COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 117.
Mass = m = ρV = ρ tA
m
I mass = ρ tI area = I area
A
1
A = bh
2
(a)
Axis AA′:
Axis BB′:
1 b 3
1 3
I AA′, area = 2 h =
hb
12
2
48
m
m 1 3
1
I AA′, mass = I AA′, area =
mb 2
⋅ hb =
1
A
48
24
bh
2
1
mb 2
24
I BB′ =
1
mh 2
18
1 3
bh
36
m
m 1 3
1
mh 2
= I BB′, area =
⋅ bh =
1
A
36
18
bh
2
I BB′, area =
I BB′, mass
(b)
I AA′ =
Axis CC′:
Eq. (9.38):
I CC ′ = I AA′ + I BB′
1
1
=
mb 2 +
mh 2
24
18
I CC ′ =
m
3b 2 + 4h 2
72
(
)