128 RESISTANCE OF MATERIALS 



which the Gordon-Rankine column formula was deduced from 

 Euler's formula (articles 54, 55), as to obtain a rational formula 

 which shall, nevertheless, conform closely to experimental results. 

 By determining the ellipticity, or deviation from roundness, and 

 the variation in thickness of the various types of tubes covered by 

 the tests mentioned above, it is found that by introducing empirical 

 constants the rational formulas can be made to fit experimental re- 

 sults as closely as any empirical formulas, with the advantage of 

 being unlimited in their range of application.* The formula so 

 obtained is 



(189) w = 



l- 



in? [ D 



where h = average thickness of tube in inches, 



D = maximum outside diameter in inches, 



= Poisson's ratio = .3 for steel, 

 m 



(7 = .69 for lap-welded steel boiler flues, 

 = .76 for cold-drawn seamless steel flues, 

 = . 78 for drawn seamless brass tubes. 



By a similar procedure for thick tubes ( >.023J a practical 



rational formula has been obtained from Lame's formula (article 75) 



for this case also, namely, 



for thick tubes 



where u c = ultimate compressive strength of the material, 



JT = .89 for lap-welded steel boiler flues. 



Only one value of K is given, as the experiments cited were all 

 made on one type of tube. 



The correction constants C and K include corrections both for 

 ellipticity, or flattening of the tube, and for variation in thickness. 



Slocum, " The Collapse of Tubes under External Pressure," Engineering. London, 

 January 8, 1909, Also abstract ol same article in Kent, 8th ed., 1910, pp. 320-322. 



