COSMOS Chapter 9 Solution 83 | Michigan State University - Edubirdie

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

2020
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2
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crawniadxfo

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 83. From Problem 9.74 I xy = −0.1596 × 106 mm 4 From Figure 9.13 I x = 0.166 × 106 mm 4 I y = 0.453 × 106 mm 4 1 I x + I y = 0.3095 × 106 mm 4 2 ( Now ) 1 I x − I y = −0.1435 × 106 mm 4 2 ( ) Using Equations (9.18), (9.19), and (9.20) Equation (9.18): I x′ = Ix + I y 2 + Ix − I y 2 ( cos 2θ − I xy sin 2θ ) ( ) = 0.3095 × 106 + −0.1435 × 106 cos ( −90° ) − −0.1596 × 106 sin ( −90° )  mm 4   = 0.1499 × 106 mm 4 or I x′ = 0.1499 × 106 mm 4 COSMOS: Complete Online Solutions Manual Organization System Equation (9.19): I y′ = Ix + I y 2 − Ix − I y cos 2θ + I xy sin 2θ 2 ( ) ( ) = 0.3095 × 106 − −0.1435 × 106 cos ( −90° ) + −0.1596 × 106 sin ( −90° )  mm 4   = 0.4691 × 106 mm 4 or I y′ = 0.469 × 106 mm 4 Equation (9.20): I x′y′ = Ix − I y 2 sin 2θ + I xy cos 2θ =  −0.1435 × 106 sin ( −90° ) + 0.1596 × 106 cos ( −90° )  mm 4 = 0.1435 × 106 mm 4 or I x′y′ = 0.1435 × 106 mm 4

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