Lesson 18 – Centroid for
Composite Bodies
Learning Objectives
 Describe composite bodies.
 Calculate the centroid of composite bodies.
1
Composite Bodies (5/4)
 For irregular shaped bodies, we can divide the
body into smaller more convenient parts and
treat each part as a finite part of the whole.
 The centroid of the whole body X Y E
is the weighted average of all the finitebodies
.
In In Z
 mx
X
m
 my
Y 
m
 mz
Z
m
 Like before, similar relations hold for
composite lines, areas, and volumes, where
the m’s are replaced by L’s, A’s, or V’s.
 See Table D/3 for common shape centroids!
2
Example 1 (Problem 5/6 in Textbook)
Locate the centroid of the shaded area.
A
sxc
1
No
no
11in
lol
18in
1
lin
Shape Arealina
x̅
1
180
9
5
IA
JA
5 1620 900
2
30
16
6.667
3
8
12
4
4
4.5m
6
127.9
480 200
96
32
84.82
18
959.2 650
x̅.EE
95t4
7.50i
Ef
E Y
9
5.08in
3
Example 2
Locate the centroid of the shape.
I
LV
free
1
x̅
Za
Din
Y
18
6.21in
S
sa
112
258
0506
ft it.sn
30
20120144
29
0
180
4
Locate the centroid of the shape.
I_reference point
Q
9 V
4
s
x̅
E 0in
Y
5.21in
1
sEsn
1120
250
sa
0.50
6
ftp.f
545
0110132
29
0
151
5