26 

 or, as before, 



Ac_ 125 Wl 2 jc U) 



12" 48 EA 2 KJ 



equals the cost per linear foot of stringer of height A. 

 For any other height we have 



Dividing (1) by (5) 



A 1 c 1 125 WZV / 5 x 



12 ~ 48 EA, 8 



Ac 



12 ch* 



AjC, " ej> 

 12 



2 



(6) 



That is to say, the cost per linear foot of stringers designed to give 

 a maximum deflection of one two-hundredths of the span decreases as 

 the square of the height, and increases with the first power only of the 

 cost per foot, B. M. The cost, therefore, will be a decreasing quan- 

 tity according to the present method of fixing the prices. 



These two curves necessarily intersect. The point of intersection is 

 a very important point and may be found for the general conditions of 

 species and length of span by solving equations (1) and (4) as simul- 

 taneous equations thus: 



Wlc 125 W^c 



from which we get 



16RA" 48EA 2 



A 2,000 R 

 / = " 48 E 



CO 



For the case under consideration the span was 14 feet and the mate- 

 rial longleaf pine, for which (see Table IV) R == 1,550 and E =720,000. 



Hence, ~ for this case is equal to-±- and A =j^ : z 15 -!"> as shown 



in the diagram. 



For heights below that of the point of intersection stringers should 

 be designed by the deflection formula; for greater heights, by the 

 cross-breaking formula. The most economical height is that at the 



point of intersection and for longleaf -pine stringers is— - of the span. 



Assuming a height of 11.5 inches for stringers, the necessary width 

 under each rail is equal to 21.8 inches, making three pieces 7± by 14£ 

 inches by 14 feet long. From Table VII we see that the length of end 

 bearing or grip on the cap necessary for these stringers is 6" + 30 per 

 cent = 6" X 1.3 = 7.8". To provide for weathering the stringers are 

 increased one-half inch on each cross-sectional dimension, making three 

 pieces under each rail 7f by 15 inches by 14 feet long. Now. since 

 7.8 inches grip are required for the grip on the cap, either a corbel 

 must be used or the stringers given a full bearing on the cap. 



