COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 93.
From Problems 9.73 and 9.81
I xy = 138.24 × 106 mm 4
I x = 51.84π × 106 mm 4
= 162.86 × 106 mm 4
I y = 103.68π × 106 mm 4
= 325.72 × 106 mm 4
I ave =
Now
1
Ix + I y
2
(
)
= 244.29 × 106 mm 4
2
R=
Ix − I y
2
+ I xy
2
= 160.4405 × 106 mm 4
2θ m = 59.5°
From Problem 9.87
Then
Then
α = 180 − 60° − 2θ m = 60.5°
I x′ = I ave + R cos α = ( 244.29 + 160.4405cos 60.5° ) × 106
= 323.29 × 106 mm 4
or I x′ = 323 × 106 mm 4
I y′ = I ave − R cos α = ( 244.24 − 160.4405cos 60.5° ) × 106
= 165.29 × 106 mm 4
or I y′ = 165.3 × 106 mm 4
I x′y′ = R sin α = 160.44 × 106 sin 60.5° = 139.6 × 106 mm 4
COSMOS Chapter 9 Solution 93
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