COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 85.
From Problem 9.79:
π
Ix =
8
tan 2θ m = −
=
Then
Iy =
I xy =
Problem 9.67:
Now, Equation (9.25):
a4
π
2
a4
1 4
a
2
2I xy
Ix − I y
=−
π
8
1
2 a4
2
a4 −
π
2
a4
8
= 0.84883
3π
2θ m = 40.326°
and
220.326°
or θ m = 20.2° and 110.2°
Also, Equation (9.27):
I max, min =
=
Ix + I y
2
2
Ix − I y
2
±
+ I xy
2
1π 4 π 4
a + a
2 8
2
2
±
1 π 4 π 4
1 4
a − a + a
2
2
2 8
2
= ( 0.981748 ± 0.772644 ) a 4
or I max = 1.754a 4
and I min = 0.209a 4
By inspection, the a axis corresponds to Imin and the b axis corresponds to
Imax.
COSMOS Chapter 9 Solution 85
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