COLUMNS AND STRUTS 



99 



58. Johnson's straight-line formula. By means of an exhaustive 

 study of experimental data on columns Mr. Thomas H. Johnson 

 has shown that for columns of moderate length a straight line 

 can be made to fit the plotted results of column tests as exactly 

 as a curve. He has therefore proposed the formula 



(130) ?-^cj, 



250 



SOU 



50 100 150 200 



FIG. 83. Wrought-Iron Column (Pin Ends) 



1, Euler's formula ; 2, T. H. Johnson's straight-line formula ; 3, J. B. Johnson's parabolic 

 formula ; 4, Rankine's formula 



or, in the notation of the preceding article, 



(131) y=v <rx, 



in which v and cr are empirical constants, this being the equation 

 of a straight line tangent to Euler's curve. This formula has the 

 merit of great simplicity, the only objection to it being that for 

 short columns it gives a value of P in excess of the actual break- 

 ing load. The relation of this formula to those which precede is 

 shown in Fig. 83. 



