80 tliilt 



208 MI: K. \ soi rnui.i.i, ON TIIK I;KXKIJAL THEORY OF ELASTIC STABILITY. 



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r9r v "~ r/ ' r 90 f IT 



Examples in Cylindrical Co-ordinates. Stability of Boiler Fines and 



Tnbular Struts. 



The Equations of Neutral Equilibrium in Cylindrical Co-ordinates enable us to deal 

 successfully with some difficult problems connected with the stability of cylindrical 

 tubes. Two examples of considerable importance will be discussed in this paper the 

 collapse of boiler flues and the strength of tubular struts. It should be noticed that 

 neither of these problems has been quite satisfactorily treated by the ordinary theory 



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Fig. 2. 



of thin shells, which requires the assumptions that the middle surface of the sbell is 

 unextended, and the inner and outer surfaces free from applied tractions* ; hence their 

 solution is a problem of considerable interest, even apart from practical considerations, 

 and has attracted a great deal of attention. It will be convenient at this point to 

 review the work which has already been done. 



The question of the stability of tubular struts is important, owing to the frequency 

 of their employment in practice. In economy of material the cylindrical tube 

 possesses an advantage over struts of solid cross-section, and both the theory of 



* Cf. A. B. BASSET, 'Phil. Trans. Roy. Soc.,' A, CLXXXI., p. 437 ; and RAYLEIGH, 'London Math. 

 Soc. Proc.,' vol. XX., p. 379. 



