9 o 



STATICS. 



[If*- 



As there are only three forces, viz. the weight Wand the reactions A 

 and B, their lines must intersect in a point E. Resolving horizontally 



and vertically, we have 



A sin a = B sin /?, 



W 



W. 



whence A= 



sin a 



sin( 



Taking moments about D, we find 

 with AD = a, DB = b, 



W 



Fig. 41. 



A - a sin DAE = B 

 or ^ cos( + 0) = Bb cos(/J - 0) ; 

 to eliminate A and B, divide by the first equation above : 



sn 

 solving for 0, we finally obtain 



sn 



151. Exercises. 



(1) A homogeneous rod yl#=2/=8ft., weighing W=2Q Ibs., 

 rests with one end A on a horizontal plane AH, and with the point E 

 on a support whose height above AH is Z^ = h = 3 ft. A horizontal 

 cord AD = d = 4 ft. holds the rod in equilibrium. Find the tension T 

 of this cord, and the reactions at A and E. 



(2) A weightless rod AB of length / can turn freely about one end A 

 in a vertical plane. A weight W is suspended from a point C of the 

 rod ; A C = c. A string BD attached to the end B of the rod holds it 

 in equilibrium in a horizontal position, the angle ABD being = 150. 

 Find the tension T of the string and the resulting pressure A on the 

 hinge at A. 



