COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 189.
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
I x = ( I x )1 − ( I x )2 − ( I x )3
Now
where
Then
( I x )1 =
1
(100 mm )(120 mm )3 = 14.4 × 106 mm 4
12
( I x )2
=
1
(80 mm )( 40 mm )3 + 3200 mm 2 ( 40 mm )2 = 5.5467 × 106 mm4
12
( I x )3
=
1
(80 mm )( 20 mm )2 + 1600 mm 2 ( 30 mm )2 = 1.4933 × 106 mm 4
12
(
(
)
)
I x = (14.4 − 5.5467 − 1.4933) × 106 mm 4 = 7.36 × 106 mm 4
or I x = 7.36 × 106 mm 4
and
k x2 =
Ix
7.36 × 106
=
= 1022.2 mm 2
A
7200
or k x = 32.0 mm