76 REINFORCED CONCRETE CONSTRUCTION 



straight line, intersecting ab at 0. In our moment calculations, 

 the position of the neutral axis was found to be of prime im- 

 portance and we can readily see that, once this is known, the 

 actual strength may be determined with little uncertainty. 

 In determining the position of the neutral axis, the formula for 

 k shows it to depend only upon the amount of steel used and 



E 



upon the ratio -=r or n. The only element of uncertainty is the 



value of E c . It might be well to take the value as determined 

 by the ordinary compression test for use in our theoretical 

 formulas, but closer results can be obtained from these formulas 

 if the value of n is taken so that for average conditions the 

 neutral axis is in as nearly as possible the same position theoret- 

 ically and experimentally. The reason that E C} as thus deter- 

 mined, will give better results at working loads, is due to the 

 effect of the remaining tension in the concrete below the neutral 



a a 1 



b b 



Fig. 40. 



axis a stress which is properly not allowed for in the resisting 

 moment. From the results of experiments by extensometers for 

 determining the position of the neutral axis, it appears that a 

 value of 15 for n is not too large for calculations of strength 

 of beams under the usual assumptions, although great accuracy 

 in this respect is found unnecessary. 



In making the experiments above described, it was observed 

 that the neutral axis raised as the loading increased, k being 

 approximately 3/8 at working loads. It was also noted that for 

 the lower loads the neutral axis as determined from the theoretical 

 formulas is more uncertain and generally lower in the beam than 

 for the higher loads. This is undoubtedly due to the relatively 

 large influence of the tensile strength of the concrete in such 

 cases. This rise of the neutral axis as the load increases is 

 shown in Fig. 41. Consider a^b^ to be the plane ab after a bending 



