Question

A vertical rod is attached at point A to the cast iron hanger shown. The force in the rod is 10 Kips acting downward. Determine (a) the stresses at points C and D, (b) the position of the neutral axis. 1 in. -3 in. (t 0.75 in. 1.5 in. 1.5 in. 3 in. 0.75 in. Section a-a 10 Kips

Please draw the shape with numbers so i can see how you get your numbers. thank you

Answer 1

Consider the cross section and centroid of the hanger: Area of point 1: A_1 = (4 in) (0.15 in) A_1 = 3 in^2 Area of the part 2 A_2 = (1.5 in) (1 in) = 1.5 in^2 Area of the part 3, A_3 = (4 in) (0.75 in) Total area of the cross section A = A_1 + A_2 + A_3 = 3 in^2 + 3 in^2 + 3 in^2 = 7.5 in^2 \r\n (a) centroid axis from the left edge of the section X bar = sigma A X bar/sigma A = (3 times 4/2) + (1.5 times 1/2) + (2 times 2)/7.5 = 1.7 in Distance of the centroid of the total cross section from the neutral axis y bar = A_1y_1 bar + A_2y_2 bar + A_3y_3 bar/A Y bar = (3) (0.75/2) + (1.5) (0.75 + 1.5/2) + 3(2.25 + 0.75/2)/7.5 = 1.5 in I = bd^2/12 + Ay_2 bar = 2((4 times 0.75^3/12) +