University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2023
Views:

491

Pages:

1
Author:

slypery5hy

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 105. I x = 0.166 × 106 mm 4 , I y = 0.453 × 106 mm 4 and I xy < 0 Given: Note: A review of a table of rolled-steel shapes reveals that the given values of I x and I y are obtained when the 102 mm leg of the angle is parallel to the x axis. For I xy < 0 the angle must be oriented as shown. (a) Now I ave = 1 1 I x + I y = ( 0.166 + 0.453) × 106 mm 4 2 2 ( ) = 0.3095 × 106 mm 4 I min = I ave − R Now R = I ave − I min or R = ( 0.3095 − 0.051) × 106 mm 4 Then = 0.2585 × 106 mm 4 2  Ix − I y  R = + I xy  2    2 From I xy = ( ) 2 2  2  0.166 − 0.453   6 4 − 0.2585 ( )    × 10 mm 2     I xy = ±0.21501 × 106 mm 4 Since (b) I xy < 0, I xy = −0.21501 × 106 mm 4 or I xy = −0.215 × 106 mm 4  −2 ( −0.21501)  2θ m = tan −1   = −56.28°  0.166 − 0.453  or θ m = −28.1° clockwise (c) I max = I ave + R = ( 0.3095 + 0.2585 ) × 106 mm 4 or I max = 0.568 × 106 mm 4

COSMOS Chapter 9 Solution 105

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