34_Problem CHAPTER 9

# 34_Problem CHAPTER 9 - PROBLEM 9.39 The centroidal polar...

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PROBLEM 9.39 The centroidal polar moment of inertia C J of the 3 2 15.5 10 mm × shaded region is 6 4 250 10 mm × . Determine the polar moments of inertia B J and D J of the shaded region knowing that 2 D B J J = and 100 d = mm. SOLUTION Have 2 B C CB J J Ad = + and 2 D C CD J J Ad = + Now 2 D B J J = Then ( ) 2 2 2 C CD C CB J Ad J Ad + = + Now ( ) 2 2 2 2 2 2 and 2 CB CD d a d d a d = + = + Substituting ( ) ( ) 2 2 2 2 4 2 C A a d J A a d + = + + or 2 2 1 2 C J a d A = + ( ) 6 4 2 2 3 2 1 250 10 mm 100 mm 13064.5 mm 2 15.5 10 mm × = + = × or 114.300 mm a = Then ( ) ( ) ( ) 2 2 6 4 3 2 250 10 mm 15.5 10 mm 114.300 mm 100 mm
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