Art. 113. 



COLUMNS FORMULAS. 



191 



Many different column formulas have been proposed, but in 

 recent years the Straight Line Formula has come into favor with 

 the engineers in this country, because a straight line can be made 

 to represent the experiments as well as any curve, for the usual 



values of which occur in practice. The Straight Line Formula 



is of the form 



p 



A 



(62) 



In this formula c is the experimental constant and, as in 

 Rankine's Formula, s max is also sometimes chosen to fit the ex- 

 periments. 



Fig. 141 shows in a general way, the relations between the 

 commonest column formulas for steel columns having an elastic 

 limit of 40,000 Ibs. per sq. in. A portion of Euler's curve is of 

 no value because it lies above the elastic limit. The ultimate 



30000 



/4&Vc\ 





V 



40 60 60 



Values of 7 



Pig. 141. 



strength of a column cannot exceed the elastic limit if its ratio 



is greater than perhaps 40. If this ratio is less than this limit, 

 it is difficult to determine the point of failure. A block will de- 

 form indefinitely, but a column will bend suddenly when the 

 yield point is passed. While the elastic limit is a proper limit 

 of strength, it would evidently not be rational to apply the same 

 factor of safety to it for the shortest columns as for the longer 



