Transcript Centroid - r. Heck

Forging new generations of engineers
Centroid
Centroid of an Area
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 is
For areas that have symmetry around an axis, the centroid is
located on that axis.
Centroid of an Area
For a triangle the centroid is located closer to the base.
h = height of triangle
h
h/3
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.
A3
=
X
Y
A1
A2
Centroid of an Area
A *y

Y
A
A3
i
X3
i
A1
i
A *x

X 
A
i
i
i
Y3
X2
A2
X1
Y1
Y2
or
A1 * x1  A2 * x 2  A3 * x3
X
A1  A2  A3
A1 * y1  A2 * y 2  A3 * y 3
Y
A1  A2  A3
Centroid of an Area
T Shape Example
All dimensions in mm
20
40
20
A1
A2
60
y1  70
y 2  30
Verify the results of the T shape example using MDSolids
Centroid of an Area
Section
A1
A2
Area, mm2
20*80=1600
40*60=2400
 A  4000
i
yi, mm
Ai* yi, mm3
70
112,000
30
72,000
A y
i
A *y

Y
A
i
i
184,000
Y
4,000
Y  46m m
i
 184,000
i