A crane supports a 1 -kip load as shown. Boom AB extends from a pinned connection on the c...

A crane supports a 1 -kip load as shown. Boom AB extends from a pinned connection on the crane carnage at an angle of 45° from horizontal. Cable CD extends from a sheave near the roof of the cab at an angle of 30° from horizontal. It supports boom AB at point C.

(a) Neatly draw (with a straightedge) the free-body diagram of the boom.

(b) Find the reaction at point A.

(c) Find the tension in cable CD.

moments created by R2 tend to be positive and moments created by the loads tend to be negative:

Note: The 500-lb load is the total uniformly distributed load of 100 lb/ft for 5 ft. Its moment arm is taken at 2.5 ft because that is the center of gravity of the uniformly distributed load.

Summing the vertical forces (Fy) with an upward force assigned a positive (+) value and a downward force given the negative (−) sign yields

Summing the horizontal forces (Fx) with a force acting to the right positive (+) and a force acting to the left assigned a negative (−) sign, since there are no horizontal force vectors on the free-body diagram, we have

The analysis above finds that the reaction R1 equals 575 lb and R2 equals 925 lb.