THE CRITICAL EXTERNAL PRESSURE OF CYLINDRICAL 

 TUBES UNDER UNIFORM RADIAL AND AXIAL LOAD, 

 by R. von Mises, 

 Berlin 

 Stodola's Festschrift, Zurich, 1929, pp. 418-430. 



Translated and Annotated 

 by D. F. Windenburg* 



The magnitude of buckling pressure and of the deformation of a cylindrical 

 tube closed at both ends and subjected to external pressure is calculated on the 

 basis of elasticity equations for thin shells. The results of the theory are com- 

 pared with tests on two series of models. Complete agreement is shown with regard 

 to the lobe formation; the problem of determining the buckling pressure has not yet 

 been completely solved. 



More than 14 years ago, in view of the conditions prevailing with regard 

 to the design of fire tubes of boilers, I calculated the buckling pressure of 

 cylindrical tubes which, with fixed ends, are subjected to external pressure. A- 

 somewhat different problem is presented when a circular cylinder, closed at the 

 ends by means of bulkheads, is deeply submerged in water and thereby exposed to 

 pressure from all sides, as is approximately the case of submarines. The changes 

 in theory caused by the introduction of axial load are not very extensive, but the 

 altered numerical ratios result in the occurrence of phenomena that necessarily 

 have a certain intrinsic interest, especially concerning the large number of waves 

 or bulges that becomes visible on the circumference of the cylinder at the moment 

 of buckling; see Fig. 6. 



In the following, I present a supplement to my previous publication along 

 the lines just indicated. The fundamental equations, which, by the way, are to be 

 found in every text book on the theory of elasticity, and the detailed calculations 

 carried out in the previous article, are not repeated; reference to that article 

 is indicated by the symbol Z. 



[Translator's Note: The translation of the previous publication, of which this 

 is the supplement, is given in U. S. Experimental Model Basin Report No. 309. It 

 should be referred to in connection with this articlej 



* Assistant Physicist, U. S. Experimental Model Basin, Washington, D. C. 

 ^ Zeit. d. Ver. deutsch. Ingen., 1914, p. 750. 



