i26 STRESSES IN THREE-HINGED ARCH 



and equilibrium polygons. The lines of action of P a and P c are par- 

 allel to each other and to the resultant R. The line of action of the 

 right reaction, R 2 , must pass through the center hinge C, and the reac- 

 tion F will be replaced by two reactions R 2 and R^ parallel to R^ 

 and R-i 1 in the arch respectively, and the force triangle will be closed 

 by drawing R in the force polygon. The intersection of force R and 

 reactions R and R 2 falls outside the limit of the diagram. 



Having obtained the reactions, the stresses in the members are 

 calculated in the same manner as in a simple truss. 



The wind load stresses must be calculated in both the windward 

 and leeward segments. The wind load stress diagram for the wind- 

 ward segment is shown in Fig. 68, and for the leeward segment in Fig. 

 69, compression being indicated in the stress diagrams by heavy lines 

 and tension by light lines. Both wind load stress diagrams and the dead 

 load stress diagram are usually constructed for the same segment of the 

 arch. By comparing wind load stress diagrams in Fig. 68 and Fig. 69, 

 it will be seen that there are many reversals in stress. The maximum 

 stresses found by combining the dead, snow and wind load stresses as 

 in the case of simple trusses and transverse bents, are used in designing 

 the members. 



