152 UNIVERSITY OF COLORADO STUDIES 



A calculation like that above for determining the necessary steel, 



might show that the rib was assumed too light, that is, of too small 



a depth. Such a case would require an unreasonable amount of 



metal. On the other hand the original assumed depths of rib might 



have been too large. If the first proportions for the rib are made 



carefully and by the dictates of experience, later only slight changes 



will be necessary in the ring proportions. For the most desirable 



and economic proportions of steel to concrete, the rib may be either 



slightly increased or decreased in depths by moving the extrados. 



n 

 This should be done in such a manner as still to keepr=Y-constant, 



and unless the movement of the extrados is quite small, especially for 

 large arches, the computations for the new proportions of ring should 

 be repeated. Large changes not only greatly affect the rib depths 

 and the dead weights of the rib, but they also essentially change the 

 position of the rib's neutral curve and closing line, and thus also 

 the values of its interscepts. Apparently no definite, proper and 

 economic ratio of steel to concrete section can be fixed at the begin- 

 ning of a computation for any given case. 



In this design, between sections 1 and 18, the ratio of steel 

 section to concrete varies from 0.0109 at the crown to 0.0054 near 

 sections 1 and 18; while between these sections and the springing 

 points, the ratio varies from 0.24 to 0.194. Throughout the main 

 part of the arch, therefore, the ratio of steel section to concrete is 

 1% or less, being only 0.5% at the crown. 



The high percentages near the springing lines of course are due 

 to the great stresses occurring there. Circular-segmental arches, as 

 has already been mentioned, are always weak at the abutments and 

 high tensions and compressions generally occur there. Other forms 

 of intrados are often more desirable. Elliptic rings and rings of 

 multicentered curves approaching in form the semi-ellipse much 

 more nearly conform in neutral curve to the shape of the true equi- 

 librium frame. Arches of such forms can be readily proportioned 

 which will take no tension at all and in which steel is only necessary 



