108 



STRENGTH OF MATERIALS 



A graphical representation of the relation between Euler's formula, 

 Rankine's formula, J. B. Johnson's parabolic formula, and T. H. .lolm- 

 son's straight-line formula (considered in the next article) is ^ 

 in Fig. 82, for the case of a wrought-iron column with pin ends.* 



FIG. 82. Wrou-ht-Inm Column (pin ends) 



1, Euler's formula; 2,T. H. Johnson's straight-lino formula; :;. J. B. Johnson's 

 parabolic formula; 4. Kankinr's fonnula 



Problem 105. A hollow wrought-iron column with flat <-nls is i" 7 in. 



internal diameter, and 10 in. external diameter. Calmhiu- it.s ultimate il 

 Rankine's and Johnson's formulas, and compare the results. 



Problem 106. Compute the ultimate Ktri-uirth of tin- built rnluinn in 1 

 lem 103 by Rankine's and Johnson's formulas, and compare the results. 



89. Johnson's straight-line formula. By means of an < \haustive 

 study of experimental data on columns, Mr. Thomas H. .John-mi 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 



.*u * T r m0re extensive comparison of these formulas see Johnson's Fm 

 8th ed., 1905, pp. 159-171; also Trans. Amer. Soc. Civ. Eng., Vol. XV, pp. 518-536. 



