60 REINFORCED CONCRETE CONSTRUCTION 



the value of A A' given above, the following equations may be 

 obtained: 



P = 



~bd 



2/3 



/= 1-3/8* 

 M c =2/3f c kj(bd*) QTbd^^^ 



In the above formulas, f s = elastic limit of the steel, and f c = 

 ultimate compressive strength of concrete. 



When using the above formulas, it should be remembered that 

 it was assumed at the outset that the amount of steel in the beam 

 is sufficient to cause the ultimate resisting moment to be due to 

 the concrete. Thus, the resisting moment of the beam may be 

 figured by using the formula for M c . If an amount of steel 

 is used such that the ultimate strength of the concrete and the 

 elastic limit of the steel would be reached simultaneously, 

 either M c or M 8 may be used to determine the ultimate resisting 

 moment. If a less amount of steel is used than the amount just 

 mentioned, the conditions of the assumption do not hold, and 

 the formulas given above cannot be used. When this happens 

 the ultimate moment may be figured by means of formulas based 

 on a parabolic variation of compression in the concrete and 

 applicable for any load up to the ultimate. The parabola for 

 such a case is not a full one and the formulas are cumbersome 

 to use and not at all fitted for practical use. 



The formulas for ultimate loads, however, can easily be em- 

 ployed in designing. The method is to find the amount of steel 

 to give equal strength in tension and compression. Then 

 either 



