COLUMNS AND STRUCTURES 243 



and it is - for metal columns. The factor "r" is the "radius 



r 



of gyration" 



Before describing this important factor the general question 

 of column formulas may well be touched on. The Euler formula 

 is intended for such long slender columns that it is not in prac- 

 tical use, being of value to investigators and mathematicians in 

 studying the effect of loads applied at the end of pieces like 

 piston rods. 



At least a century ago Tredgold proposed a general form for 

 column formulas and this was later modified by Professor Gordon, 

 so it appeared as follows: 

 c 



1 + A; 



()' 



in which / = reduced unit fiber stress, 



c = allowable compressive unit stress, 



k a constant, 



L = length, 



<l - diameter, or least thickness. 



The constant "k" depended not only upon the material but 

 on the shape of the section. 



With the Gordon formula it was necessary to make innumerable 

 experiments and thus obtain constants. It would be necessary 

 to make columns of many sizes and of every imaginable shape, 

 built up in every conceivable way, and test them to destruction 

 in order to be able to design similar columns. 



Professor Rankine, who succeeded Gordon as Professor of 

 Civil Engineering in the University of Glasgow, modified the 

 Gordon formula by substituting the radius of gyration for the 

 diameter. A great many writers refer to the Gordon formula 

 when they mean the Rankine formula, and others refer to the 

 Rankine formula as the Gordon-Rankine. There appears to 

 be considerable confusion as to what constitutes the difference, 

 and some men do not appear to realize that there is any difference. 



The Rankine formula is essentially a modification of the Euler 

 formula by combining the underlying principles of that formula, 

 which dealt with a thread, with the Gordon formula which took 

 into account the fact that a column had thickness as well as 

 length. The Rankine formula is known in Germany as the 



