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p4 - Problem Set 4 Problem 4.1 Moment of inertia by...

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Problem Set 4 Problem 4.1 Moment of inertia by integration Determine the moment of inertia of the shaded area about the y -axis. Figure P4.1: Problem 4.1
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Problem 4.2 Moment of inertia of composite cross section Determine ¯ y which locates the centroidal x 0 -axis, for the cross section of the beam, and then find the moments of inertia I x 0 x 0 and I yy . Figure P4.2: Problem 4.2
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Problem 4.3 Determine the moment of inertia about the x -axis of the shaded area shown in Fig. P4.3 where m = h/b and b = h = 1 m. Use integration. y = m x b y x h y = m x b y x h y d y ( b , y ) ( x , y ) Figure P4.3: Problem 4.3
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Problem 4.4 Determine the moments of inertia and the products of inertia about the centrodial axes of the shaded area shown in Fig. P4.4, where a = 1 in. Find the centroid polar moment of inertia. The mass center of the shaded area is at C . C a a a a 3 a x y 1 2 3 Figure P4.4: Problem 4.4 Solution % ICxx = b h^3/12; ICyy = h b^3/12 % upper rectagle 1 A1 = 3*a^2; IC1xx = (3*a)*a^3/12; IC1yy = a*(3*a)^3/12; Ixx1 = IC1xx + (a^2)*A1; Iyy1 = IC1yy + 0*A1; % Ixx1 = (13*a^4)/4 = 3.250 (in^4) % Iyy1 = (9*a^4)/4 = 2.250 (in^4)
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