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

2021
Views:

82

Pages:

1
Author:

salcignofi15

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 88. From Problems 9.75 and 9.82 I x = 0.70134 × 106 mm 4 I y = 7.728 × 106 mm 4 I xy = 1.5732 × 106 mm 4 Then 1 I x + I y = 4.2147 × 106 mm 4 2 ( ) 1 I x − I y = −3.5133 × 106 mm 4 2 ( Equation (9.25): ) tan 2θ = − 2I xy Ix − I y =− ( 2 1.5732 × 106 6 ) 0.70134 × 10 − 7.728 × 106 = 0.44778 Then 2θ m = 24.12° 204.12° and or θ m = 12.06° and 102.1° Also, Equation (9.27): I max, min = Ix + I y 2 2  Ix − I y  2 ±  I  2  xy   = 4.2147 × 106 ± 6 2 × 106 ) 2 = ( 4.2147 ± 3.8494 ) × 106 mm 4 or I max = 8.06 × 106 mm 4 and I min = 0.365 × 106 mm 4 By inspection, the a axis corresponds to I min and the b axis corresponds to I max .

COSMOS Chapter 9 Solution 88

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