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122_Problem CHAPTER 9 - PROBLEM 9.101 Using Mohr's circle...

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PROBLEM 9.101 Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.74 SOLUTION From Problems 9.74 and 9.83 6 4 6 4 6 4 0.166 10 mm , 0.453 10 mm , 0.1596 10 mm x y xy I I I = × = × = − × Define points ( ) ( ) 6 4 6 4 0.166, 0.1596 10 mm and 0.453, 0.1596 10 mm X Y × × Now ( ) ( ) 6 4 ave 1 1 0.166 0.453 10 mm 2 2 x y I I I = + = + × 6 4 0.3095 10 mm = × and ( ) ( ) 2 2 6 2 2 6 0.166 0.453 10 0.1596 10 2 2 x y xy I I R I = + = + × 6 4 0.21463 10 mm = × Also ( ) 1 1 2 2 0.1596 2 tan tan 48.04
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