CHAPTER 5
PROBLEM 5.1
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Rectangle 72 mm by 45 mm.
Area 2: Triangle b = 27 mm, h = 45 mm.
2
,mmA ,mm
x
,mm
y
3
,mmxA 3
,mmyA
PROBLEM 5.2
Locate the centroid of the plane area shown.
SOLUTION
PROBLEM 5.3
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Rectangle 42 mm by 44 mm.
Area 2: Triangle b = 18 mm, h = 12 mm.
Area 3: Triangle b = 24 mm, h = 12 mm.
PROBLEM 5.4
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Triangle b = 60 mm, h = 75 mm.
Area 2: Four triangles b = 60 mm, h = 75 mm forming the diamond.
PROBLEM 5.5
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Rectangle 6 in. by 4 in.
Area 2: Triangle b = 6 in., h = 3 in.
PROBLEM 5.6
Locate the centroid of the plane area shown.
SOLUTION
PROBLEM 5.7
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Rectangle 16 in. by 8 in.
Area 2: Semicircle radius of 5 in.
PROBLEM 5.8
Locate the centroid of the plane area shown.
SOLUTION
2
,inA
,in.x
,in.y
3
,inxA
3
,inyA
PROBLEM 5.9
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Square 75 mm by 75 mm.
Area 2: Quarter circle radius of 75 mm.
PROBLEM 5.10
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Parabolic Spandrel, refer to fig 5.8A for centroid location.
Area 2: Rectangle 16 in. by 3 in.
2
,in.A ,in.x ,in.y 3
,inxA 3
,inyA
PROBLEM 5.11
Locate the centroid of the plane area shown.
SOLUTION
PROBLEM 5.12
Locate the centroid of the plane area shown.
SOLUTION
Area 1: Outer semicircle diameter 120 mm.
Area 2: Inner semicircle diameter 72 mm.
2
,mmA ,mm
x
,mm
y
3
,mmxA 3
,mmyA
PROBLEM 5.13
Locate the centroid of the plane area shown.
SOLUTION
PROBLEM 5.14
Locate the centroid of the plane area shown.
SOLUTION
First note that symmetry implies 0X
PROBLEM 5.15
Locate the centroid of the plane area shown.
SOLUTION
PROBLEM 5.16
Determine the y coordinate of the centroid of the shaded area
in terms of r
1
, r
2
, and
.
SOLUTION
PROBLEM 5.17
Show that as r
1
approaches r
2
, the location of the centroid
approaches that for an arc of circle of radius
12
()/2.
rr
SOLUTION
First, determine the location of the centroid.
PROBLEM 5.17 (Continued)
Using Figure 5.8B,
Y
of an arc of radius
12
1()
2rris
2
12
2
12
2
sin( )
1()
2()
1cos
()
2()
Yrr
rr
(1)