Question

Compute the area moments of inertia (Iz and Iy) about the horizontal and vertical centroidal (x and y) axes, respectively, and the centroidal polar area moment of inertia (J-Iz -Iz +Iy) of the cross section of Problem P8.12. Answer: 1x-25.803 in. Ц-167.167 in. and J-192.97 in

Answer 1

Given that we have divided the given composite big into simple figure figure 1 A_1 = 0.5 times 5 = 2.5 in^2 m = 5/2 = 2.5 in y_1 = 0.5/2 = 0.25 in figure 2 A_2 = 0.5 times 3 = 1.5 in^2 x-2 = 4.5 + 0.5/2 = 4.75 in y_2 = 0.5 + 3/ 2 = 2in figure 3 A_3 = 6 times 0.5 = 3 in^2 x_3 = 4.5 + 6/2 = 7.5 in y_3 = 3.5 + 0.5/2 = 3.75 in figure 4 A_4 = 0.5 times 3 = 1.5 in^2 n_4 = w + 0.5/2 = 10.25 y_4 = 2 in figure 5 A_5 = 0.5 times 5 = 2 .5in^2 y_5 = 0.25 in n_1 = 10 + 5/2 = 125 t = A_1 y_1 + A_2 y_2 + A_3 y_3