10–21.
Determine the moment of inertia for the shaded area about
the x axis.
SOLUTION
1
y
x
2 m
2 m
y2 2x
y x
10–22.
Determine the moment of inertia for the shaded area about
the y axis.
SOLUTION
1
7
y
x
2 m
2 m
y2 2x
y x
10–23.
Determine the moment of inertia for the shaded area about
the x axis.
SOLUTION
a
1
a
35
b
x
y
a
y2 —x
b2
a
y — x2
b
a2
*10–24.
Determine the moment of inertia for the shaded area about
the y axis.
SOLUTION
b
b
35
b
x
y
a
y2 —x
b2
a
y — x2
b
a2
10–25.
Determine the moment of inertia of the composite area
about the xaxis.
SOLUTION
y
6 in.
3 in.
3 in.
10–26.
Determine
the moment of inertia of the composite area
about the
yaxis.
SOLUTION
Composite
Parts: The composite area can be subdivided into three segments as
y
6 in.
3 in.
3 in.
10–27.
The polar moment of inertia for the area is
JC
= 642 (106) mm4, about the z
′
axis passing through the
centroid C. The moment of inertia about the y
′
axis is
264 (106) mm4, and the moment of inertia about the x axis is
938 (106) mm4. Determine the area A.
SOLUTION
y
200 mm
Cx
¿
¿
*10–28.
50 mm
x
–
y
50 mm
250 mm
Determine the location of the centroid of the channel’s
cross-sectional area and then calculate the moment of
inertia of the area about this axis.
y
SOLUTION
10–29.
Determine
y
, which locates the centroidal axis
x′
for the
cross-sectional area of the T-beam, and then find the
moments of inertia
Ix′
and
I
y
′
.
SOLUTION
x′
75 mm
x¿
y¿
C
75 mm
20 mm
y
10–30.
Determine the moment of inertia for the beam’s cross-
sectional area about the x axis.
SOLUTION
8 in.
y
x
10 in.
3 in.
1 in.
1 in.
1 in.
SOLUTION
10–31.
Determine the moment of inertia for the beam’s cross-
sectional area about the y axis.
8 in.
y
x
10 in.
3 in.
1 in.
1 in.
1 in.
SOLUTION
*10–32.
Determine the moment of inertia Ix of the shaded area
about the x axis.
Ox
150 mm
150 mm
100 mm 100 mm
75 mm
150 mm
y
SOLUTION
10–33.
Determine the moment of inertia Ix of the shaded area
about the x axis.
Ox
150 mm
150 mm
100 mm 100 mm
75 mm
150 mm
y
10–34.
y
50 mm
150 mm
150 mm
Determine
the moment of inertia of the beam’s cross-
sectional area about the
yaxis.
SOLUTION
M
oment of Inertia: The dimensions and location of centroid of each segment are
moment of inertia about
yaxis for each segment is simply
(Iy)i=(Iy¿)i.
10–35.
Determine which locates the centroidal axis for the
cross–sectional area of the T-beam, and then find the
moment of inertia about the x¿ axis.
x
¿
y
,
SOLUTION
=206.818 mm
y=
©yA
©A=125(250)(50) +(275)(50)(300)
250(50) +50(300)
C
y
x¿
y
x¿
250 mm
50 mm
150 mm
150 mm
SOLUTION
*10–36.
Determine the moment of inertia about the x axis.
150 mm
150 mm
y
x
C
200 mm
200 mm
20 mm
20 mm
10–37.
Determine the moment of inertia about the y axis.
SOLUTION
150 mm
150 mm
y
x
C
200 mm
200 mm
20 mm
20 mm
SOLUTION
10–38.
Determine the moment of inertia of the shaded area about
the x axis.
x
6 in.
3 in.
6 in.
y
6 in.
SOLUTION
10–39.
Determine the moment of inertia of the shaded area about
the y axis.
x
6 in.
3 in.
6 in.
y
6 in.
SOLUTION
*10–40.
Determine the distance
y
to the centroid of the beam’s
cross-sectional area; then find the moment of inertia about
the centroidal
x′
axis.
y
x
3 in. 1 in.
1 in.
4 in.
1 in.
y¿
x ¿
C
y
3 in.