STRENGTH OF MATERIALS 



299 



The straight-line formula is more convenient for determining 

 the value of 5, and is now in extensive use. It is only 

 approximate, giving values of 5 that differ somewhat from those 

 obtained by Rankine's formula; but the difference is on the 

 side of safety. For the same notation as before, the straight- 



/ 

 line formula is s = s u k 



r 



The values of s u and k are given in the accompanying 



table, in which will also be found the limit of within which 



/ r 



the formula may be used. When exceeds this limit, Euler's 



formula, which follows, should be used. 



CONSTANTS FOR THE STRAIGHT-LINE AND EULER'S 

 FORMULAS 



EXAMPLE. What is the ultimate strength per square inch 

 of a medium-steel column 25 ft. long both ends of which are 

 fixed and the radius of gyration of which is 2.5? 



SOLUTION. By the straight-line formula, 



25 X 12 

 5 = 60,000 -1 79 X : 38,520 Ib. per sq. in. 



2.5 

 Using Rankine's formula, 



60,000 



(25X12)1 



25,000X2.52 



38,070 Ib. persq. in. 



