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 bd g h l 12 1 4 1 3 4 4 − − ^ h : D in which g = slope of flange = ( h − l )/( b − t ) = 10 . 0 ∕ 6 for standard I-beams
Section
n
t
a
d 2
4 1 3 4 4 + + − − ^ ^ h h
12 1
d
h
dt a s n bd g h l 2 :
D
dt + 2 a ( s + n )
d bd g h l 6 1 4
1 3 4 4 − − ^ h : D
y l
b
d 2
d
s h
bd h b t bd h b t 12 3 3 − − − − ^ ^ h h 6 @
bd h b t 12 3 3 − − ^ h
d bd h b t 6 3 3 − − ^ h
t
bd − h ( b − t )
y
b
12 1
b d h lt g b t 3 4 4 − + + − ^ ^ h h 6
3
l
n
b b d h lt g b t 6 1 4 3 3 4 4 − + + − ^ ^ h h 6 @
t
y
b 2
A I
4 @ in which g = slope of flange = ( h − l )/( b − t ) = 1 ∕ 6 for standard I-beams
b
dt + 2 a ( s + n )
a
d h
s
b
s
1 ∕ 3 + ay 3 − ( b − t )( d − y − s ) 3 − ( a − t )( y − s ) 3 ] 3 [ b ( d − y )
d − [ td 2 + s 2 ( b − t ) + s ( a − t )(2 d − s )] ÷ 2 A
d
h
bs + ht + as
y I
A I
t
y
s
a
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