Question

400 1000 mm 2) Bar AB in the figure is supported by cables BC and BD and a ball socket support at A. Cable BC is parallel to the Z axis, while cable BD is parallel to the X axis. The 200-N weight of the bar acts at its midpoint. What are the tensions in the cables and the reactions at A 600 mm 600 A Check Answer: Tension in Cable BD equals 166.7 N -200j (N) 2

Answer 1

sigma F_x = A_x - T_BD = 0 sigma F_y = A_y - 200N = 0 rightarrow A_y = 200 N. sigma F_z = A_z - T_BC = 0 sigma M_A = (500 i^cap + 300 j^cap + 200 k^cap) times (-200 j^cap) + (R_B/A) times (-T_BD i^cap - T_BC k^cap) = 0 R_B/A = 1000 i + 600 j + 400 k mm sigma M_A = 4000 i^cap - 10000 k^cap - 600 T_BC i^cap + (1000 T_BC - 400 T_BD) j^cap + 600 T_BD k^cap = 0 T_BC = 40000/600 = 66.667 N T_BD = 100000/600 = 166.667 N A_x = T_BD = 166.667 N A_z = T_BC = 66.667 N.