3 UGA LTE 1:25 PM a uga.view.usg.edu PZ) A frame is made up of three straight me

Question

3 UGA LTE 1:25 PM a uga.view.usg.edu PZ) A frame is made up of three straight members AR BC and DCE. A welght W-500 iD is hung from the palley m E by a rope which goes around the pulley and is attached to member BC at ins midpoint G There are esternal pins at A and D. There are internal pins at Cand E The size o the palley is not known and not neglgible Al is 2 ft long, BCis 1.5 ft long and DCE is 35 long Determine the couple moment f chat needs to be applied on AB to maintain equi brium is the position shown 075075 2ft

Explanation / Answer

Force on member BC at point G, RG = Tension force on rope = W = 500 Ib

Horizontal component of RG = RG,x = RG cos 50o = W cos 50o = 500 x 0.643 = 321.5 Ib

Vertical component of RG = RG,y = RG sin 50o = W sin 50o = 500 x 0.766 = 383 Ib

Considering free body diagram of member BGC,( as there is zero force in the member GC due to balancing forces of RE and RD in opposite directions and no force generation at point C)

RB,x = 321.5 Ib

RB,y = 383 Ib

Considering the forces and moment on the member AB and considering the equillibrium of the point A,

MA = 0

RB,x x 2 sin 60o - RB,y x 2 cos 60o - M = 0

or M = 321.5 x 2 x 0.866 - 383 x 2 x 0.5

or M = 173.838 Ib-ft

The couple moment to be applied = 173.838 Ib-ft

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