CONCRETE DESIGN 307 



impossible, the bridge may be constructed in parallel sections 

 running lengthwise of the arch. By following this method 

 of construction, the arch is not materially weakened, for 

 each ring may be considered as a complete unit of the arch. 



The manufacturers of Kahn bars have suggested an approxi- 

 mate method of reinforced-concrete arch design. This method 

 is based on an article by F. F. Weld, C. E., published in the 

 Engineering Record. It consists in using an empirical 

 formula obtained from a study of many existing arches 

 and original designs analyzed by more elaborate methods. 



The first step in the design is to determine the rise of the 

 arch. This should be at least one-tenth of the span. 



The curve that the arch takes, especially where uniform 

 loads are expected, is often a parabola. This parabolic 

 curve is usually followed by the center line of the arch ring, 

 and not by the curve of the intrados. This curve may be 

 drawn by plotting a sufficient number of points determined 

 by the following formula: 



in which Y is the rise of parabola, in feet, at any point under 

 consideration; H, the rise, in feet, at the center of the arch; 

 A", the horizontal distance, in feet, from vertical center line 

 of arch to point under consideration; and 5, the spa'n of the 

 arch, in feet. 



As an example, lay out the parabolic curve for the center 

 line of an arch where the span is 88 ft. 



First, the rise must be determined; this is at least one- 

 tenth of the span, which is 8.8, or practically 9, ft. Having 

 the rise and the span, proceed to lay out the curve shown in 

 Fig. 10 as follows: First lay off to a convenient scale the 

 line a b equal to the span. At the center of a b, or c, erect a 

 perpendicular, and on it measure c d equal to the rise H. 

 Then, the points o, d, and b lie on the required curve. 



To obtain other points, proceed as follows: Divide the 

 span into any number of convenient parts, say in this case, 

 eight, because eight is an even number, which makes one 

 division point at c. Then, each division is 11 ft. long. 

 Now, the first division immediately to the right of c is e. 



