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

2024
Views:

312

Pages:

2
Author:

Nossardisd7p

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 81. From Problem 9.73, I xy = 138.24 × 106 mm 4 I x = ( I x )1 + ( I x )2 ( I x )1 = ( I x )2 4 π = 2  (120 mm )  8  = 51.84π × 106 mm 4 ( )1 + ( I y )2 ( I y )1 = ( I y )2 Iy = Iy π 4 2 2 π = 2  (120 mm ) + (120 mm ) ( 60 mm )  2 8  = 103.68π × 106 mm 4 ( ) = 2 ( 51.84π × 10 ) = 103.68π × 10 Have I x = 2 25.92π × 106 = 51.84π × 106 mm 4 and Iy Then 1 I x + I y = 77.76π × 106 mm 4 2 and 6 ( ) 1 I x − I y = −25.92π × 106 mm 4 2 ( ) 6 mm 4 COSMOS: Complete Online Solutions Manual Organization System Now, from Equations 9.18, 9.19, and 9.20 Equation 9.18: I x′ = 1 1 Ix + I y + I x − I y cos 2θ − I xy sin 2θ 2 2 ( ) ( ) = 77.76π × 106 − 25.92π × 106 cos ( −60° ) − 138.24 × 106 sin ( −60° )  mm 4 = 323.29 × 106 mm 4 or I x = 323 × 106 mm 4 Equation 9.19: I y′ = 1 1 Ix + I y − I x − I y cos 2θ + I xy sin 2θ 2 2 ( ) ( ) = 77.76π × 106 + 25.92π × 106 cos ( −60° ) + 138.24 × 106 sin ( −60° )  mm 4 = 165.29 × 106 mm 4 or I y′ = 165.29 × 106 mm 4 Equation 9.20: I x′y′ = 1 I x − I y sin 2θ + I xy cos 2θ 2 ( ) =  −25.92π × 106 sin ( −60° ) + 138.24 × 106 cos ( −60° )  mm 4 = 139.64 × 106 mm 4 or I x′y′ = 139.6 × 104 mm 4