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100_Problem CHAPTER 9

# 100_Problem CHAPTER 9 - PROBLEM 9.84 Determine the moments...

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PROBLEM 9.84 Determine the moments of inertia and the product of inertia of the L5 × 3 × 1 2 -in. angle cross section of Problem 9.78 with respect to new centroidal axes obtained by rotating the x and y axes through o 30 counterclockwise. SOLUTION From Problem 9.78 4 2.8125 in xy I = From Figure 9.13 4 4 9.45 in , 2.58 in x y I I = = Now ( ) 4 1 6.015 in 2 x y I I + = ( ) 4 1 3.435 in 2 x y I I = Using Equations (9.18), (9.19), and (9.20) Equation (9.18): cos2 sin 2 2 2 x y x y x xy I I I I I I θ θ + = + ( ) ( ) 4 4 6.015 3.435cos 60 2.8125sin 60 in 5.2968 in
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