136_Problem CHAPTER 9

136_Problem CHAPTER 9 - PROBLEM 9.112 Using the invariance...

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PROBLEM 9.112 Using the invariance property established in the preceding problem, express the product of inertia xy I of an area A with respect to a pair of rectangular axes through O in terms of the moments of inertia x I and y I of A and the principal moments of inertia min I and max I of A about O . Use the formula obtained to calculate the product of inertia xy I of the 76 × 51 × 6.4-mm angle cross section shown in Fig. 9.13B knowing that its maximum moment of inertia is 34 524 10 mm . × SOLUTION ( a ) ( b ) From Problem 9.111 have, constant xy x y II I ′′ −= Now consider the following two cases Case 1 : , x yx y x y I I ′′′ == = Case 2 :
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