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Centroid

Also known as the center of gravity or center of mass if you’re dealing with a 3-D object.The centroid is a point where you could suspend a body with a string and the body would not have a tendency to rotate.The symbol for the centroid isFor areas that have symmetry around an axis, the centroid is located on that axis.

Centroid of an Area

For areas that don’t have symmetry the location of the centroid can be calculated by dividing the area up into simple geometric shapes. The location of the centroid has coordinates of X and Y.

For a triangle the centroid is located closer to the base.

h

h/3

h = height of triangle

XY

= A1 A2

A3

Centroid of an Area

A1

A2

A3

1X

1Y

2X

3X

2Y

3Y

i

ii

A

xAX

*

i

ii

A

yAY

*

321

332211 ***

AAA

xAxAxAX

321

332211 ***

AAA

yAyAyAY

or

Centroid of an Area

  

60

T Shape ExampleAll dimensions in mm

20 20

40

A1

A2

302 y701 y

Verify the results of the T shape example using MDSolids

Centroid of an Area

Section Area, mm2 yi, mm Ai* yi, mm3

A1 20*80=1600 70 112,000

A2 40*60=2400 30 72,000

   4000 iA 000,184 ii yAmmY

Y

A

yAY

i

ii

46

000,4

000,184

*

Centroid of an Area