Machinery's Handbook, 31st Edition
242
MOMENTS OF INERTIA AND OTHER FORMULAS Moments of Inertia, Section Moduli, and Radii of Gyration Moments of Inertia, Section Moduli, and Radii of Gyration (Continued)
Section A = area y = distance from axis to extreme fiber
Radius of Gyration k A I =
Section Modulus Z y I =
Moment of Inertia I
Square and Rectangular Sections
d
3
2
d
bd
bd 6
. 0289 =
d
y
12
12
b
A = bd y = d ∕ 2
y
d
d
3
2
bd 3
bd 3
. 0577 =
d
3
b
A = bd y = d
b
b d bd 2 +
b d b d 3 3 + ^ h 2
b d b d 6 2 2 2 2 +
y
2
. 6 0408 ^
h
6 2
d
b d bd 2 +
=
2
A bd y = =
b d bd +
2 2
α
cos 2 2
sin 2 2
d
b
α
+
α
bd d
bd 6
cos α + α ^ sin 2 2 b 2 2
y d
. 12 0289
12
#
=
cos cos 2 2 d
sin α α α sin 2 2 b b + +
d
sin 2 2 #
h
α
b
a
k
cos 2 2
d
b
α
α
+
A = bd
2 ( d cos α + b sin α )
y = 1 ∕
k
d
bd hk 3 −
3
bd hk 12 3 −
3
d bd hk 6 3 −
3
y
12
bd hk −
h
^
b h
. bd hk bd hk 0289 3 3 − −
=
A = bd − hk y = d ∕ 2
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