REENFORCED CONCRETE 



165 



It is desirable to express the load P in terms of the total area of 

 the cross section A. For this purpose let k denote the percentage 

 of reinforcement, or the ratio of the area of the steel to the total 

 area ; that is, let 



Then A c = A-A s = A-kA 



Therefore P = Pc A c + p s A 8 = p c A (1 - k) + npJcA ; 



whence P = p c A [1+ (w - 1) fe] . 



If the column was plain concrete without reenforcement, its safe 

 load would be P 1 = p c A. The relative strength of a plain concrete 

 column as compared with one reenforced is therefore 



Thus, if & = 1 per cent and n = 15, we have 



that is, a reenforcement of 1 per cent of metal increases the strength 

 14 per cent. 



In the case of reenforcement in the form of hoops or spirals, the 

 increase in strength depends on the effect of the hoops or coils in 

 preventing lateral deformation. The results of tests show that this 

 effect is very slight for loads up to the ultimate strength of plain 

 concrete, but beyond this point there is a notable increase in the 

 ultimate strength of the column. Tests on hooped columns made 

 under the direction of Professor A. N. Talbot at the University of 

 Illinois showed that the ultimate strength of the column in terms 

 of the percentage of steel reenforcement may be calculated by 

 the formulas 



for mild steel, p = 1600 + 65,000 &, 



for high steel, p = 1600 + 100,000 k ; 



where p denotes the stress per square inch, and k is the percentage 

 of steel with reference to the concrete core inside the hoops. The 

 compressive strength of plain concrete is here assumed to be 

 1600 lb./in. 2 As regards ultimate strength, the effect of the 



