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
. tan d 2 3 30 0866 2 2 ° = d
. cos 1 2 30 0104 2 2 3 ° ° + = ^ h cos
2
. cos d 48 30 1 2 30 0264 2 cos 2 ° +
2
cos 1 2 30 006 2 2 ° +
d
A d
A d
h
h
^
^
°
°
;
E
;
E
. d 69 4 30
. cos d 12 4 30 4 =
. cos d d 2 30 0577 ° =
d
y
=
2
( 1 2 22 cos 2 +
)
y
( 1 2 22 cos 2 +
)
A d
2
. d 48 22 1 2 22 0257 2 cos cos 2 1 2 + = °
(
)
2 1
°
d
°
°
A d
2 1
2 1
<
F
<
F
. cos d 12 4 22 0055 2 =
. cos d 6 4 22 0109 2 =
d 2
2 1
°
2 d 2 tan 22 1 ∕
2 ° = 0.828 d 2
°
2 1
d
4
3
Circular, Elliptical, and Circular Arc Sections
. d 32 0098 3 3 π = d
. d 64 0049 4 4 π = d
. d 4 07854 2 2 π = d
d 2
d 4
d
y
. 12 9 64 0132 2 π π − =
d
2
y
h
^
. 6 3 4 0288 π π − = ^ h
d
3
. d 192 3 4 9 64 0024 2 d 3 π π − − = ^ ^ h
. 1152 9 64 0007 2 π π − =
4
d
h
^
. 8 0393 2 d =
π
2
h
d
d
d
4
d
d
4 4
2 2
D d
D d
h
π − ^
h
π − ^
4 4
D 2
D D d
h
π − ^
D d 4 2
2 +
. 4 07854 ^
64
D
d
. 32 0098
y
2 2
4 4
. 0049
D d −
D d −
h
h
^
=
=
D D d 4 −
4
=
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