CHAPTER XIV. 

 STRESSES IN TWO-HINGED ARCH. 



Introduction. A two-hinged arch is a frame-work or beam with 

 hinged ends which has inclined reactions for vertical loads. The bot- 

 tom chords of two-hinged arches are usually cambered, however, a 

 simple truss becomes a two-hinged arch if the ends are fixed to the 

 abutments so that deformation in the direction of the length of the 

 truss is prevented. 



The horizontal components of the reactions may be supplied either 

 by the abutments or by a tie connecting the hinges. In the latter case 

 the deformation of the tie must be considered in determining the hori- 

 zontal reactions. Two-hinged arches are statically indeterminate struc- 

 tures and their design is subject to the same uncertainties as continuous 

 and swing bridges. 



Two-hinged roof arches are rigid and economical, but have been 

 used to a very limited extent on account of the difficulties experienced 

 in their design. The methods outlined in this chapter are quite simple 

 in principle, although they necessarily require quite extended calcula- 

 tions. Two-hinged roof arches with open framework, only, will be 

 considered in this chapter. 



CALCULATION OF STRESSES. The vertical reactions in a 

 two-hinged arch are the same as in a simple truss or a three-hinged arch 

 having the same loads and span. The horizontal reactions, however, de- 

 pend upon the deformation of the framework and cannot be determined 

 by simple statics alone. Before the deformations can be calculated, the 

 sizes of the members must be known, and conversely, before the sizes 



