COSMOS Chapter 9 Solution 79 | Answer Key - Edubirdie

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

2019
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313

Pages:

1
Author:

behend6abs

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 79. π Ix = From Figure 9.12: ( 2a )( a )3 16 π = 8 a4 π Iy = 16 = π 2 ( 2a )3 ( a ) a4 I xy = From Problem 9.67: 1 4 a 2 1 1 π π  5 I x + I y =  a4 + a4  = π a4 2 2 8 2  16 ( First note ) 1 1π π  3 I x − I y =  a4 − a4  = − π a4 2 2 8 2  16 ( ) Now use Equations (9.18), (9.19), and (9.20). Equation (9.18): I x′ = = Equation (9.19): I y′ = = Equation (9.20): I x′y′ = 1 1 Ix + I y + I x − I y cos 2θ − I xy sin 2θ 2 2 ( ) ( ) 5 3 1 π a 4 − π a 4 cos 2θ − a 4 sin 2θ 16 16 2 1 1 Ix + I y − I x − I y cos 2θ + I xy sin 2θ 2 2 ( ) ( ) 5 3 1 π a 4 + π a 4 cos 2θ + a 4 sin 2θ 16 16 2 1 I x − I y sin 2θ + I xy cos 2θ 2 =− ( ) 3 1 π a 4 sin 2θ + a 4 cos 2θ 16 2

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