115_Problem CHAPTER 9

115_Problem CHAPTER 9 - PROBLEM 9.97 For the quarter...

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PROBLEM 9.97 For the quarter ellipse of Problem 9.67, use Mohr’s circle to determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. SOLUTION From Problem 9.79: 44 82 xy I aI a π == Problem 9.67: 4 1 2 xy I a = The Mohr’s circle is defined by the diameter XY , where 4 4 11 , and 2 2 Xa a Ya a ππ    Now () 4 ave 0.98175 22 8 2 I II a a a =+ = + = and 2 24 4 4 1 8 2 2 x y RI I I a a a 
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