320 REINFORCED CONCRETE 







2. For one and the same material, the unit stresses at differ- 

 ent points of a beam subjected to bending are proportional 

 to their distances from the neutral axis. 



3. The unit stresses in steel and concrete at points equi- 

 distant from the neutral axis are proportional to their respec- 

 tive moduli of elasticity. 



4. The concrete is assumed to take only congressional 

 stresses, all the tensional stresses being carried by the steel. 



5. The internal stresses in the section of a reinforced-con- 

 crete beam subjected to bending form a couple consisting of the 

 resultant of all compressional stresses taken by the concrete, 

 on one hand, and the tensional stresses taken by the steel, on 

 the other hand. 



It is also assumed that the value of the ratio of the moduli 

 of elasticity of steel and concrete (usually denoted by n) is 

 constant within the limits of the working stresses of the mate- 

 rials. This value of n greatly varies with the qualities of the 

 material and labor employed in the manufacture of the con- 

 crete, and is usually specified by city ordinances. 



The reinforced-concrete tables given later are computed for 

 n= 12 and n = 15, which are prevalent in the present engineer- 

 ing practice. 



Definitions. The economic steel ratio is that ratio of the 

 area of steel to the area of concrete at which both the steel and 

 concrete can be stressed to their maximum allowable limit at 

 the same time, and is denoted by p e - If a lower ratio is used, 

 the stress in the concrete will not reach its limit without over- 

 stressing the steel, and if a higher ratio is employed the full 

 strength of the steel cannot be utilized without overstressjncr 

 the concrete. The economic steel ratio, or as it is also caTled 

 the critical value of steel, is not a fixed quantity; it depends on 

 the ratio of the allowable maximum unit stresses of steel and 

 concrete. 



The stress ratio is the ratio of the stresses actually produced 

 in the steel and concrete by a given external moment. When 

 n is constant, the value of the stress ratio depends only on thr 

 amount of steel used. For the critical value of steel, the stress 

 ratio equals the ratio of the allowable maximum unit stress in 

 steel and that in concrete. 



