160 W. H. WARREN. 



The diagram Figs. 12 ai and 12 a 2 , shows the values of 

 — , x and c for the concrete used in the three beams, but 

 with different values of p. In 12 a 2 the values of f = 

 42000 lbs., n = 0*9 and — - = 12 have been substituted in 

 the equation given in Fig. 12 a,. 



This subject has been investigated in Europe and 

 America by various experimenters. The elaborate work 

 of M. Considere 1 and Professor Hatt 2 may be specially 

 mentioned. The equations obtained by these authorities 

 are very similar to those given by the writer, and are 

 expressed as follows for the sake of comparison : 



Considere obtains : — 



*(!-«) + fp=fd(£. ... (2) 



m == bir- { *(*-«) (» + «) + fp (**!r*) ) (3) 



Using the same data as before and applying the equations 



to the beam tested we obtain : — 

 a?= 0*444 

 c = 2750 lbs. per square inch. 



M 



bli -' 



= 508*512. 







Professor Hatt obtains :— 







M 



bh 2 



= ~ + tf(«- 



-#)., 



..(1) 



2 

 3 CX 



> = pf ...(2) 







1 E c 



(t*-#) = |^ 2 • 



..(3) 





(3) can be simplified by solving 



for x 



thus 



x = 



/3 p E s u 3 p 

 ' 2 E c 4 



•(4) 



1 Experimental researches on reinforced concrete by Armand Considere, 

 Ingenieur en Chef des Ponts et Chausees, Paris. 

 3 See Engineering News, July 1902. 

 3 B. R. Leffler, Engineering News, Vol. l., No. 15, page 320. 



