244 REINFORCED CONCRETE CONSTRUCTION 



Thus, if a c is the area of the concrete, and a s is the area of the 

 steel = a + a! ; then the equivalent area 



A = a c + na s = bt + n(a + a') 



If 7 C is the moment of inertia of the concrete about the 

 gravity axis, and I 8 is the moment of inertia of the steel about 

 the same axis, then 



(fc) = W (+)Wx oXl 

 (f' e ) 



If we denote p and p' by j- and j- respectively, then the 



distance from the face most highly stressed to the center of 

 gravity of the transformed section is (by moments) 



btQ+nad+na'd' 



bt 

 ' 



bt+n(a+a') 

 t/2+npd+np'd' 



I s =a(d-u) 2 +a'(u-d') 2 

 / = / c + n/ 8 =| u*+(t-u) 3 \ 



If the reinforcement is symmetrical, then u = - and 



npbt(l/2t- d') 

 Since, A = bt + n (a + a') = bt + nbt (p 4- p') 



Wr - 



(/c) W ( + ) _ ^2 _ 



(A) bt+nbt(p+p') (-) 

 75. Case I. Compression Over the Whole Section. The 



formulas above developed apply when the stress is either com- 

 pression over the entire section, or when there is compression 

 over a portion of the section with a tension over the remainder 

 not exceeding the allowable tensile stress in the concrete. The 

 formulas we shall use will assume rectangular sections with 



