Determine the moment of inertia of area about the centroidal

Determine the moment of inertia of area about the centroidal axis X (para to the base axis shown) of the composite shape. related to you conceptual equations. Circle your answer with appropriate units.

Solution

the moment of inertia of the solid rectangle about the x axis is = 1/12*l*h^3 =1/12*6*(5)^3 = 62.5 inches^4

and the moment of inertia of the cutout about the x axis is = 1/12*l*h^3 = 1/12*4*(3)^3 = 9 inches^4

=> Moment of inertia about the x axis is = Ix = 62.5 - 9 = 53.5 inches^4

Total area of the composite = A = 2(3*1) + (6*2) = 18 inches^2

and te distance between the x axis and the dottes axis about which we need to find the moment of inertia = d = 5 inches

=> By the parallel axis theorem

I = Ix + Ad^2 = 53.5 + 18*(5)^2 = 503.5 inches^4

hence the moment of inertia of the area is = 503.5 inches^4