Question

Homework Problem 1

"4m Determine the components of reaction at the ball-and-socket joint A and the tension in each cable necessary for equilibrium of the rod. 150 N/m A R om 400m

Answer 1

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Ans: shoun The FBD for the given problem has been attached below: eco, -4,6) Az D(0, 4, 6) Te ACO,0,0) То, AX Ay 450N B (12,0,0) 400N 6 Os - Since Xoads cables CB and DB are located symmetrically about point A, the tensions in both these cables will be same. Te = To The cable can be written in vector form Co=4-12, 4, 67 The cable DB be written in vector form as, DB =*-12, 4,67. The Tension in cable et can be given as, Teo= IC K12, tv, Te 1-127 -4 9 +6ky 3 = Tc (-4,-4/3,2) The Tension in cable DB can be given as, can - TOB = To ( 229 + 4 + 62 3 = To (-4,4/3,2 - For equilibrium of moment about y-arts, EMy =0 = 450x4 +400x6- T, X2 = TGX 2=0 - 4 T = 4200 = T = 1050 N and T = 105oN ( : Te =To)

for x-axis equilibrium of point A, Ax + Tel Tc/ 3)+1065 =) Ax-4 Te-4 Tao =) Ax = 8 Te = (8400N For y-axis equilibrium of point A Ay + Te (3) + To (4) => Ay =ON - for 2-axis equilibrium at point 2, A₂ - 450-400 + Te X2 + TDX2=0 =) A-850+ 4x 1050=0 =) Az N (downwards) 41=0 --3350 N