CONCRETE DESIGN 309 



of the total rise. As will be observed, these values are 

 independent of the span. 



As an example, consider an arch having a span of 70 ft. 

 and a rise of 8 ft. In this case, H = 8 and the height of the 

 curve at 70-5-10 = 7 ft. from each end is .36X8 = 2.88 ft. 

 At 14 ft. from each end, the height of the curve above the 

 spring line is .64X8 = 5.12 ft., and so on, until the necessary 

 number of points on the curve are located. The curve may 

 then be drawn, passing through these points. 



Having determined the rise to be given to the arch, the 

 next step is to find the thickness of the arch ring at the 

 crown. This may be found by the formula proposed by 

 F. F. Weld, C. E., which is as follows: 

 L F 



in which D is the crown thickness, in inches; 5, the span of 

 the arch, in feet; L, the live load per square foot; and F, the 

 dead load at crown per square foot, exclusive of the weight 

 of the arch itself. 



Thus, for example, take an arch whose span is 64 ft., whose 

 live load is 100 Ib. per sq. ft., and whose dead load is 200 Ib. 

 per sq. ft., and determine its thickness at the crown. 



In this case, S = 64, L = 100, and F = 200. Then, 

 i 64 100 200 



D -^ + Io + ^ + S5- 15 - 4in ' 



If there is no live load, the formula may still be used. 

 Thus, find the thickness of an arch at the crown when the 

 span is 40 ft. and the dead load at the crown is 150 Ib. per 

 sq. ft. Here, S = 40, L = 0, and F=150. Therefore, 



>= Vlo+^+O-l- = 10.6996, say 11, in. 



The arch ring is made thinner at the crown than else- 

 where. The custom is to increase gradually the thickness of 

 the arch ring from the crown to the abutments. The thick- 

 ness of the arch ring directly above points on the spring line, 

 one-quarter of the span from the abutments, is made from 

 one and one-fourth to one and one-half times the thickness 

 at the crown. From these points to the abutments the arch- 



