122_Problem CHAPTER 9 - PROBLEM 9.101 Using Mohr's circle determine for the area indicated the orientation of the principal centroidal axes and the

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Unformatted text preview: 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 I x = 0.166 106 mm 4 , I y = 0.453 106 mm 4 , I xy = -0.1596 106 mm 4 Define points Now X ( 0.166, -0.1596 ) 106 mm 4 I ave = and Y ( 0.453, -0.1596 ) 106 mm 4 1 1 I x + I y = ( 0.166 + 0.453) 106 mm 4 2 2 ( ) = 0.3095 106 mm 4 and R= Ix - I y 2 + I xy = 2 2 ( 0.166 - 0.453)106 6 + -0.1596 10 2 2 ( ) 2 = 0.21463 106 mm 4 Also -2 I xy 2 m = tan -1 Ix - I y -2 ( -0.1596 ) = tan -1 = -48.04 0.166 - 0.453 m = -24.02 or = -24.0 clockwise Then I max, min = I ave R = ( 0.3095 0.21463) 106 mm 4 or I max = 0.524 106 mm 4 and I min = 0.0949 106 mm 4 Note: From the Mohr's circle it is seen that the a axis corresponds to I min and the b axis corresponds to I max . ...
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