35_Problem CHAPTER 9

35_Problem CHAPTER 9 - PROBLEM 9.40 Determine the...

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PROBLEM 9.40 Determine the centroidal polar moment of inertia C J of the 3 2 10 10 mm × shaded area knowing that the polar moments of inertia of the area with respect to points A , B , and D are 6 4 45 10 mm A J = × , 6 4 130 10 mm B J = × , and 6 4 252 10 mm D J = × , respectively. SOLUTION Have 2 2 2 where A C CA CA J J Ad d a = + = Then 2 A C J J Aa = + (1) Have 2 2 2 2 where B C CB CB J J Ad d a d = + = + Then ( ) 2 2 B C J J A a d = + + (2) Have 2 2 2 2 where 4 D C CD CD J J Ad d a d = + = + Then ( ) 2 2 4 D C J J A a d = + + (3) Then Equation (3) Equation(2):
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