12G 



LECTURE 



sustain three loads instead of a siugle one, we shall have a structure 



such as Figure 45. 



If the number of loads 

 is very great, or, what is 

 the same thing, if the load 

 is distributed over the 

 whole span, we shall have 

 the framing in the form 

 of a polygon of a great 

 number of sides, or an 

 arch, as in Figure 46. 

 Since the pieces com- 



Fig. 45. 



posing such a framing or arch are small, and are only subjected to a 



force of compression, they may 

 be economically made of stone 

 or of cast iron. 



In Figure 44, by a well-known 

 principle of mechanics, the 

 amount of thrust^ or tendency to 

 separate the abutments, com- 

 pared with the weight supported, 

 (W,) maybe readily determined, 



and it will be found to increase with the nearer approach of the 



l?rV 



Fig. 46. 



Fig. 47. 



oblique pieces to the horizontal position, so that a framing, like 



■ Fig. 48. 



Figure 47, or an arch, like Figure 48, will exert a greater thrust 



than either Figure 44 or Figure 

 46, when loaded with the same 

 weight. The distance, A B, is 

 termed the rise of the arch, C D, 

 the span, and upon their relative 

 values the thrust of the arch will 

 depend. In a semi-circular arch, 

 Figure 49, no thrust is exerted at 

 its very lowest points, A and B ; it 

 Fig. 49, does not become sensible until we 



