166 RESISTANCE OF MATERIALS 



hoop reenforcement was found to be from 2 to 4 times as great 

 as for the same amount of metal in the form of longitudinal rods. 

 From extensive investigations and experiments on hooped col- 

 umns, Considere has derived the formula 



where P = ultimate strength of the column, 



p c = ultimate strength of the concrete, 

 p s = elastic limit of the steel. 



This formula indicates that hoops or spirals are 2.4 times as effec- 

 tive as the same amount of metal in the form of longitudinal rods. 

 When longitudinal rods are used without hoops, it is necessary 

 to tie them together at intervals to prevent them from buckling 

 and pulling away from the concrete. The distance apart for these 

 horizontal ties may be determined by considering the longitudinal 

 reenf orcing rods as long columns and applying Euler's formula ; 

 namely, ^ ^ EI 



~~ 



Assuming a factor of safety of 5, and taking #=25,000,000 lb./in. 2 

 for wrought iron, we have 



10 x 25,000,000 x - f 

 2 _ ir*JSI = _ 64 



5P , 



where d denotes the diameter of the reenf orcing rods, from which 

 the unsupported length I of the rods, or distance between ties, is 

 found to be 



For instance, suppose that a concrete column 12 in. square, carry- 

 ing a load of 80,000 lb., is reenforced with four rods | in. in diam- 

 eter placed in the four corners, 1 in. from the outer faces. Then 

 A = 144 in. 2 , A. = 4 (.6013) = 2.4052 in. 2 , 



- 460 lb.in* 



