the case of tubes under both radial and end-loading, recent experimental 

 results lend some further validity to the use of Equation (83) for cylin- 

 drical shell structures subjected to hydrostatic pressure. 



Elimination of T f rom Equations (81) and (83) leads to the following 

 expression for the critical stress in the inelastic buckling range for plate 

 and shell structures: 



(84) 



^ 1 7 



1 + T S^r 

 4 erg 



In particular, Equation (84) is of interest in deriving an empirical formula 

 for inelastic buckling of cylindrical shells. 



In analogy to the Euler formula for elastic buckling of columns, we 

 have the Von Mises formula, i.e.. Equation (57), or the Von Sanden and 

 Tolke formula, i.e.. Equation (60), or even the Reynolds solution, i.e.. 

 Equation (62), for elastic panel buckling of ring -stiffened cylinders under 

 hydrostatic pressure. At this point, the form of the equation for the 

 elastic buckling pressure p^. is not as important as the assumption that 

 the "average stress" for buckling in the elastic range is given by 



PgR _ 



C = — B (85) 



erg; h ^ ' 



where B is a factor which can be determined from some appropriate 

 formula resulting from the general expression for circumferential stress 

 at midbay, i.e.. Equation (16). The possibilities for B, which reflects the 

 reduction in circumferential stress at midbay due to the presence of the 



61 



