CHAPTER XIII. 

 STRESSES IN THREE-HINGED ARCH. 



Introduction. An arch is a structure in which the reactions are 

 inclined for vertical loads. Arches are divided, according to the num- 

 ber of hinges, into three-hinged arches, two-hinged arches, one-hinged 

 arches, and arches without hinges or continuous arches. Three-hinged 

 arches are in common use for exposition buildings, train sheds and other 

 similar structures. Two-hinged arches are rarely used in this country ; 

 continuous arches are used only in dome construction. 



A three-hinged arch is made up of two simple beams or trusses. 

 Trussed three-hinged arches, only, will be considered in this chapter, 

 and trussed two-hinged arches in the next. 



CALCULATION OF STRESSES. The reactions for a three- 

 hinged arch can be calculated by means of simple statics with slightly 

 more work than that necessary to obtain the reactions in simple trusses. 

 Having determined the reactions the stresses may be calculated by the 

 ordinary algebraic and graphic methods used in the solution of the 

 stresses in simple roof trusses. 



Calculation of Reactions: Algebraic Method. Let H and V> 

 H l and F 1 be the horizontal and vertical reactions at the left and right 

 supports for a concentrated load P, placed at a distance x from the 

 center hinge C in the three-hinged arch in Fig. 65, 



From the three fundamental equations of equilibrium 



2 horizontal components of forces = o (a) 



2 vertical components of forces = o (b) 



S moments of forces about any point = O (c) 



