Ml;. K. V. SMITH WELL ON THE GEXKKAL THEORY OF ELASTIC STABILITY. L'.'if) 



accurate as far as terms in t 3 ; we shall assume that (104) gives the same approxi- 

 mation, which for practical purfxises is quite sufficient. We then find, for values of k 

 other than and 1, the expression 



When k = 1, the axis does not remain straight after distortion of the tube has 

 occurml. This is the type of distortion (sometimes called " primary flexure ") which 

 was discussed by ?]UI,KK, and it is easy to see that his result is identical with that of 

 equation (104), which Incomes in this case 



(106) 



The exact expression for the length of the tube, in terms of q, is not a matter of 

 great importance in the present problem, because the wave-length corresponding to a 

 minimum value of the collapsing pressure is in all cases small, and the strength of 

 iiny strut of ordinary dimensions will therefore be given by equations (90) or (105), 

 into which the li-n^th does not enter. As in the case of the boiler-flue problem, we 



\Murs ofZj 4 6 8 



Fig. 6. Strength of Tubular Struts. 



10 



12 



may illustrate the effects of length upon the collapsing thrust by plotting the 

 intensity of stress, or Sfj^at, against q~\ For this purpose we must take some 

 definite value of the ratio t/a, and draw separate curves for different integral values 

 of k. The result is shown by tig. 6, in which the following values are assumed : 



m = 



E = 3 x 10 7 pounds per sq. inch. 



= 2 '07 x 10" dynes per sq. cm. 

 2 H 2 



