ON BRIDGES. 



127 



Fig. 50. 



reach a point a little 

 higher, C D, and then 

 the arch acts as in Figure 

 46. 



What is known as a 

 bow-string girder, Figure 

 50, is only a cast - iron 

 arch, with a tension rod, and the single iron mass ipay be replaced 

 by bricks, as in Figure 51, 

 while, still further, by tak- 

 ing away the tie rod and 

 substituting the abut- 

 ments, we come again to 

 the familiar form of the 

 arch, as in Figure 48. 



In fact, we may build 

 an arch which has no curved surfaces of any kind, as in Figure 

 52, in which it is evident 



Fig. 51. 



IZZ 



T 



I , I 



Fig. 52. 



we have sacrified nothing 

 of the principle by per- 

 mitting the spaces above 

 and below the dotted lines 

 to be filled up by the 

 projection of the arch 

 stones. 



Since the weight upon 

 an arch acts always vertically downwards, the portion at the croivn 

 or top. A, Figure 

 53, acts with all its T" 



weight in the direc- 

 tion of a radius, A 

 0, of the circle, but 

 the portions of the 

 load towards the 

 haunches, as at B C, 

 only act with a por- 

 tion of their weight 

 in the radial direc- 

 tion B ; and if we 



desire to equalize . " Fig. 53. 



these radial strains, 

 we must increase the weight upon the haunches by loading them 

 with additional material, as at D. Theoretically the upper surface 

 of this loading should have the form shown at E, in order that the 

 forces acting along all the radii should be equal : in practice it is 

 usual to build up to the level of the top, as at F, by which the con- 

 ditions of the problem are nearly fulfilled. Sometimes in large works 

 the roadway over the part E is supported by small arches, the space 

 under them being left open, thereby more nearly conforming to what 

 is required by the theory. 



