircle-4 -1,413.72 60.00 12.73 -84,823.00

Sum 12,786.28 959,177.00

75.02 mm

Area (mm2)

axx

a

ay

ya

ay

600,000.00

100,000.00

-32,000.00

-18,000.00

650,000.00

50.84 mm

100

120

40

40

20

30 30 3020 20

50

20

a 92.0144913556


1 Rect-1 12,882.03 46.01 592,666.66

2 Rect-2 -11,041.74 46.01 -508,000.00

3 Semi-Circle-3 7,696.90 -29.71 -228,666.67

4 Semi-Circle-4 -5,654.87 -25.46 144,000.00

Sum 3,882.33 0.00

0.00 mm

Area (mm2)

axx

a

ay

ya

ay

0.00

0.00 mm

60mm

a

a

10mm

10mm

y

xO

Fig. Q4(c)


1 Quad-1 7,853.98 42.44 42.44 333,333.33

2 Semi-Circle-2 -3,926.99 50.00 21.22 -196,349.54

3

4

Sum 3,926.99 136,983.79

34.88 mm

Area (mm2)

axx

a

ay

ya

ay

333,333.33

-83,333.33

250,000.00

63.66 mm

O 100mm


1 Rect-1 600.00 15.00 10.00 9,000.00

2 Semi-Circle-2 -39.27 15.00 17.88 -589.05

3 Quad-3 -50.27 26.60 3.40 -1,337.30

4

Sum 510.46 7,073.65

13.86 mm

Area (mm2)

axx

a

ay

ya

ay

6,000.00

-702.06

-170.67

5,127.27

10.04 mm

100mm


1 Rect-1 600.00 -125.00 6.00 -75,000.00

2 Rect-2 1,500.00 -106.00 74.50 -159,000.00

3 Rect-3 600.00 125.00 131.00 75,000.00

4 Semi-Circle-4 19,704.07 0.00 184.53

5 Semi-Circle-5 -15,707.96 0.00 179.44

Sum 6,696.11 -159,000.00

-23.75 mm

Area (mm2)

axx

a

ay

ya

ay

3,600.00

111,750.00

78,600.00

3,636,076.14

-2,818,657.63

1,011,368.50

151.04 mm

S.No Name of Fig

Area Ordinatesax

a x

mm

1 Rect-1 50000 125 6250000

2 Triangle 12000 40 480000

3 Semi Circle -15708 42.44132 -666667

46292 6063333

6063333130.9801 mm

46292

mm2 mm3

Area ax

Y

250mm

r=100mm

0x

y

X

120mm

S.No Name of Fig

Area Centroidal Ordinatesax ay

a x y

mm mm

1 Tri-1 20000 -66.6667 33.33333 -1E+006 666667

2 Tri-2 20000 33.33333 -66.6667 666667 -1E+006

3 Quad-3 31415.93 -84.8826 -84.8826 -3E+006 -3E+006

4 Rect-4 10000 50 50 500000 500000

3 Quad-5 -15708 57.55868 57.55868 -904130 -904130

65708 -4E+006 -4E+006

-4E+006-56.8799 mm

65708-4E+006

-56.8799 mm65708

mm2 mm3 mm3

Area ax ay

3

y

x

O

r=100mm

r=200mm

X

Y

1

23

5

4

S.No Name of Fig

Area Centroidal Ordinatesax ay

a x y

mm mm

1 Rect-1 10000 100 25 1000000 250000

2 Tri-2 2500 133.3333 66.66667 333333 166667

3 Semi-Cir-3 3926.991 50 -21.22066 196350 -83333.3

4 Circ-4 -1963.5 150 25 -294524 -49087.4

14463.5 1235159 284246

123515985.39834 mm

14463.5284246

19.65265 mm14463.5

mm2 mm3 mm3

Area ax ay 100mm

50mm

y

x

100mm

R=50mm

r=25mm50m

m

Quadrant 4

Rectangle

Triangle

Semicircle

Quadrant

and 2 2

b dx y

x

y

x

y

and 3 3

b dx y

x

y

x

y

4 4 and

3 3

R Rx y

x

x

y

4 and

3

Rx R y

x

y

x

y

x

y

Date post:	11-Apr-2016
Category:	Documents
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Centroid s

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