Moments of Inertia, Section Moduli, and Radii of Gyration (Continued)
Radius of Gyration, k A I =
Section Modulus, Z y I =
Distance from Neutral Axis to Extreme Fiber, y
Area of Section, A
Moment of Inertia, I
Section
R r 3 3
. 4 0424 3
R r
y I
A I
h
π − − ^ ^
2 2
R r
4 4
. 01098 0283 .
R r −
h
π − ^
h
^
y
2 2
. 2 15708 ^
h
r R
2 2
R r R r R r + − ^
h
2 2 3 3
R r R r − −
2 2
R r −
−
h
=
=
y
a
a 2
. 4 07854 3
. 4 07854 2
π ab = 3.1416 ab
a
a b π =
a b π =
a b 3
a b 2
b
b
d
y
π ( ab − cd ) = 3.1416( ab − cd )
. 4 07854 3
a a b c d a 3 3 −
π −
h
π − ^
2 1
. 4 07854 3 ^
a b c d 3
a
ab cd a b c d 3 3 − −
h
3
3
a b c d −
a b c d 3
h
^
=
a c
=
I-Sections
s d
bd h b t sb ht 2 3 3 − − + ^ h
b
b 2
2 3
3 +
2 3
3 +
bd − h ( b − t )
sb ht 12
b sb ht 6
y
12
@
6
t d
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