15-2.Moment of inertia of area（13〜24）
13
Cross-sectional area A
π*（a*b-c*d） =
a=
b=
c=
d=
Moment of inertia of area I
（a
3
*b-c
3
*d）*π/4 =
Moment of inertia Z=I/e
π*（a
3
*b-c
3
*d）／(4*a) =
Moment of inertia of area k
2
=I/A
（a
3
*b-c
3
*d）／(4*（a*b-c*d）) =
14
Cross-sectional area A
b
2
*h
2
-2*b
1
*h
1
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（b
2
*h
2
3
-2*b
1
*h
1
3
）/12 =
Moment of inertia Z=I/e
（b
2
*h
2
3
-2*b
1
*h
1
3
） ／(6*h
2
) =
Moment of inertia of area k
2
=I/A
（b
2
*h
2
3
-2*b
1
*h
1
3
） ／(12*（b
2
*h
2
-2*b
1
*h
1
）)
=
15
Cross-sectional area A
b
2
*h
2
-b
1
*h
1
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（b
2
*h
2
3
-b
1
*h
1
3
）/12 =
Moment of inertia Z=I/e
（b
2
*h
2
3
-b
1
*h
1
3
） ／(6*h
2
) =
Moment of inertia of area k
2
=I/A
（b
2
*h
2
3
-b
1
*h
1
3
） ／(12*（b
2
*h
2
-b
1
*h
1
）) =
16
Cross-sectional area A
b
2
*h
2
-b
1
*h
1
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（b
2
*h
2
3
-b
1
*h
1
3
）/12
=
Moment of inertia Z=I/e
（b
2
*h
2
3
-b
1
*h
1
3
） ／(6*h
2
)
=
Moment of inertia of area k
2
=I/A
（b
2
*h
2
3
-b
1
*h
1
3
） ／(12*（b
2
*h
2
-b
1
*h
1
）)
=
17
Cross-sectional area A
2*b
1
*h
1
+b
2
*h
2
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（2*b
1
*h
1
3
+b
2
*h
2
3
）/12
=
Moment of inertia Z=I/e
（2*b
1
*h
1
3
+b
2
*h
2
3
） ／(6*h
2
)
=
Moment of inertia of area k
2
=I/A
（2*b
1
*h
1
3
+b
2
*h
2
3
） ／(12*（2*b
1
*h
1
+b
2
*h
2
))
=
18
Cross-sectional area A
b
1
*h
1
+2*b
2
*h
2
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（b
1
*h
1
3
+2*b
2
*h
2
3
）/12
=
Moment of inertia Z=I/e
（b
1
*h
1
3
+2*b
2
*h
2
3
） ／(6*h
2
)
=
Moment of inertia of area k
2
=I/A
（b
1
*h
1
3
+2*b
2
*h
2
3
） ／(12*（b
1
*h
1
+2*b
2
*h
2
))
=
19
Cross-sectional area A
b
1
*h
1
+b
2
*h
2
=
b1=
b2=
h1=
h2=
Moment of inertia of area I
（b
1
*h
1
3
+b
2
*h
2
3
）/12 =
Moment of inertia Z=I/e
（b
1
*h
1
3
+b
2
*h
2
3
） ／(6*h
2
) =
Moment of inertia of area k
2
=I/A
（b
1
*h
1
3
+b
2
*h
2
3
） ／(12*（b
1
*h
1
+b
2
*h
2
))
=
20
Cross-sectional areaA
b
1
*h
1
+b
2
*h
2
=
b1=
b2=
b3=
h1=
h2=
h3=
Moment of inertia of area I
（b
3
*e
2
3
-b
1
*h
3
3
+b
2
*e
1
3
）/3
=
Moment of inertia Z=I/e
Moment of inertia of area k
2
=I/A
e
2
=（b
1
*h
1
2
+b
2
*h
2
2
）／(2*（b
1
*h
1
+b
2
*h
2
）)
=
Z
2
=I/e
2
=
e
1
=h
2
-e
2
=
Z
1
=I/e
1
=
k
2
=(b
3
*e
2
3
-b
1
*h
3
3
+ b
2
*e
1
3
)/(3*(b
1
*h
1
+b
2
*h
2
))
=
21
Cross-sectional area A
b
1
*h
1
+2*b
2
*h
2
=
b1=
b2=
b3=
h1=
h2=
h3=
Moment of inertia of area I
（b
3
*e
2
3
-b
1
*h
3
3
+2*b
2
*e
1
3
)/3
=
Moment of inertia Z=I/e
Moment of inertia of area k
2
=I/A
e
2
=（b
1
*h
1
2
+2*b
2
*h
2
2
)／(2*（b
1
*h
1
+2*b
2
*h
2
))
=
Z
2
=I/e
2
=
e
1
=h
2
-e
2
=
Z
1
=I/e
1
=
k
2
=(b
3
*e
2
3
-b
1
*h
3
3
+ 2*b
2
*e
1
3
)/(3*(b
1
*h
1
+2*b
2
*h
2
))
=
22
Cross-sectional area A
2*b
1
*h
1
+b
2
*h
2
=
b1=
b2=
b3=
h1=
h2=
h3=
Moment of inertia of area I
（b
3
*e
2
3
-2*b
1
*h
3
3
+b
2
*e
1
3
）/3
=
Moment of inertia Z=I/e
Moment of inertia of area k
2
=I/A
e
2
=（2*b
1
*h
1
2
+b
2
*h
2
2
）／(2*（2*b
1
*h
1
+b
2
*h
2
))
=
Z
2
=I/e
2
=
e
1
=h
2
-e
2
=
Z
1
=I/e
1
=
k
2
=(b
3
*e
2
3
-2*b
1
*h
3
3
+b
2
*e
1
3
)/(3*(2*b
1
*h
1
+b
2
*h
2
))
=
23
Cross-sectional area A
2*b
1
*h
1
+b
2
*h
2
+2*b
3
*h
3
=
b1=
b2=
b3=
b4=
b5=
h1=
h2=
h3=
h4=
h5=
Moment of inertia of area I
（b
4
*e
1
3
-2*b
1
*h
5
3
+b
5
*e
2
3
-2*b
3
*h
4
3
）/3
=
Moment of inertia Z=I/e
Moment of inertia of area k
2
=I/A
e
2
=[b
2
*h
2
2
+2*b
3
*h
3
2
+2*b
1
*h
1
*（2*h
2
-h
1
)] /(2*（2*b
1
*h
1
+b
2
*h
2
+2*b
3
*h
3
）)
=
Z
2
=I/e
2
=
e
1
=h
2
-e
2
=
Z
1
=I/e
1
=
24
Cross-sectional area A
b
1
*h
1
+b
2
*h
2
+b
3
*h
3
=
b1=
b2=
b3=
b4=
b5=
h1=
h2=
h3=
h4=
h5=
Moment of inertia of area I
（b
4
e
1
3
-b
1
*h
5
3
+b
5
*e
2
3
-b
3
*h
4
3
)/3
=
Moment of inertia Z=I/e
Moment of inertia of area k
2
=I/A
e
2
=[b
2
*h
2
2
+b
3
*h
3
2
+b
1
*h
1
*(2*h
2
-h
1
)] /(2*(b
1
*h
1
+b
2
*h
2
+b
3
*h
3
)) =
Z
2
=I/e
2
=
e
1
=h
2
-e
2
=
Z
1
=I/e
1
=
Reference: "Machine Design Handbook for Engineers" (Revised version by Saburo Kano) Applied Structural Mechanics Beams and Pillars, page 133 Refer to A, I, Z, k of various cross sections.