34 REINFORCED CONCRETE CONSTRUCTION 



stresses in the steel and concrete of a reinforced concrete column 

 will be as their moduli of elasticity. Thus, 



/._#. 



fc E c 



This ratio of the moduli is generally denoted by the letter n, or 



' f.=*f. 



The term n, then, is the subject of this discussion and is the 

 .value referred to in the various specifications and building codes. 



The equation just given shows that if the stress in either the 

 steel or concrete of a concrete column is known, the stress in the 

 other material can be found, and this relation is made use of in the 

 derivation of column formulas. Fig. 10 shows that the modulus 

 of elasticity of concrete in compression is less for the greater 

 loads, and hence the value of n is greater. Thus, it is plain that 

 with increasing loads in concrete columns the steel receives a 

 greater proportionate stress, the variation in the amount carried 

 by the steel depending on the variation in the value of n. In 

 order to take account of the fact that under increasing loads 

 the steel receives an increasing proportion, it is desirable to use 

 a value of n in the computations for design somewhat larger than 

 that which is obtained by taking a value of E c corresponding to 

 working loads on small prisms (about 10). A value of 15 for n 

 may well be used for all ordinary mixtures and for all types of 

 columns. The value of 12 sometimes specified is now considered 

 unduly low. 



In concrete beams, experiments show that the tension which 

 remains in the concrete just below the neutral axis, and properly 

 not allowed for in the derivation of the beam formulas, has its 

 effect in the position of the neutral axis and the strength of the 

 beam. It is found that a value of 15 for n the same as is used 

 for columns is not too large for calculations of strength of 

 beams under the usual assumptions, although great accuracy in 

 this respect is not necessary. This value of 15 for n is the one 

 most generally used, but a value of 12 is also frequently employed. 

 The value of 15 corresponds to a value of E c of 2,000,000 which 

 is somewhat low as determined by compressive tests. 



Comparatively few tests have been made on the elasticity of 

 concrete in tension, but these seem to indicate that for small 

 stresses, it is practically the same as in compression, although 

 probably slightly less. 



