Machinery's Handbook, 31st Edition
MOMENTS OF INERTIA AND OTHER FORMULAS 241 Formulas for Moments of Inertia, Section Moduli, etc.— On the following pages are given formulas for moments of inertia and other properties of forty-two different cross sections. The formulas give the area of the section A , and the distance y from the neu- tral axis to the extreme fiber, for each example. Where the formulas for the section modulus and radius of gyration are very lengthy, the formula for the section modulus, for example, has been simply given as I y ' . The radius of gyration is sometimes given as I A ' to save space. Moments of Inertia, Section Moduli, and Radii of Gyration
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
a
3
a 12 4
a
a
. 0289 =
a
y
6
12
a
A = a 2 y = a ∕ 2
a
y
4
a
a
3
a
. 0577 =
a
3
3
3
a
A = a 2 y = a
a
a 12 4
3
a
a
. 0289 =
a
3
. 0118
a
y
=
12
6 2
a
A = a 2
. 2 0707 = =
y a
a
a
a b b
4 4 −
4 4 −
a b 12
a a b 6
a b +
2 2
y
12
. 0289
a b +
2 2
=
A = a 2 − b 2 y = a ∕ 2
a
a a b a 12 4 4 −
. 2 0118 ^
4 4 −
h
a b 12
a b +
2 2
b
12
y b
4 4
a b −
. 0289
a
a b +
2 2
=
=
A a b 2 2 = −
y a 2 =
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