136 



STRESSES IN TWO-HINGED ARCH 



truss with a horizontal thrust, H 1 , of 20000 Ibs. as shown in (c). The 

 quantities for calculating the deformations of the simple truss with 

 vertical loads are given in Table VII, and the deformation diagram 

 is shown in (fr) Fig. 72. The quantities for calculating the deforma- 

 tions of the simple truss With a horizontal thrust of 20000, Ibs. are given 

 in Table VIII, and the deformation diagram is shown in (c) Fig. 72. 

 The true value of H is found by the proportion 



H : 20000 : : .956 : .574 

 H = 33400 Ibs. 



The stress diagram for the two-hinged arch with V = V = 42000 

 Ibs., and H H 33400 Ibs. is shown in (b) Fig. 73. 



The difference in the stresses in the members of a simple truss 

 and a two-hinged arch may be seen by comparing stress diagram (b) 

 Fig. 71, and stress diagram (b) Fig. 73, both diagrams being drawn 



o' 10' ao' 30' 



20000 40000 



Two Hinged Arch 

 (a) 



FIG. 73. 



Stress Diagram 



Two Hinged Arch 



(b) 



to the same scale. The stresses in the arch may be found from the 

 stresses given in Tables VII and VIII by adding the stresses in column 

 4, Table VII, to the corresponding stresses in column 4, 

 Table VIII, multiplied by 1.67, the ratio between the actual and as- 



