Art. 46. 



REACTIONS FOR A SINGLE FORCE. 



59 



fastened to the tops of columns at 'A and B, in which case it is 

 customary to assume the horizontal components of the reactions 

 equal. This would not give parallel reactions in Fig. 38. 



In Fig. 39, P! is the resultant of the wind loads at the 

 joints of AC and P 2 of the vertical loads at the joints of AC and 



Fig. 39. 



CB. This case may be reduced to that of Fig. 23 by finding 

 the resultant R, of P l and P 2 ; it must pass through D. Now 

 R t , R, and R 2 being in equilibrium, must meet in the point E> 

 This gives the direction of R 1 and the force polygon determines 

 the amounts of R t and R 2 (33) . 



Should any of the intersections be very acute, resort should 

 be had to the string polygon, but the original forces should not 

 be used unless their resultants are not readily located. 



A hinge is a joint about which the parts of a structure are 

 free to turn; it is assumed to be frictionless and, therefore, the 

 moment at its center is zero for a structure in equilibrium. 



Fig. 40 shows a symmetrical three-hinged arch with a 

 single load P on the left half. Considering the right half by 

 itself it is evident that there are but two forces acting upon it, 

 the reaction R 2 and the pressure of the left half through the 

 hinge at C. Since two forces to be in equilibrium must act in 

 the same straight line, the line of R 2 must pass through the 

 center hinge at C. This determines the point D, and since R t 



