COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 196.
I xy = −11.0 in 4
From Problem 9.195
Compute I x and I y for area of Problem 9.195
3
Ix =
5 in. × ( 0.5 in.)
12
( 0.5 in.)( 4 in.)3
2
+ 2
+ ( 4 in. × 0.5 in.)(1.0 in.)
12
= 9.38542 in 4
( 0.5 in.)3 ( 4 in.)
0.5 in. × ( 5 in.)3
2
Iy = 2
+ ( 4 in. × 0.5 in.)( 2.75 in.) +
12
12
= 35.54167 in 4
X ( 9.38542, −11) ,
Define points
Now
I ave =
Ix + I y
2
=
R=
Y ( 35.54167, 11)
9.38542 in 4 + 35.54167 in 4
= 22.46354 in 4
2
2
and
and
Ix − I y
+ I xy
2
( )
2
2
=
2
9.38542 − 35.54167
+ (11.0 )
2
= 17.08910 in 4
Also
Then
− 2 ( −11.0 )
2θ m = tan −1
= − 40.067
9.38542 − 35.54167
or θ m = − 20.0° clockwise
I max, min = I ave ± R = 22.46354 ± 17.08910
= 39.55264, 5.37444
Note: The a axis corresponds to I min and b axis corresponds to I max .
or I max = 39.6 in 4
I min = 5.37 in 4
COSMOS Chapter 9 Solution 196
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