COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 190.
First note that
A = A1 − A2 − A3
= (100 mm )(120 mm ) − ( 80 mm )( 40 mm )
− ( 80 mm )( 20 mm )
= (12 000 − 3200 − 1600)mm 2 = 7200 mm 2
( )1 − ( I y )2 − ( I y )3
Iy = Iy
Now
where
( I y )1 = 121 (120 mm )(100 mm )3 = 10 × 106 mm 4
( I y )2 = 121 ( 40 mm )(80 mm )3 = 1.7067 × 106 mm 4
( I y )3 = 121 ( 20 mm )(80 mm )3 = 0.8533 × 106 mm 4
Then
I y = (10 − 1.7067 − 0.8533) × 106 mm 4 = 7.44 × 10 mm
or I y = 7.44 × 106 mm 4
And
k y2 =
Iy
A
=
7.44 × 106 mm 4
= 1033.33 mm 2
7200 mm 2
k = 32.14550 mm
or k y = 32.1 mm
COSMOS Chapter 9 Solution 190
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