Question

The rig shown consists of a 1200-lb horizontal member ABC and a vertical member DBE welded together at B. The rig is being used to raise a 3600-lb crate at a distance x-12 ft from the vertical member DBE. If the tension in the cable is 4 kips, determine the reaction at E, assuming that the cable is (a) anchored at F as shown in the figure, (b) attached to the vertical member at a point located 1 ft above E.

Answer 1

Draw the free body diagram of the structure 3.75 ft 17.5 ft 5 ft 3.75 ft 6.5 ft 3600 lb 10 ft Irrespective of the attachment of the cable, the external force acting on the structure applies only at point C, which only must be considered at the point of free body diagram. The tension in the cable is, T 4 kips - 4000 11b Calculate the horizontal reaction at point E. Apply the equilibrium equation along x direction.

Calculate the vertical reaction at point E. Apply the equilibrium equation along y direction. E, 3600-W -T 0 E, 3600-1200- 4000 0 E,-8800 Ib(t) Calculate the moment at point E. take the moment about the point E. +(3600 Ib)(x)+(W) (6.5 ft) (T) (3.75 ft)-ME-0 +(3600 1b (12 ft) (1200 1b) (6.5 ft)-4000 1b (3.75 ft)-ME 0 Mr 432007800 15000 -36000 1b ft ME 36 kip ft(clock-wise) Draw the free body diagram of the structure 6.5 ft 3600 lb

As soon as the cable is attached to the structure, the tension acting in the cable becomes an internal force, and there is no need to consider it in the free body diagram. Calculate the horizontal reaction at point E. Apply the equilibrium equation along x direction. Calculate the vertical reaction at point E. Apply the equilibrium equatiorn along y direction. E, 3600-W0 E, 3600-1200 0 E, 4800 1b() Calculate the moment at point E. take the moment about the point E. (3600 1b)(x)+(W) (65 ft)-ME 0 (3600 1b (12 f) (1200 1b) (6.5 ft)-ME 0 ME 43200 7800 MF 51000 1b ft ME 51 kip ft(clock-wise)