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
A a b 2 2
2
12
y
@
12 7 6
2 + − h
^
y
a
cos a t a at t 2 − + − h
2
a
2
A I
t (2 a
− t )
ab a b − ^ h
y I
−
2 2 ^
45
°
t
t
in which b = ( a − t )
a
y
t
c t
t b a t ab c b t 12 2 2 3 3 + − − − ^ ^ h h 6 @
3 − − ^ h
3 − − ^ h
ab c b t 12 2 3
b ab c b t 6 2 3
b 2
t [ b + 2( a − t )]
b
d
a
t
t
a
a t b a c c d a cd 6 2 2 6 3 3 2 − + − − ^ ^ h h
t b a t b a c c d a cd 12 2 2 6 3 3 2 + − + − − ^ ^ h h 6 @
b a c c d a cd 12 2 6 3 3 2 + − − ^ h
2 −
a t 2
t [ b + 2( a − t )]
y a
c
d
b
t
td s b t td s b t 12 3 3 + − + − ^ ^ h h 6 @
s
d
td s b t 12 3 3 + − ^ h
d td s b t 6 3 3 − − ^ h
d 2
dt + s ( b − t )
y
b
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