220 Kansas Academy of Science. 



Proceeding now to an examination of some of these formulas in 

 detail, a value for y of (1) can be found as follows : 



If the rods are small, fg and fg^ may be taken as the intensity of 

 stress throughout the entire section of the rods in tension and com- 

 pression, respectively. 



For equilibrium : 



The sum of the compressive stresses = the sum of the tensile 

 stresses, or symbolically, 



Fc = Ft (ly 



Let Cg and Ct equal the compressive and tensile stresses in a 

 concrete beam of the same dimensions as the reenforced beam. 



Let So and St equal the excess of stress in the steel over that in 

 the same area of concrete in the same position in the beam. 



Then (i) may be expressed 



{2} 



(3) 

 U) 

 (5) 

 (6) 



[f,A,-(^^fe)A,] (7) 



Now, since by our assumption the strain in any fiber is propor- 

 tional to its distance from the neutral axis, and since — = — - , A 



A and 1 remaining the same for either material at a given position 



in the bea 



sideration. 



F 

 in the beam, — must vary as E, A representing any area under con- 



