192 



COLUMN FORMULAS. 



Art. 113. 



columns. This difficulty is, however, of little importance, as very 

 few practical columns have ratios of less than 40 or greater 



than 150. The portions of the curves shown dotted are of little 

 importance. 



Rankine's and the Straight Line formulas are experimental, 

 and Fig. 141 shows that the strength of the practical column is 



considerably below that of the ideal for the usual values of ? 



and particularly for those occurring oftenest in practice. No 

 numerical values for the empirical constants are given in these 

 equations, because they vary widely in the formulas as applied 

 to the different sets of experiments that have so far been made. 1 

 For definite values the student should refer to the various stand- 

 ard spcifications. 



There is no reason why the Straight Line and Rankine's 

 Curve should cut the vertical axis in the same point or at the 

 particular value of s c shown in Fig. 141; it is only a question of 

 having these lines represent the average of the experiments 



within the usual values of . Neither is there any definite value 



r 



at which these lines meet Enler's Curve; this depends upon the 

 end conditions and the kind of material. Nearly all experiments 

 show that Euler's Curve is applicable for the larger values of 



values usually above those used in practice. 



'For diagrams showing the results of a num'ber of sets of experi- 

 ments on columns, and for column formulas fitted to them, see Burr's 

 Elasticity and Resistance of the Materials of Engineering, pp. 479 to 

 50, Cth Edition. 



For diagrams showing the results of some very careful tests made 

 by Tetmajer, see Johnson's Materials of Construction. Figs. 297 and 

 298, or Trans. Am. Soc. C. E., Vol. XXXIX, pp. 109 and 111. 



For diagrams showing the results of experiments made in this 

 country before 1885, see a paper by Thos. H. Johnson, M. Am. Soc. 

 C. E. in the Trans. Am. Soc. C. E., Vol. XV, page 517. This paper gives 

 the Straight Line formulas which Mr. Johnson proposed. 



For the results of some very careful experiments upon columns 

 of single angles, beams, channels, tees, and tubes, see papers by Mr. 

 James Christie, Trans. Am. Soc. C. E., Vol. XIII, pp. 86 and 254. 



