Statics: Calculate the reactions

Two children are swinging from 12-ft long jungle gym that weighs 50-lbs. Child C weighs 70-lbs and the child at D weighs 60-lbs. Calculate the reactions for the pin at A and the roller at B.

Solution

↻+ (clockwise positive)

↻+ΣM_A = 0

70lb (4ft) + 50lb (8ft) + 60lb (9ft) - By(12ft) = 0

By = 101.667 lb

B = 101.667 lb 

↻+ΣM_B = 0

Ax(0) + Ay(12) - 70(8) - 50(4) - 60(3) = 0

Ay = 78.333 lb

A = 78.333 lb

Checking;

 ↑+ΣFy = 0

78.333 - 70 - 50 - 60 + 101.667 = 0
0 = 0