.14- 



h/a = 0.00717 



£ calc. = 4»8 atm. 



h/a = 0.00537 



£ calc. = 2.85 atm. 



h/a = 0.00537 



£ calc. = 2.15 atm. 



2a = 6 inches, a// = 0.1 



£ expt. = 4*6 a* 

 2a = 8 inches B./1 = O.I33 



£ expt. = 2.75 at 

 2a = 8 inches a/f = 0.1 



£ expt. = 2.18 at 

 Also Falrbairn observed the increase of the number of lobes with the de- 

 crease In the length of the tube in agreement with our theory. 



In general we might say that the available experimental data do not per- 

 mit decisive conclusions, but point to the usefulness of the formula in design. 



Concluding Remarks. 



It is possible to object to the practical application of the formula 

 here developed, since very frequently the collapse of boiler flues follows only 

 from pressures that do not satisfy eq. (21). In these c.ases, the proportional 

 limit Is exceeded and our derivation is no longer valid. The behavior here is 

 quite similar to the ordinary buckling phenomena. For rods which are not very 

 slender, the Euler formula is no longer applicable but must be replaced with em- 

 pirical formulas. 



We might, however, refer here to the expedient that is applied with suc- 

 cess in the theory of buckling. The formulas for the critical pressure remain the 

 same if in place of E another suitable value is substituted. In the first ap- 

 proximation we might substitute E-|_ from the slope - in general variable - of the 

 stress-strain curve. It is more accurate, as v. Karman (Mitteilungen Qber Forsch- 

 ungsarbeiten, Vol. 8I) has shown, to choose an intermediate value between the 

 slope value and the elastic constant E. (Translator's note: The resulting mod- 

 ulus E* that should be used in eq. (D) is in general an intermediate value between 

 the two moduli E - within the proportional limit - and E^^ - at failing stress - 



and can be expressed as E' »_4_^5l . See v. Karman, loo. cit. p. 20). The 



place at which the slope is to be chosen must of course be found through a pre- 

 vious estimate. 



Another range of application, for which the above derivation is again 

 not valid can also be pointed out. For corrugated tubes the principal results 

 can be applied. It is only necessary to Introduce in the fundamental equations 

 an increased bending rigidity in the circular section: In the expression Eq.(5) 

 a value must be substituted for K2 that represents the increase of the moment of 



