Question

(1) Determine the moments of inertia and radius of gyration of the shaded area with respect to the x and y axes. (All dimensions are in inches). -2.0000 - 2.0000 9XX 2.0000 1.0000 1.0000 1.0000 1.0000 5.0000

Answer 1

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nd the moment of Inertia about & and y are seen by I calculating moment of calculati Inertia of whole Recrangle of 5000 x 6000 and substract 2 Recrangles mot from it. -- 1xx - bd) 500lerode I 20000 2000 x 7 @ Ixx © - 4000X20004 4000% 20000 *(1000x1000) 12 200 12 60000 1000 = 8. 4667x10# 1000 100 12 12 12 12 40000 1000ốt 4000oricool x Croocol 5000) = 0.933x107 in Ixx = 9x107 _ 3-4667x107 0.933x10'7 = 4.6003x10 7 unit", now Buy = 60000 X 50000 2000% 40000 - 10000X 600,000 (Dyy = 4.65x10't nao Area of Shaded portion = 50,800 x 60,000 - (40,000x 20000) - looo x 410000) A - 18x108) A = Radius of guyration 8xx = ax = (4.606841 ? V 18x168 | 6x = S186 2636 = I = (4.68x1d7 18x108 Vyy = 16072.7512