266_Problem CHAPTER 9

266_Problem CHAPTER 9 - PROBLEM 9.181 CONTINUED K 2 : For...

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Unformatted text preview: PROBLEM 9.181 CONTINUED K 2 : For this case, the set of equations to be solved consists of Equations (9.54a), (9.54b), and (9.57). Now - I xy x + I y - K y - I yz z = 0 Substituting for the moments and products of inertia. 1 1 3 - - ma 2 x + ma 2 - K y - - ma 2 z = 0 2 2 2 2 2 or 1 1 3 x + - y + z = 0 2 2 2 2 2 (iv) ( ) (9.54b) Substituting the value of 2 into Eqs.(i) and (iv) 1 13 19 - ( x )2 + y 2 2 12 12 1 3 19 ( x )2 + - y 2 2 2 12 or and Adding yields and then Substituting into Equation (9.57) 0 2 ( )2 - 1 ( z )2 = 0 2 ( )2 + 2 1 2 ( z )2 = 0 - ( x )2 + 1 y 2 ( )2 - ( z )2 = 0 ( x )2 - 2 y 6 ( )2 + ( z )2 = 0 ( y )2 = 0 ( z )2 = - ( x )2 ( x ) 2 + ( y ) 2 + ( - x ) 2 2 2 = 1 2 and =1 =- 1 2 or ( x )2 ( z )2 ( x )2 = 45.0 y ( )2 = 90.0 ( z )2 = 135.0 (c) Principal axes 1 and 3 lie in the vertical plane of symmetry passing through points O and B. Principal axis 2 lies in the xz plane. ...
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