COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 50.
Data for C 250 × 30:
A = 3780 mm 2
I x = 32.6 × 106 mm 4
I y = 1.14 × 106 mm 4
Dimensions in mm
A = 2 3780 mm 2 + (10 mm )( 375 mm ) = 15.06 × 103 mm 2
Total Area,
3
2
1
I x = 2 32.6 × 106 mm 4 + 2 ( 375 mm )(10 mm ) + ( 375 mm )(10 mm )(132 mm )
12
= 65.2 × 106 mm 4 + 130.74 × 106 mm 4
= 195.94 × 106 mm 4
k x2 =
I x 195.94 × 106 mm 4
=
= 13.01 × 103 mm 2
3
2
A
15.06 × 10 mm
or
I x = 195.9 × 106 mm 4
or
k x = 114.0 mm
2
3
1
I y = 2 1.14 × 106 mm 4 + 3780 mm 2 (115.3 mm ) + 2 (10 mm )( 375 mm )
12
(
)
= 102.783 × 106 mm 4 + 87.891 × 106 mm 4
= 190.674 × 106 mm 4
k y2 =
Iy
A
=
190.674 × 106 mm 4
= 12.661 × 103 mm 2
15.06 × 103 mm 2
or
I y = 190.7 × 106 mm 4
or
k y = 112.5 mm
COSMOS Chapter 9 Solution 50
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