298 STRENGTH OF MATERIALS 



COLUMNS 



The strength of a compression member depends on the ratio 

 of its length to its least lateral dimension, or, what is the 

 same thing, on the ratio of slenderness; that is, the ratio of its 

 length to its radius of gyration. 



For compression members whose ratio of slenderness does 



p 

 not exceed 30, the formula 5 = , for simple stress, may be used. 



n 



When this ratio exceeds 30, but is not more than 150, 5 

 should be reduced by Rankine's formula, 



in which s u is the ultimate strength in compression, which 

 should be divided by a suitable factor of safety; I, the length; 

 and r, the radius of gyration. Both / and r are expressed in the 

 same unit. The values of ki which depend on the material 

 of the column and the condition of its ends that is whether 

 fixed or round are given in the following table: 



VALUES OF ki (RANKINE'S FORMULA) 



When the value of exceeds 150, Euler's formula, which is 

 r 



given later, should be used. 



